7

Ebert, Sebastian, (Bonn Graduate School of Economics)

**Improved Modeling of Double Default Effects in Basel - An Endogenous
Asset Drop Model without Additional Correlation**

Authors: Sebastian Ebert, Eva Luetkebohmert

In 2005 the Internal Ratings Based (IRB) approach of `Basel II' was
enhanced by a `treatment of double default effects' to account for
credit risk mitigation techniques such as ordinary guarantees or credit
derivatives. This paper reveals several severe problems of this approach
and presents a new method to account for double default effects. This
new asset drop technique can be applied within any structural model
of portfolio credit risk. When formulated within the IRB approach
of Basel II, it is very well suited for practical application as it
does not pose extensive data requirements and economic capital can
still be computed analytically.

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8

Elliott, Robert, (University of Calgary)

**American Option Prices in a Markov Chain Market Model.**

Authors: John van der Hoek

This paper considers a model for asset pricing in a world where the
randomness is modeled by a Markov chain rather than Brownian motion.
We develop a theory of optimal stopping and related variational inequalities
for American options in this model. A version of Saigal's Lemma is
established and numerical algorithms developed.

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11

Rémillard, Bruno, (HEC Montreal)

**Optimal hedging in discrete and continuous time**

Authors: Bruno Rémillard and Sylvain Rubenthaler

In this article we find the optimal solution of the hedging problem
in continuous time by minimizing the mean square hedging error, when
the underlying assets are modeled by a regime-switching geometric
Lévy process. It is also shown that the continuous time solution can
be approximated by discrete time Hidden Markov models processes. In
addition, in the case of the regime-switching geometric Brownian motion,
the optimal prices are the same as the prices under an equivalent
martingale measure, making that measure a natural choice. However,
the optimal hedging strategy is not the usual delta hedging but it
can be easily computed by Monte Carlo methods.

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17

Pirvu, Traian, (McMaster University)

**Portfolio management with hyperbolic discounting**

Authors: Ivar Ekeland and Traian Pirvu

This paper considers the Merton portfolio management problem. We are
concerned with non-exponential discounting of time, which has received
much attention lately, especially in the area of behavioural ?nance.
It is a better description of the behaviour of investors, but it leads
to problems of time inconsistency, so that the notion of optimal strategy
no longer is appropriate. We introduce the notion of subgame perfect
strategies, henceforth called policies, and for CARA preferences we
characterize them by an integral equation. We then de?ne a value function
in this context, and we prove that it is characterized by an integral
equation. We then solve this integral equation, and thereby prove
the existence of a policy. As an application, we show that for certain
values of the parameters, the consumption increases up to a certain
time, after which it decreases: this pattern does not occur in the
case of exponential discounting, and is therefore known in the litterature
as the "consumption puzzle."

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18

Kanamura, Takashi, (J-POWER)

**Convenience Yield-Based Pricing of Commodity Futures**

Authors:

This paper proposes a convenience yield-based pricing for commodity
futures, which embeds the incompleteness of commodity futures markets
in convenience yield. By using the pricing method, we conduct empirical
analyses of crude oil, heating oil, and natural gas futures traded
on the NYMEX in order to assess the incompleteness of energy futures
markets. It is shown that the fluctuation from incompleteness is partly
owed to the fluctuation from convenience yield. Then, the market price
of risk implied from crude oil futures prices is applied to the pricing
of Asian call option written on the crude oil futures.

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19

Nadtochiy, Sergey, (Oxford University)

**Market Models fro Call Options via Tangent Levy Density**

Authors: Sergey Nadtochiy, Rene Carmona

The classical approach to modeling prices of financial instruments
is to identify a (small) family of underlying processes, whose dynamics
are then described explicitly, and compute the prices of corresponding
financial derivatives by taking expectations or maximizing the utility
function. However, as certain types of derivatives became liquid,
it appeared reasonable to model their prices directly and use these
market models to price or hedge exotic securities. This framework
was originally advocated by Heath, Jarrow and Morton for the Treasury
bond markets. We discuss the characterization of arbitragefree dynamic
stochastic market models based on the European call options of all
strikes and maturities. The present work can be viewed as an extension
of the dynamic local volatility approach, proposed earlier by Carmona
and Nadtochiy. Since the usage of local volatility as a code-book
for option prices is limited (for example, it can only be used if
the paths of the underlying are continuous), we outline a general
approach to constructing the market models for call options, introducing,
in particular, the tangent LÂ´evy density as the appropriate code-book
(substitute to local volatility) in the case when the underlying is
a pure jump process. We capture the information contained in the surface
of option prices in some LÂ´evy density and then prescribe its dynamics
via an ItÂˆo stochastic process in function space. The main thrust
of our work is to characterize consistency between option prices produced
by the dynamic LÂ´evy density and their definition as the conditional
expectations of corresponding payoffs. We then prove an existence
result, providing a simple way to construct and implement a large
class of tangent LÂ´evy models (notice that we havenÂ't been able
to obtain such a result in the case of dynamic local volatility).

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20

Schlogl, Erik, (University of Technology, Sydney)

**A Hybrid Commodity and Interest Rate Market Model**

Authors: Kay Pilz and Erik Schlogl

A joint model of commodity and interest rate risk is constructed analogously
to the multi-currency LIBOR Market Model (LMM). Beyond a "re-interpretation"
of the LMM, issues in the application to commodity market data are
addressed. Firstly, liquid prices are only available for options on
commodity futures, thus the difference between forward and futures
prices is taken into account. Secondly, we construct a procedure to
fit the model to market data for interest options, commodity options
and historical correlations between interest rates and commodity prices.
We illustrate the model on market data and derive formulas for commodity
spread options.

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21

Blanchet-Scalliet, Christophette, (Ecole centrale de LYON)

**CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP**

Authors: S. ANKIRCHNER, C. BLANCHET-SCALLIET, A. EYRAUD-LOISEL

This paper is concerned with the determination of credit risk premia
of defaultable contingent claims by means of indifference valuation
principles. Assuming exponential utility preferences we derive representations
of indifference premia of credit risk in terms of solutions of Backward
Stochastic Differential Equations (BSDE). The class of BSDEs needed
for that representation allows for quadratic growth generators and
jumps at random times. Since the existence and uniqueness theory for
this class of BSDEs has not yet been developed to the required generality,
the first part of the paper is devoted to fill that gap. By using
a simple constructive algorithm, and known results on continuous quadratic
BSDEs, we provide sufficient conditions for the existence and uniqueness
of quadratic BSDEs with discontinuities at random times.

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22

Swishchuk, Anatoliy, (University of Calgary)

**Modeling and Pricing of Variance Swaps for Local Stochastic
Volatilities with Delay and Jumps**

Authors: Swishchuk, Anatoliy

The valuation of the variance swaps for local stochastic volatility
with delay and jumps is discussed in this paper. We provide some analytical
closed forms for the expectation of the realized variance for the
stochastic volatility with delay and jumps. Besides, we also present
a lower bound for delay as a measure of risk. As applications of our
analytical solutions, numerical examples with plots using S&P60 Canada
Index (1998-2002) and S&P500 Index (1990-1993) are then provided to
price variance swaps with delay and jumps.

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23

Frei, Christoph, (Ecole Polytechnique)

**Convergence results for the indifference value based on the
stability of BSDEs**

Authors: Christoph Frei

We study the exponential utility indifference value $h$ for a contingent
claim $H$ in an incomplete market driven by two Brownian motions.
The claim $H$ depends on a nontradable asset variably correlated with
the traded asset available for hedging. We provide an explicit sequence
that converges to $h$, complementing the structural results for $h$
known from the literature. Our study is based on a convergence result
for quadratic backward stochastic differential equations, which is
shown in a general continuous filtration under weak conditions.

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26

Djehiche, Boualem, (Royal Institute of Technology (KTH))

**Optimal stopping of expected profit and cost yields in an investment
under uncertainty**

Authors: Boualem Djehiche, Said HamadÃ¨ne, Marie-AmÃ©lie Morlais

We consider a finite horizon optimal stopping problem related to trade-off
strategies between expected profit and cost cash-flows of an investment
under uncertainty. The optimal problem is first formulated in terms
of a system of Snell envelopes for the profit and cost yields which
act as obstacles to each other. We then construct both a minimal and
a maximal solution using an approximation scheme of the associated
system of reflected backward SDEs. We also address the question of
uniqueness of solutions of this system of SDEs. When the dependence
of the cash-flows on the sources of uncertainty, such as fluctuation
market prices, assumed to evolve according to a diffusion process,
is made explicit, we also obtain a connection between these solutions
and viscosity solutions of a system of variational inequalities (VI)
with interconnected obstacles.

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29

Muhle-Karbe, Johannes, (University of Vienna)

**Pricing Options on Variance in Affine Stochastic Volatility
Models**

Authors: Jan Kallsen, Johannes Muhle-Karbe, Moritz Voß

We consider the pricing of options written on the quadratic variation
of a given stock price process. Using the Laplace transform approach,
we determine semi-explicit formulas in general affine models allowing
for jumps, stochastic volatility and the leverage effect. Moreover,
we show that the joint dynamics of the underlying stock and a corresponding
variance swap again are of affine form. Finally, we present a numerical
example for the model of Barndorff-Nielsen and Shephard (2001) with
leverage. In particular, we study the effect of approximating the
quadratic variation with its predictable compensator.

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**31**

**Douady, Raphael** (CNRS)

**The Stress VaR: a new risk concept for superior fund allocation**

Authors Ilija Zovko
and Cyril Coste.

In this paper we introduce a novel approach to risk estimation
based on nonlinear factor models - the "StressVaR" (SVaR).
Developed to evaluate the risk of hedge funds, the SVaR appears to
be applicable to a wide range of investments. The computation of the
StressVaR is a 3 step procedure whose main components we describe
in relative detail. Its principle is to use the fairly short and sparse
history of the hedge fund returns to identify relevant risk factors
among

a very broad set of possible risk sources. This risk profile is obtained
by calibrating a collection of nonlinear single-factor models as opposed
to a single multi-factor model. We then use the risk profile and the
very long and rich history of the factors to asses the possible impact
of known past crises on the funds, unveiling their hidden risks and
so called "black swans".

In backtests using data of 1060 hedge funds we demonstrate that the
SVaR has better or comparable properties than several common VaR measures
- shows less VaR exceptions and, perhaps even more importantly, in
case of an exception, by smaller amounts.

The ultimate test of the StressVaR however, is in its usage as a fund
allocating tool. By simulating a realistic investment in a portfolio
of hedge funds, we show that the portfolio constructed using the StressVaR
on average outperforms both the market and the portiolios constructed
using common VaR measures.

For the period from Feb. 2003 to June 2009, the StressVaR constructed
portfolio outperforms the market by about 6% annually, and on average
the competing VaR measures by around 3%.

The performance numbers from Aug. 2007 to June 2009 are even more
impressive. The SVaR portfolio outperforms the market by 20%, and
the best competing measure by 4%.

33

Devin, Siobhán (Ribarits, Thomas), (European Central Bank (European
Investment Bank))

**A finite-dimensional HJM model: ***How important
is arbitrage-free evolution?*

Authors: Siobhán Devin, Bernard Hanzon, Thomas Ribarits

We consider a two-factor Heath-Jarrow-Morton (HJM) model under the
risk-neutral measure and show that it may be decoupled into a dynamic
Nelson-Siegel (NS) model plus a somewhat counter-intuitive adjustment
(lying outside the NS family) which keeps it arbitrage-free. We assess
the importance of the adjustment for arbitrage-free pricing by comparing
the HJM model with a novel NS model which is selected using projection
techniques. We analyze forward curves and derivative prices generated
by the HJM and projected NS model, showing that the influence of the
adjustment term on arbitrage-free evolution is small.

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36

Dai, Min, (National University of Singapore)

**Trend Following Trading under a Regime Switching Model**

Authors: Min Dai, Qing Zhang, Qiji Zhu

This paper is concerned with the optimality of a trend following trading
rule. The idea is to catch a bull market at its early stage, ride
the trend, and liquidate the position at the first evidence of the
subsequent bear market. We characterize the bull and bear phases of
the markets mathematically using the conditional probabilities of
the bull market given the up to date stock prices. The optimal buying
and selling times are given in terms of a sequence of stopping times
determined by two threshold curves. Numerical experiments are conducted
to validate the theoretical results and demonstrate how they perform
in a marketplace.

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39

Naujokat, Felix, (Humboldt University)

**Curve Following in Limit Order Markets**

Authors: Felix Naujokat and Nicholas Westray

In this talk the problem of curve following in a limit order market
is addressed. The optimal control is characterised in terms of the
solution to a coupled FBSDE involving jumps via the technique of the
stochastic maximum principle. Analysing this FBSDE, we further show
that there are buy and sell regions. In the case of quadratic penalty
functions the FBSDE admits an explicit solution which is determined
via the four step scheme. The dependence of the optimal control on
the target curve is studied in detail.

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40

Tappe, Stefan, (ETH Zürich)

**Term structure models driven by Wiener processes and Poisson
measures: Existence and positivity**

Authors: Damir Filipovic, Stefan Tappe, Josef Teichmann

We investigate term structure models driven by Wiener processes and
Poisson measures with forward curve dependent volatilities. This includes
a full existence and uniqueness proof for the corresponding Heath-Jarrow-Morton
type term structure equation. Furthermore, we characterize positivity
preserving models by means of the characteristic coefficients, which
was open for jump-diffusions. Additionally we treat existence, uniqueness
and positivity of the Brody-Hughston equation of interest rate theory
with jumps, an equation which we believe to be very useful for applications.

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41

Nishide, Katsumasa, (Yokohama National University)

**Optimal Investment Timing with Linearly Additive Geometric Brownian
Motions: The General Case**

Authors: Katsumasa Nishide

In this paper, we present simple extensions of earlier works on the
optimal time to exchange one basket of log Brownian assets for another.
A superset and subset of the optimal stopping region in the case where
both baskets consist of multiple assets are obtained. It is also shown
that a conjecture of Hu and Oksendal (1998) (Finance Stoch. 2:295--310,
1998) is false except in the trivial case where all the assets in
a basket are the same processes.

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46

Casas, Isabel, (Aarhus University)

**Unstable volatility: the break preserving local linear estimator**

Authors: Isabel Casas and Irene Gijbels

Markov switching models (Hamilton, 1989) and threshold models (Lin
and Terasvirta, 1994) are amongst the most popular models to describe
the behaviour of data with structural breaks. Nonparametric techniques
are interesting because the assumptions needed in parametric models
can be relaxed and a consistent estimator of the functional forms
be found. The goal of this paper is to present the break preserving
local linear (BPLL) estimator which is a kernel smoothing estimator
and an extension of the popular local linear (LL) estimator. The prominent
innovation of the BPLL estimator is its consistency at the break points

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49

Yoon, Ji Hee, (KAIST)

**Optimal Portfolio Selection under Disappointment Averse Utility**

Authors: JiHee Yoon.

In this paper, I consider a portfolio choice problem for Gul (1991)'s
disappointment averse investors in a continuous-time economy. Assuming
a complete market and general geometric Brownian motions for asset
prices, I provide an analytic method to derive the formulas for the
optimal wealth and portfolio weight. In order to explore some important
implications, I use the disappointment averse preferences of Gul (1991)
associated with the constant relative risk aversion and compare it
to the standard constant relative risk averse preference. I show that
the portfolio weight with disappointment aversion is less than one
without it. This result partially explains the portfolio puzzle of
Mankiw and Zeldes (1991) that a large part of the population does
not invest in risky assets. Also, I find that the portfolio weight
under the disappointment aversion model is changed among the time
horizon.

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51

Schlueter, Stephan, (University of Erlangen-Nuremberg)

**Pricing an European Gas Storage Facility using a Continuous-Time
Spot Price Model with GARCH Diusion**

Authors: Stephan Schlueter, Matt Davison

This article presents both a theoretical framework and a solved example
for pricing a European gas storage facility and computing the optimal
strategy for its operation. Because the Dutch TTF day-ahead gas prices
we use have time-varying volatility, we introduce a new continuous-time
model which incorporates GARCH diffusion into an Ornstein-Uhlenbeck
process. Based on this model we use dynamic programming to derive
partial differential equations for pricing a storage facility. Using
the numerical solutions of these equations, we investigate the effects
of multiple contract types and perform a sensitivity analysis for
all model parameters.

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52

He, Xuedong, (Columbia University)

**Hope, Fear and Aspiration**

Authors: Xuedong He and Xunyu Zhou

In this paper, we propose a new portfolio choice model in continuous
time which features three key human incentives in decision-making:
hope, fear and aspiration. By applying recently developed quantile
formulation, we solve this model completely. Three quantitative indices:
fear index, hope index and lottery-likeness index are proposed to
study the impact of hope, fear and aspiration respectively on the
investment behavior. We find that the extreme fear prevents the agent
from risking too much, leading to portfolio insurance endogenously.
On the other side, the hope drives the agent aggressive, and the more
hopeful he is, the more aggressive he will be. Finally, a high aspiration
leads to a lottery-like terminal payoff, indicating that the agent
takes high leverage.

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53

Henderson, Vicky, (Oxford Man Institute)

**Prospect Theory, Partial Liquidation and the Disposition Effect**

Authors: Vicky Henderson

We solve an optimal stopping problem for an agent with prospect theory
preferences who seeks to sell a portfolio of (divisible) claims on
an underlying asset. Our methodology enables us to consider different
formulations of prospect preferences in the literature, and diffusion
price processes. We find that these differences in specification are
important - for instance, with piecewise power functions (but not
piecewise exponentials) the agent may voluntarily liquidate at a loss
relative to break-even. This is consistent with the disposition effect
documented in empirical and experimental studies. The ability to partially
liquidate also has significant consequences. The prospect agent liquidates
the entire position at once, in contrast to behavior under standard
concave preferences.

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54

De Larrard, Adrien, (Paris VI)

**Arcsine law and a simple model for economic default**

Authors: Xin Guo, Adrien de Larrard and Robert Jarrow

Recently, an investigation by Guo, Jarrow and Lin (2009) of the distressed
debt prices led to a surprising finding about the nature of default,
and a new concept of ``economic default'' was coined. In this talk,
we propose a mathematical model for ``economic default'' and apply
fluctuation theory in probability to analyze the model. Consistent
with the empirical analysis in GJL (2009), we identify an Arcsine-Law
type of distributions for the distance between the economic default
and the traditional default date.

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56

Matsumoto, Koichi, (Kyushu University)

**Simple Improvement Method for Upper Bound of American Option**

Authors: Mika Fujii, Koichi Matsumoto, Kengo Tsubota

We study the pricing of American options. An upper bound of the price
can be made from a martingale and an optimal martingale attains the
true price. But it is not easy to find an optimal martingale and then
the improvement of the upper bound is an important problem. In this
study we propose a simple improvement method of the upper bound by
stopping times. The stopping times are made from a lower bound process
of the continuation value. We show that a higher lower bound process
improves an upper bound more. Finally we show numerically that our
method works.

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58

Rodrigues, Paulo, (Goethe University Frankfurt)

**Stochastic Volatility and Jumps: Exponentially Affine Yes or
No? An Empirical Analysis of S&P500 Dynamics**

Authors: Katja Ignatieva, Paulo Rodrigues, Norman Seeger

This paper analyzes exponentially affine and non-affine stochastic
volatility models with jumps in returns and volatility. Markov Chain
Monte Carlo technique is applied within a Bayesian inference framework
to estimate model parameters and latent variables using daily returns
from the S&P 500 stock index. There are two approaches to overcome
the problem of misspecification of the square root stochastic volatility
model. The first approach investigates non-affine alternatives of
the volatility process. The second approach consists in examining
more heavily parameterized models by adding jumps to the return and
possibly to the volatility process. The aim of this paper is to combine
both model frameworks and to test by using statistical and economical
measures whether the class of affine models is outperformed by the
class of non-affine models if we include jumps into the stochastic
processes. We conclude that the non-affine model structure have promising
statistical properties and are worth further investigations. Further,
we find affine models with jump components that perform similar to
the non affine models without jump components. Since non affine models
yield economically unrealistic parameter estimates, and research is
rather developed for the affine model structures we have a tendency
to prefer the affine jump diffusion models.

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59

Ignatieva, Katja, (Macquarie University)

**Modelling Co-movements and Tail Dependency in the International
Stock Market via Copulae**

Authors:: Eckhard Platen

This paper examines international equity market co-movements using
time-varying copulae. We examine distributions from the class of

Symmetric Generalized Hyperbolic (SGH) distributions for modelling
univariate marginals of equity index returns. We show based on the
goodness-of-fit testing that the SGH class outperforms the normal
distribution, and that the Student-t assumption on marginals leads
to the best performance, and thus, can be used to fit multivariate
copula for the joint distribution of equity index returns. We show
in our study that the Student-t copula is not only superior to the
Gaussian copula, where the dependence structure relates to the multivariate
normal distribution, but also outperforms some alternative mixture
copula models which allow to reflect asymmetric dependencies in the
tails of the distribution. The Student-t copula with Student-t marginals
allows to model realistically simultaneous co-movements and to capture
tail dependency in the equity index returns. From the point of view
of risk management, it is a good candidate for modelling the returns
arising in an international equity index portfolio where the extreme
losses are known to have a tendency to occur simultaneously. We apply
copulae to the estimation of the Value-at-Risk and the Expected Shortfall,
and show that the Student-t copula with Student-t marginals is superior
to the alternative copula models investigated, as well the Riskmetics
approach.

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62

Yi, Chuang, (Royal Bank of Canada)

**Dangerous Knowledge:Credit Value Adjustment with Credit Triggers/Simulating
Multiple Defaults and Migration II: Credit Value Adjustment of Credit
Default Swaps**

Authors: Chuang Yi

We generalize the arbitrage-free valuation framework for counterparty
credit risk (CCR) adjustments when credit triggers are allowed in
the contract. The settlement of the deal for the investor could be
either obliged or optional to execute when the counterparty hits its
credit trigger before any default events. General formulas for credit
value adjustment (CVA) are given for all four cases: obliged unilateral,
obliged bilateral, optional unilateral and optional bilateral. We
show that adding credit triggers will decrease the unilateral CVA
for both obliged and optional cases, which are in line with the motivation
of investors to reduce CCR. However, adding credit triggers may not
necessarily reduce bilateral CVA. Counter-intuitively, we show that
the bilateral CVA may actually increase by adding credit triggers.
Moreover, the increased amount of bilateral CVA due to credit triggers
for one party is exactly the same amount of bilateral CVA reduced
for the other party. The CVA calculation is subjected to large uncertainty
of model risks, mostly due to the lack of data for calibrating jump-to-default
probabilities. Some explicit models for obliged unilateral CVA are
discussed with special caveats on the model assumptions. Numerical
examples are also given to illustrate the model risk of CVA calculation
due to the uncertainty of jump sizes, even though pure jump models
are assumed. / Yi (2009b) proposed an efficient algorithm for simulating
joint defaults and migration based on the first passage times of multi-variate
Brownian motions. In this article, we extend the algorithm to a multi-step
simulation that utilizes a minimal approximation for the CVA calculation.
We then study the credit value adjustment (CVA) for credit default
swaps (CDS) using this multi-step simulation. Particularly, the impacts
of the distance to default (DD) correlations on CVAs are analyzed
comprehensively. The order of the creditworthness of the three parties
invovled is found to be relevant for the sensitivities of the CVAs
with respect to DD correlations. Theoretical justification is also
provided. The designed simulation algorithm can easily be applied
to calculate CVAs for other instruments in different markets such
as Equity, IR, FX and Commodity. This is described in details in a
companion paper titled: Simulating Multiple Defaults and Migration
III: Comprehensive Credit Value Adjustment System.

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66

Lee, Jungwoo, (Yonsei University)

**A Multiscale Model with Stochastic Elasticity**

Authors: Jeong-Hoon Kim, Jungwoo Lee, Suk-Hyun Yu and Song-Ping Zhu

In this paper, we develop a multi-scale hybrid model for option pricing
in an asymptotic form by introducing a concept of 'stochastic elasticity'
that extends the well-known constant elasticity of variance model.
We use asymptotic analysis to obtain the corrected price of European
options under our multi-scale model. The implied volatility surface
predicted by our model has a smile effect, which overcomes the major
drawback of the Black-Scholes model, and moves in the same direction
with the underlying asset, which fits observed market behavior and
overcomes local volatility model's possible instability of hedging.

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67

Gobet, Emmanuel, (Grenoble Institute of Technology)

**Time dependent Heston model**

Authors: E. Benhamou, E. Gobet, M. Miri

The use of the Heston model is still challenging because it has a
closed formula only when the parameters are constant [Hes93] or piecewise
constant [MN03]. Here, using a small volatility of volatility expansion
and Malliavin calculus techniques, we derive an accurate analytical
formula for the price of vanilla options for any time dependent Heston
model. The accuracy is less than a few bps for various strikes and
maturities, while the advantage over Fourier based methods is its
rapidity (gain by a factor 100 or more). Error estimates are also
provided.

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68

Lee, Minku, (Yonsei University)

**A Delay Financial Model with Stochastic Volatility; Martingale
Method**

Authors: Jeong-Hoon Kim and Min-Ku Lee

In this paper, we extend a delayed geometric Brownian model by adding
a stochastic volatility term, which is assumed to have fast mean reversion,
to the delayed model. Combining a martingale approach and an asymptotic
method, we develop a theory for option pricing under this hybrid model.
Core result obtained by our work is a proof that a discounted approximate
option price can be decomposed as a martingale part plus a (ignorable)
small term. We demonstrate a correction effect driven by the option
price under our new model.

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70

Hanson, Floyd B., (University of Illinois)

**Stochastic Calculus of Heston's Stochastic-Volatility Model**

Authors: Floyd B. Hanson

The Heston stochastic-volatility model is a square-root diffusion
model for the stochastic-variance. It gives rise to a singular diffusion
for the distribution as noted by Feller (1951). Hence, there is an
order constraint on the relationship between the limit that the variance
goes to zero and the limit that time-step goes to zero, so that any
non-trivial transformation of the Heston model leads to a transformed
diffusion in the Ito Calculus. Several transformations are introduced
that lead to proper diffusions and preservation of the non-negativity
of the variance in a perfect-square form.

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75

Steg, Jan-Henrik, (Bielefeld University)

**Irreversible Investment in Oligopoly**

Authors: Jan-Henrik Steg

\begin{abstract} We take the general perspective on capital accumulation
games with open loop strategies, as they have been formalized by Back
and Paulsen (2009). With such strategies, the optimization problems
of the individual players are of the monotone follower type. We obtain
consistency in equilibrium by proving that with common assumptions
from the oligopoly literature on instantaneous revenue, equilibrium
determination is equivalent to solving a single monotone follower
problem. In the unique open loop equilibrium, only the currently smallest
firms invest. This result is valid for arbitrary initial capital levels
and general stochastic shock processes, which may be non-Markovian
and include jumps. We explicitly solve an example, the specification
of Grenadier (2002) with a L\'evy process. \end{abstract}

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77

Nakagawa, Hidetoshi, (Hitotsubashi University)

**Modeling of Contagious Downgrades and Its Application to Multi-Downgrade
Protection**

Authors: Hidetoshi NAKAGAWA

In this paper, we apply a multivariate affine jump process to model
the downgrade intensities for several categories of business sector
in credit portfolios. Since multivariate affine jump structure enables
us to consider self-exciting effects as well as mutually exciting
effects, the model can explain the downgrade clusterings observed
in the Japanese market. Also, we propose a new credit derivative named
multi-downgrade protection as an application of our model and discuss
its fair pricing.

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78

Kardaras, Constantinos, (Boston University)

**Numeraire-invariant preferences in financial modeling**

Authors: Constantinos Kardaras

We provide an axiomatic foundation for the representation of numeraire-invariant
preferences. Our simple axioms are equivalent to the following choice
rule: an outcome is preferred over another if and only if the expected
(under a subjective probability) relative rate of return of the latter
outcome with respect to the former is nonpositive. With the addition
of a transitivity requirement, this last preference relation has an
extension with numerical representation given by expected log-utility.
In a dynamic environment, where consumption streams are the objects
of choice, a result concerning a canonical representation of unit-mass
optional measures enables to explicitly solve the investment-consumption
problem. An application to the problem of optimal investment with
a random time-horizon will be given.

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80

Groth, Martin, (Brummer & Partners)

**An empirical study of commodity trading advisors and implications
for **

structured products

Authors: Martin Groth

Alternative investment strategies often involve a touch of secrecy.
The risk of competitors replicating a successful strategy makes fund
managers reluctant to share information, such as daily returns, with
prospective clients, forcing investors to assess the risk of investing
by means of monthly data. Commodity Trading Advisors (CTAs) is a subset
of the hedge fund universe mainly occupied by systematic managers
with a directional bias. Using a set of 72 CTA funds we investigate
the differences between daily and monthly return figures. We find
a high degree of non-normality and long-term memory in the daily time
series which is not evident in monthly figures and investigate the
implications for structured products.

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81

Chen, An, (University of Bonn)

**In Arrear Term Structure Products: No Arbitrage Pricing Bounds
and The Convexity Adjustments**

Authors: An Chen, Klaus Sandmann

Convexity adjustments are widely used by practitioners as a rule of
thumb in the valuation of in-arrear term structure products. This
paper brings forward a strong argument that supports the convexity
adjustment approach. We show that these convexity adjustments are
in effect model-independent pricing bounds in every arbitrage-free
model. More specifically, they are proven to be a lower pricing bound
for in-arrear payer swaps and in-arrear caps and an upper bound for
in-arrear receiver swaps and in-arrear floors. To address the goodness/tightness
issue of the bounds, convexity adjustments are compared with the exact
pricing formulae obtained in LIBOR market model.

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83

Nutz, Marcel, (ETH)

**The Bellman Equation for Power Utility Maximization with Semimartingales**

Authors: Marcel Nutz

We consider optimal consumption and investment with power utility
in a general semimartingale model with portfolio constraints. In this
talk we describe the \emph{local structure} of this problem via dynamic
programming and the corresponding Bellman equation, which can be stated
as a BSDE or as an equation of predictable characteristics in this
setting. The optimal strategies are described pointwise in terms of
the so-called opportunity process, which is defined as a reduced form
of the value process and is also characterized as the minimal solution
of the Bellman equation. Furthermore, we provide a sharp verification
theorem for this equation. [Preprint arXiv:0912.1883]

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84

Bernard, Carole, (University of Waterloo)

**Explicit Representation of Cost Efficient Strategies**

Authors: Carole Bernard, Phelim Boyle

This paper uses the preference free framework proposed by Dybvig (1988)
and Cox and Leland (1982,2000) to analyze dynamic portfolio strategies.
We derive an explicit representation of cost-efficient strategies.
In general there will be a set of dynamic strategies that have the
same payoff distribution and we are able to characterize a lowest
cost strategy. As an application, for any given path-dependent strategy,
we show how to construct a financial derivative that dominates in
the sense of first-order stochastic dominance. We provide new cost-efficient
strategies with the same payoff distributions as some well-known option
contracts and this enables us to compute the relative efficiency of
these standard contracts. We illustrate the strong connections between
cost-efficiency and stochastic dominance.

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85

Cohen, Samuel, (University of Adelaide)

**Existence and Comparisons for BSDEs in general spaces**

Authors: Samuel N. Cohen and Robert J. Elliott

We present a theory of Backward Stochastic Differential Equations
in continuous time with an arbitrary filtered probability space. No
assumptions are made regarding the continuity of the filtration, or
of the predictable quadratic variations of martingales in this space.
We present conditions for existence and uniqueness of square-integrable
solutions, using Lipschitz continuity of the driver. These conditions
unite the requirements for existence in continuous and discrete time,
and allow discrete processes to be embedded with continuous ones.
We also present conditions for a comparison theorem, and hence construct
time consistent nonlinear expectations in these general spaces.

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86

Kang, Boda, (University of Technology Sydney)

**The Evaluation of Barrier Option Prices Under Stochastic Volatility**

Authors: Carl Chiarella, Boda Kang and Gunter H. Meyer

This paper considers the problem of numerically evaluating barrier
option prices when the dynamics of the underlying are driven by stochastic
volatility following the square root process of Heston 1993. We develop
a method of lines approach to evaluate the price as well as the delta
and gamma of the option. The method is able to efficiently handle
both continuously monitored and discretely monitored barrier options
and can also handle barrier options with early exercise features.
In the latter case, we can calculate the early exercise boundary of
an American barrier option in both the continuously and discretely
monitored cases.

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87

Chiarella, Carl, (The University of Technology, Sydney)

**The Evaluation of Swing Contracts with Regime Switching**

Authors: Carl Chiarella, Les Clewlow and Boda Kang

A gas swing contract is an agreement between a supplier and a purchaser
for the delivery of variable daily quantities of gas, between specified
minimum/maximum daily limits, over a certain period at a specified
set of prices. We propose a framework for pricing such swing contracts
for an underlying gas forward price curve that follows a regime-switching
process. With the help of a recombing pentanonial tree, we evaluate
the prices of the swing contracts and compare the cash flow distribution
of the seller of the contracts under the optimal decisions with regime
switching by implementing different hedging strategies.

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88

Lleo, Sebastien, (Imperial College London)

**Risk-Sensitive Asset Management in a Jump-Diffusion Factor**

Authors: Sebastien Lleo and Mark Davis

In this article we extend earlier work on the jump-diffusion risk-sensitive
asset management problem by allowing for jumps in both the factor
process and the asset prices as well as stochastic volatility and
investment constraints. In this case, the HJB equation is a PIDE.
By combining viscosity solutions with a change of notation, a policy
improvement argument and classical results on parabolic PDEs we prove
that the PIDE admits a unique smooth solution. A verification theorem
concludes the resolutions of this problem.

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90

Zhou, Wei, (The University of Hong Kong)

**Callable stock loan and beyond**

Authors: S.C.P. Yam, S.P. Yung, W. Zhou

A stock loan is a loan in which the borrower, who owns one share of
a stock, obtains a loan from the lender with the stock as a collateral.
In their work, Xia and Zhou (2007) provided the first quantitative
analysis of stock loans under the Black-Scholes framework and determined
the fair price charged by the lender for providing such a service.
In this talk, I shall consider the pricing issue of stock loans with
a callable feature that the lender can call back the loan at any time
before maturity; upon calling the loan, lender has the right to enforce
the borrower either to immediately redeem the stock by paying back
the loan at a reduced amount or surrender his share of stock. Financial
products with such a feature are commonly traded under the name: Callable
REPO. Explicit solution together with range of loan-to-value ratio
for marketable loans will be illustrated in infinite time horizon
setting; while for the finite time counterpart, a couple of integral
equations characterizing the two exercising boundaries will be shown.A
stock loan is a loan in which the borrower, who owns one share of
a stock, obtains a loan from the lender with the stock as a collateral.
In their work, Xia and Zhou (2007) provided the first quantitative
analysis of stock loans under the Black-Scholes framework and determined
the fair price charged by the lender for providing such a service.
On the other hand, in a recent work of Kunita and Seko (2007), they
attempted to identify the exercising region of game call options (with
δ-penalty) with finite time to maturity. In this talk, I shall
also illustrate a complete solution to the same problem which is in
contrast to their expected results; indeed, by applying similar method,
we had shown the non-trival nature of the pair of exercising boundaries
of the corresponding optimal stopping game (Dynkin's game).

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91

Bion-Nadal, Jocelyne, (CNRS, Ecole Polytechnique)

**Bid-ask dynamic pricing in financial markets with transaction
costs and liquidity risk**

Authors: Jocelyne Bion-Nadal

The axiomatic of Time Consistent Pricing Procedure (TCPP) is motivated
by markets with transaction costs and liquidity risk. We prove that
every arbitrage free TCPP admits an equivalent probability measure
R such that the ask price process associated with every financial
instrument is a R-supermartingale admitting a càdlàg version. We study
TCPP calibrated on option prices when the basic asset satisfies a
stochastic volatility model. TCPP allow also for the construction
of dynamic order books when the dynamics of reference assets have
jumps. We prove that the framework of TCPP is even well adapted to
the context of uncertain volatility.

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92

Zhu, Qiji, (Western Michigan University)

**Term Structure of Interest Rates with Consumption Commitments**

Authors: J. Duan and Q. Zhu

We study the term structure of interest rates in the presence of consumption
commitments using an equilibrium model. Under reasonable assumptions
we prove the existence and uniqueness of the equilibrium and develop
computation methods. Examples are analyzed to illustrate the effect
of consumption commitments on the term structure and its manifestations.

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94

Prokopczuk, Marcel, (Henley Business School)

**Commodity Derivatives Valuation with Autoregressive and Moving
Average Components in the Price Dynamics**

Authors: Raphael Paschke and Marcel Prokopczuk

In this paper we develop a continuous time factor model of commodity
prices that allows for higher-order autoregressive and moving average
components. The need for these components is documented by analyzing
the convenience yield's time series dynamics. The proposed model is
analytically tractable and allows us to derive closed-form pricing
formulas for futures and options. Empirically, a parsimonious version
of the general model is estimated for the crude oil futures market.
We demonstrate the model's superior performance in pricing nearby
futures contracts in- and out-of-sample. Most notably, the model substantially
improves the pricing of long-horizon contracts with information from
the short end of the futures curve.

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95

Bichuch, Maxim, (Carnegie Mellon University)

**Asymptotic Analysis for Optimal Investment with Two Risky Assets
and Transaction Costs**

Authors: Maxim Bichuch, Steven E. Shreve

We consider an agent who seeks to optimally invest and consume in
the presence of proportional transaction costs. The agent can invest
in two types of futures contracts, and in a money market account.
She may also consume and get utility $U(c)\stackrel{\triangle}{=}\frac{c^p}{p},~
c\ge 0$, where $p\in(0,1)$ and $c$ is the rate of consumption. The
agent can control the rate of consumption and influence the evolution
of wealth by controlling the number of futures contracts held. Proportional
transaction costs $\lambda_i=\alpha_i\lambda$ are charged for every
trade in futures contracts of type $i,~i=1,2$. The agent wishes to
maximize the expected discounted integral over $[0,\infty)$ of the
utility of consumption. We compute an asymptotic expansion of the
value function in powers of $\lambda^{\frac13}.$

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96

Crépey, Stéphane, (Université d'Evry)

**Delta-hedging Correlation Risk**

Authors: Areski Cousin, Stéphane Crépey, Yu Hang Kan

Local default intensity is the credit correlation analog of local
volatility. In this paper one compares the performances of a local
intensity delta and of the Gaussian copula delta, in terms of hedging
a CDO tranche by its credit index. In practice the local intensity
delta fails to outperform the Gaussian copula delta, and one provides
hints to the fact that it can be so even though the local intensity
model is a dynamic credit model fitting the market over the full set
of CDO tranches, whereas the Li model is a static device only providing
a per tranche fit.

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99

Brodén, Mats, (Lund University)

**Errors from discrete hedging in exponential Lévy models: the
L2 approach**

Authors: Mats Brodén and Peter Tankov

We analyze the errors arising from discrete rebalancing of the hedging
portfolio in exponential Lévy models, and establish the rates at which
the expected squared discretization error goes to zero when the length
of the rebalancing step decreases. Different hedging strategies and
option pay-offs are considered. The case of digital options is studied
in detail, and it turns out that in this case quadratic hedging produces
different rates from the usual delta hedging strategy and that for
both strategies the rates of convergence depend on the Blumenthal-Getoor
index of the process.

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100

Desmettre, Sascha, (Fraunhofer ITWM)

**Own-Company Stockholding and Work Effort Preferences of an Unconstrained
Executive**

Authors: Sascha Desmettre; John Gould; Alexander Szimayer

We develop a framework for analyzing an executive's own-company stockholding
and work effort preferences. The executive, characterized by risk
aversion and work effectiveness parameters, invests his personal wealth
without constraint in the financial market, including his own company's
stock whose value he can influence with work effort. His utility-maximizing
personal investment and work effort strategy is derived in closed
form, and a utility indifference rationale is applied to determine
his required compensation. Being unconstrained by performance contracting,
the executive's work effort strategy establishes a base case for the
assessment of the benefits or otherwise of constraining executives
with performance contracting.

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101

Fruth, Antje, (TU Berlin)

**Optimal execution in limit order books with stochastic liquidity**

Authors: Antje Fruth, Torsten SchÃneborn, Mikhail Urusov

We want to minimize the expected costs from buying a given amount
of shares. Our linear liquidity price impact is described by an SDE
instead of being constant in time and extends the limit order book
model with resilience proposed by Obizhaeva, Wang. The optimal buying
strategy is not deterministic anymore, but adapts to the liquidity.
Under specific assumptions on the SDE there is a unique optimal strategy
that can be described by a wait and a buy region being separated by
a unique barrier. The barrier is numerically analyzed. Trading can
be passive respectively aggressive in the liquidity.

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103

Vellekoop, Michel, (University of Amsterdam)

**Sahara Utility and Optimal Investment**

Authors: A.Chen & A. Pelsser & M. Vellekoop

We develop a new class of utility functions, SAHARA utility, with
the distinguishing feature that they implement the assumption that
agents may become less risk-averse for very low values of wealth.
This means that SAHARA utility can be used to characterize risk gambling
behavior of an economic agent in a financial crisis. The class contains
the most frequently used exponential and power utility functions as
limiting cases and its two parameters can be easily calibrated in
terms of quantities with a clear economic meaning such as a target
default probability and a target relative risk aversion coefficient.
We investigate the optimal investment problem under SAHARA utility
and derive the optimal strategies in an explicit form using dual optimization
methods. We also show how SAHARA utility functions can be used for
indifference pricing in incomplete markets. Throughout the paper,
we compare SAHARA with exponential and power utility functions to
highlight their qualitative differences.

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105

Jiao, Ying, (Université Paris 7)

**Multiple defaults and contagion risks with global and default-free
information**

Authors: Ying Jiao

We consider multiple default events where the global market information
is modelled as progressive enlargement of filtrations. The main idea
is to establish a relationship between the global information filtration
and the reference default-free filtration, so that we can work with
the latter one on each default scenario. We follow this idea to provide
a general pricing formula for credit portfolio derivatives. On each
default scenario, the formula can be interpreted as a Radon-Nikodym
derivative of random measures. We also study the optimal investment
problem in a contagion risk model and show that the optimization can
be effectuated in a recursive manner with respect to the default-free
filtration.

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108

Yao, Song, (University of Michigan)

**Optimal Stopping for Non-linear Expectations**

Authors: Erhan Bayraktar, Song Yao

We develop a theory for solving continuous time optimal stopping problems
for non-linear expectations. Our motivation is to consider problems
in which the stopper uses risk measures to evaluate future rewards.

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109

Byelkina, Svitlana, (Bank of Montreal)

**Implementation and Calibration of the Extended Affine Heston
Model for Basket Options and Volatility Derivatives**

Authors: Svitlana Byelkina (Bank of Montreal) and Alex Levin (Royal
Bank of Canada)

A stochastic model considered in the presentation belongs to a family
of multi-factor affine diffusion models with one common stochastic
variance described by the CIR process with a time dependent mean reversion
level. This "quasi-elliptical" construction results in the skewed
and heavy-tailed distributions for the basket log-returns and corresponding
smiles/smirks of the basket option implied volatilities. Calibration
of time-dependent parameters based on the closed-form solutions for
European option prices allows for better fit into the implied volatility
surfaces and variance swap price term structures as demonstrated with
the VIX term structure. Basket option prices are calculated using
Monte Carlo simulations.

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110

Platen, Eckhard, (University of Technology Sydney)

**Simulation of Diversified Portfolios in a Continuous Financial
Market**

Authors: Eckhard Platen and Renata Rendek

We analyze the simulated behavior of well diversified portfolios in
large continuous financial markets. In particular, we focus on the
equally weighted portfolio and the market portfolio. We illustrate
that the equally weighted portfolio constitutes a good proxy of the
growth optimal portfolio. The multi-asset market models considered
include the Black-Scholes model, the Heston model, the ARCH diffusion
model, the geometric Ornstein-Uhlenbeck volatility model and two multi-asset
versions of the minimal market model. When benchmarked primary security
accounts are strict supermartingales then the equally weighted portfolio
outperforms the market portfolio remarkably.

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111

Arai, Takuji, (Keio University)

**Convex risk measures on Orlicz spaces**

Authors: Takuji Arai

We focus on convex risk measures defined on Orlicz spaces. In particular,
we investigate basic properties of inf-convolutions defined between
a convex risk measure and a convex set, and between two convex risk
measures. Moreover, we study shortfall risk measures, which are convex
risk measures induced by the shortfall risk. By using results on inf-convolutions,
we obtain a robust representation result for shortfall risk measures
defined on Orlicz spaces under the assumption that the set of hedging
strategies has the sequential compactness in a weak sense. We discuss
in addition a construction of an example having the sequential compactness.

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112

Ziveyi, Jonathan, (UTS)

**American Option Pricing Under Two Stochastic Volatility Processes**

Authors: Jonathan Ziveyi and Carl Chiarella

In this paper we consider the pricing of an American call option whose
underlying asset evolves under the influence of two independent stochastic
volatility processes of the Heston (1993) type. We derive the associated
partial differential equation (PDE) for the option price using standard
hedging arguments. An integral expression for the general solution
of the PDE is derived using Duhamel's principle, which is expressed
in terms of the yet to be determined trivariate transition density
function for the driving stochastic processes. We solve the backward
Kolmogorov PDE satisfied by the transition density function by first
transforming it to the corresponding characteristic PDE using a combination
of Fourier and Laplace transforms. The characteristic PDE is solved
by the method of characteristics. Having determined the density function
we provide a full respresentation of the American call option price.
By approximating the early exercise surface with a bivariate log -
linear function, we develop a numerical algorithm for the pricing
function. Numerical results are compared with those from the method
of lines algorithm.

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114

Grüll, Georg, (Universität Duisburg-Essen)

**Pricing CO2 permits using approximation approaches**

Authors: Grüll, Georg and Kiesel, Rüdiger

Equilibrium models have been widely used in literature with the aim
of showing theoretical properties of emission trading systems. First,
a new equilibrium model is derived. Second, it is shown that the theoretical
permit price is related to changes in the expectation of how long
regulated companies will need to exhaust the remaining permits. Third,
by application to real data we demonstrate that emission trading systems
are inherently prone to jumps.

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116

Papapantoleon, Antonis, (TU Berlin)

**A new approach to LIBOR modeling**

Authors: Martin Keller-Ressel, Antonis Papapantoleon, Josef Teichmann

We provide a general and flexible approach to LIBOR modeling based
on the class of affine factor processes. Our approach respects the
basic economic requirement that LIBOR rates are non-negative, and
the basic requirement from mathematical finance that LIBOR rates are
analytically tractable martingales with respect to their own forward
measure. Additionally, and most importantly, our approach also leads
to analytically tractable expressions of multi-LIBOR payoffs. This
approach unifies therefore the advantages of well-known forward price
models with those of classical LIBOR rate models. Several examples
are added and prototypical volatility smiles are shown. We believe
that the CIR-process based LIBOR model might be of particular interest
for applications, since closed form valuation formulas for caps and
swaptions are derived.

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119

Donnelly, Catherine, (ETH Zurich)

**Convex duality in constrained mean-variance portfolio optimization
under a regime-switching model**

Authors: Catherine Donnelly and Andrew Heunis

We solve a mean-variance portfolio optimization problem with portfolio
constraints in a regime-switching model. Speci fically, we seek a
portfolio process which minimizes the variance of the terminal wealth,
subject to convex portfolio constraints. We establish the existence
and characterization of the solution to the given problem using a
convex duality method. Using these results, we solve explicitly the
problem when the portfolio constraints lie in a closed, convex cone.

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121

Londoño, Jaime, (Universidad Nacional de Colombia)

**A New Theory of Inter-temporal Equilibrium for Security Markets**

Authors: Jaime A. Londoño

A new theory of inter-temporal equilibrium for security markets in
a continuous time setting with Brownian Filtrations for complete and
incomplete markets is developed. A simple characterization of equilibrium
when agents maximize a state dependent utility functional, as proposed
in J.A. Londoño. State Dependent Utility. J. App. Prob. 46 (2009),
no. 1, 55-70 is given. Some simple examples that include economies
when securities pay no dividends or when there are no income for agents
are presented.

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122

Park, Sang-Hyeon, (Yonsei University)

**Asymptotic Method for Singularity in Path-Dependent Option Pricing**

Authors: Sang-Hyeon Park, Jeong-Hoon Kim and Sun-Yong Choi

The valuation of path-dependent options in finance creates many interesting
mathematical challenges. Among them are a large Delta and Gamma near
the expiry leading to a big error in pricing those exotic options
as well as European vanilla options. Also, the higher order corrections
of the asymptotic prices of the derivatives in some stochastic volatility
models are difficult to be evaluated. In this paper we use the method
of matched asymptotic expansions to obtain more practical values of
lookback and barrier option prices near the expiry. Our results verify
that matching asymptotics is a useful tool for PDE methods in path-dependent
option pricing.

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123

Choi, Sunyong, (Yonsei University)

**Pricing and Hedging with Constant Elasticity and Stochastic
Volatility**

Authors: Sun-Yong Choi, Jean-Pierre Fouque ,Jeong-Hoon Kim

In this paper, asymptotic option pricing theory is developed based
upon the extended CEV model with stochastic volatility. Assuming the
stochastic volatility has fast mean reversion,we use singular perturbation
method to derive the pricing PDEs for both the leading order term
and the first correction term of the extended option price. Also,
calibration results are shown. This work(research) is financially
supported by the Ministry of Knowledge Economy(MKE) and Korea Institute
for Advancement in Technology (KIAT) through the Workforce Development
Program in Strategic Technology

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127

Vidal Nunes, Joao Pedro, (ISCTE-IUL NIF: 501510184)

**Two Extensions to Forward Start Options Valuation**

Authors: Joao Pedro Vidal Nunes and Tiago Ramalho Viegas Alcaria

Under the general affine jump-diffusion framework of Duffie, Pan and
Singleton (2000), this paper proposes an alternative pricing methodology
for European-style forward start options that does not require any
parallel optimization routine to ensure square-integrability. Therefore,
the proposed methodology is shown to possesses a better accuracy-efficiency
trade-off than the usual Hong (2004) approach that is based on the
knowledge of the forward characteristic function. Explicit pricing
solutions are also offered under the nested jump-diffusion setting
proposed by Bakshi, Cao and Chen (1997), which accommodates both stochastic
volatility and stochastic interest rates.

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128

Munk, Claus, (Aarhus University)

**Optimal Housing, Consumption, and Investment Decisions over
the Life-Cycle**

Authors: Holger Kraft, Claus Munk

We provide explicit solutions to life-cycle utility maximization problems
involving dynamic decisions on investments in stocks and bonds, consumption
of perishable goods, and the rental and the ownership of residential
real estate. House prices, stock prices, interest rates, and the labor
income of the decision-maker follow correlated stochastic processes.
The individual has time-additive Cobb-Douglas utility of perishable
goods and housing services. The explicit consumption and investment
strategies are simple and intuitive and are thoroughly discussed and
illustrated in the paper. For a calibrated version of the model we
find, among other things, that the fairly high correlation between
labor income and house prices imply much larger life-cycle variations
in the desired exposure to house price risks than in the exposure
to the stock and bond markets.

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129

Bick, Björn, (Goethe-University Frankfurt)

**Investment, Income, and Incompleteness**

Authors: Björn Bick, Holger Kraft, Claus Munk

The utility-maximizing consumption and investment strategy of an individual
investor receiving an unspanned labor income stream seems impossible
to find in closed form and very difficult to find using numerical
solution techniques. We suggest an easy procedure for finding a specific,
simple, and admissible consumption and investment strategy, which
is near-optimal in the sense that the wealth-equivalent loss compared
to the unknown optimal strategy is very small. We first explain and
implement the strategy in a simple setting, but we also show that
our ideas extend to the case of more complicated models.

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130

Scherer, Matthias, (Technischen Universität München)

**CIID default models and implied copulas**

Authors: J.-F. Mai, M. Scherer, R. Zagst

A unified approach for multivariate default models with conditionally
independent and identically distributed default times is presented.
Desirable statistical properties of such models are introduced axiomatically.
It is shown how commonly used models, stemming from quite different
mathematical and economic motivations, can be translated into this
framework. After a discussion of popular specifications, two new models
are introduced. The default times in the first approach have an Archimax
survival copula. The second innovation is based on a CGMY-type process
and is capable of producing default patterns with desirable statistical
properties. The portfolio loss distribution (approximation) is available
in both cases.

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131

Hillairet, Caroline, (Ecole Polytechnique)

**Information Asymmetry in Pricing of Credit Derivatives**

Authors: C. Hillairet, Y. Jiao

We study the pricing of credit derivatives with asymmetric information.
The managers have complete information on the value process of the
firm and on the default threshold, while the investors on the market
have only partial observations, especially about the default threshold.
Different information structures are distinguished using the framework
of enlargement of filtrations. We specify risk neutral probabilities
and we evaluate default sensitive contingent claims in these cases.

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132

Grzelak, Lech Aleksander, (Delft University of Technology)

**An Equity-Interest Rate Hybrid Model with Stochastic Volatility
and the Interest Rate Smile**

Authors: Lech A. Grzelak, Cornelis W. Oosterlee

We define an equity-interest rate hybrid model in which the equity
part is driven by the Heston stochastic volatility, and the interest
rate (IR) is generated by the displaced-diffusion stochastic volatility
Libor Market Model. We assume a non-zero correlation between the main
processes. By an appropriate change of measure the dimension of the
corresponding pricing PDE can be greatly reduced. We place by a number
of approximations the model in the class of affine processes, for
which we then provide the corresponding forward characteristic function.
We discuss in detail the accuracy of the approximations and the efficient
calibration. Finally, by experiments, we show the effect of the correlations
and interest rate smile/skew on typical equity-interest rate hybrid
product prices. For a whole strip of strikes this approximate hybrid
model can be evaluated for equity plain vanilla options in just milliseconds.

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133

Iscoe, Ian, (Algorithmics Incorporated)

**Pricing Synthetic CDOs based on Exponential Approximations to
the Payoff Function**

Authors: I. Iscoe, K. Jackson, A. Kreinin, X. Ma

Structural models in the conditional independence framework, are widely
used in practice for pricing derivatives, such as Collateralized Debt
Obligations (CDO), to capture correlated default events among the
underlying obligors. An essential part of these models is the accurate
and efficient evaluation of the expected loss of the specified tranche,
conditional on a given value of a systematic factor (or values of
a set of systematic factors). Unlike other approaches that focus on
how to evaluate the loss distribution of the underlying pool, in this
paper we focus on the tranche loss function itself. It is approximated
by a sum of exponentials so that the conditional expectation can be
evaluated in closed form without having to evaluate the pool loss
distribution. As an example, we apply this approach to synthetic CDO
pricing.

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138

Veraart, Luitgard, (Karlsruhe Institute of Technology)

**The effect of estimation in high-dimensional portfolios**

Authors: A. Gandy, L.A.M. Veraart

We study the effect of estimated model parameters in investment strategies
on expected log-utility of terminal wealth. The market consists of
a riskless bond and a potentially vast number of risky stocks modeled
as geometric Brownian motions. The well-known optimal Merton strategy
depends on unknown parameters and thus cannot be used in practice.
We consider the expected utility of several estimated strategies when
the number of risky assets gets large. We suggest strategies which
are less affected by estimation errors and demonstrate their performance
in a real data example.

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142

Zhang, Bowen, (Delft University of Technology)

**An Efficient Pricing Algorithm for Swing Options Based on Fourier
Cosine Expansions**

Authors: B.Zhang and C.W.Oosterlee

Swing options give contract holders the right to modify amounts of
future delivery of certain commodities, such as electricity or gas.
In this paper, we assume that these options can be exercised at any
time before the end of the contract, and more than once. However,
a recovery time between any two consecutive exercise dates is incorporated
as a constraint to avoid continuous exercise. We introduce an efficient
way of pricing these swing options, based on the Fourier cosine expansion
method, which is especially suitable when the underlying is modeled
by a L\'evy process. Keywords: Early--exercise swing option pricing,
Fourier Cosine Expansions, State--dependent recovery time, L\'evy
jump processes

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144

Kwak, Minsuk, (KAIST)

**Optimal Investment and Consumption Decision of Family with Life
Insurance**

Authors: Minsuk Kwak, Yong Hyun Shin, U Jin Choi

We study an optimal portfolio and consumption choice problem of family
that combines life insurance for parents who receive deterministic
labor income until the fixed time T. We consider utility functions
of parents and children separately and assume that parents have uncertain
lifetime. If parents die before the time T, children have no labor
income and they choose the optimal consumption and portfolio with
remaining wealth and life insurance benefit. The object of family
is to maximize the weighted average of utility of parents and that
of children. We obtain analytic solutions for the value function and
the optimal policies, and then analyze how the changes of the weight
of parents' utility function and other factors affect the optimal
policies.

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147

Li, Jing, (University of Bonn)

**The Uncertain Force of Mortality Framework: Pricing Unit-Linked
Life Insurance Contracts**

Authors: Jing Li, Alexander Szimayer

Unit-linked life insurance contracts link the financial market and
the insurance market together. In a complete and arbitrage-free financial
market, financial risk can be hedged perfectly, but perfect hedging
is not possible when mortality risk is embedded in a financial product.
For many years, this problem was ignored by assuming that the force
of mortality is deterministic. Under this assumption, an insurance
company can hedge against mortality risk by pooling a large number
of policyholders together. It then only needs to deal with the financial
risk. However, in recent years it has been acknowledged that the force
of mortality is actually stochastic and researchers have tried to
model this stochastic process. The drawback of this procedure is that
it cannot provide a nearly perfect hedge against mortality risk unless
a large number of mortality-linked financial products are liquidly
traded. In contrast to specifying a stochastic model for the force
of mortality, we provide a framework where the force of mortality
is uncertain but stays within lower and upper bounds. Within this
framework, we obtain upper and lower price bounds for European-style
unit-linked life insurance contracts by applying optimal control theory
and PDE methods. In particular, the upper and lower price bounds are
obtained by seeking out the worst and best scenarios for varying forces
of mortality. The PDE formulation of the pricing problem is solved
with finite difference methods. The upper and lower price bounds enable
us to enhance hedging strategies and reduce exposure to financial
and mortality risks.

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149

Lai, Yongzeng, (Wilfrid Laurier University)

**Pricing and Hedging American Options under Exponential Subordinated
Levy Processes by Malliavin Calculus**

Authors: Yongzeng Lai, Yiqi Wang

In this talk, we discuss the simulation of American option prices
and Greeks, Delta in particular, with multiple underlying assets under
the exponential subordinated Levy processes (also known as time-changed
Brownian motions). By using the Malliavin calculus, integration by
parts in particular, we are able to express the conditional expectations
in terms of unconditional expectations involving Malliavin weights.
Thus, American option price and Delta (or Gamma) values can be simulated
by Monte Carlo and quasi-Monte Carlo methods. Formulas and algorithms
used in simulation under this special type of Levy process will be
presented. Numerical results will be provided if time permits.

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153

Kim, Kyu Yoon, (Yonsei University)

**Real options under the CEV Diffusion with Stochastic Volatility**

Authors: Kyu-Yoon Kim, Jeong-Hoon KIm, So-Young Sohn, Won-Sang Lee

As empirical tests on finacial option has shown the non-constant features
of the implied volatility, an extension to the real option needs a
same analysis with different financial circumstances. Here, we consider
a real option pricing model with stochastic volatility for the first
time, and a goal of this research is providing CEV diffusion with
stochastic volatility(SVCEV) into the real option especially for Technology
Financing. Furthermore, an empirical test with dicrete annual Technology
Financing Data is examined with interesting analogies.

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154

Sanz Chacon, Carlos, (Goethe University Frankfurt)

**Efficient Price Sensitivity Estimation of Path-Dependent Derivatives
by Weak Derivatives**

Authors: Carlos Sanz-Chacon and Peter Kloeden

In this article we present the stochastic gradient estimation method
of weak derivatives (WD) aiming at the construction of efficient algorithms
for the estimation of "Greeks" of financial derivatives with path-dependent
payoff function. The key idea is to replace the derivative of the
probability measure of the underlying model by its WD. The WD method
has the same advantageous property of the well-known score function
method that the form of the Greek estimator does not depend on the
details of the payoff function but only on the probability density
of the underlying model. The simulation study indicates that the WD
estimator outperforms the score function and finite difference estimator.

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156

Zhang, Kai, (University of Warwick)

**Weak and Strong Numerical Schemes for the LIBOR Market Model
in the Terminal Measure**

Authors: Kai Zhang

This paper investigates the convergence properties of various methods
for drift approximation in the LIBOR market model in the terminal
measure. The methods we consider are Ito-Taylor schemes and strong
Taylor approximations based on perturbed stochastic differential equations.
We propose an improvement of the latter. The pricing errors of various
methods are compared in both single and multiple step cases. We criticize
that the strong Taylor approximation approaches do not converge as
the number of time steps increases and therefore should not be used
for discretization.

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159

Khedher, Asma, (University of Oslo)

**ROBUSTNESS OF OPTION PRICES AND THEIR DELTAS IN MARKETS MODELLED
BY JUMP-DIFFUSIONS**

Authors: Fred Espen Benth- Giulia Di Nunno- Asma Khedher

We study the robustness of option prices to model variation within
a jump-di ffusion framework. In particular we consider models in which
the small variations in price dynamics are modeled with a Poisson
random measure with infi nite activity and models in which these small
variations are modeled with a Brownian motion. We show that option
prices are robust. Moreover we study the computation of the deltas
in this framework with two approaches, the Malliavin method and the
Fourier method. We show robustness of the deltas to the model variation.

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162

Chudjakow, Tatjana, (Bielefeld University)

**Exercise Strategies for American Exotic Options under Ambiguity**

Authors: Tatjana Chudjakow, Joerg Vorbrink

We analyze several exotic options of American style in a multiple
prior setting and study the optimal exercise strategy from the perspective
of an ambiguity averse buyer in a discrete time model of Cox--Ross--Rubinstein
style. The multiple prior model relaxes the assumption of a known
distribution of the stock price process and takes into account decision
maker's inability to completely determine the underlying asset's price
dynamics. In order to evaluate the American option the decision maker
needs to solve a stopping problem. Unlike the classical approach ambiguity
averse decision maker uses a class of measures to evaluate her expected
payoffs instead of a unique prior. Given time-consistency of the set
of priors an appropriate version of backward induction leads to the
solution as in the classical case. Using a duality result the multiple
prior stopping problem can be related to the classical stopping problem
for a certain probability measure -- the worst-case measure. Therefore,
the problem can be reduced to identifying the worst-case measure.
We obtain the form of the worst-case measure for different classes
of exotic options explicitly exploiting the observation that the options
can be decomposed in simpler event-driven claims.

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163

Lee, Roger, (University of Chicago)

**Displaced Lognormal Volatility Skews: Analysis and Applications
to Stochastic Volatility Simulations**

Authors: Roger Lee and Dan Wang

We prove the global monotonicity, and bound the at-the-money slope,
of implied volatility skews generated by displaced lognormal diffusions,
which therefore cannot reproduce some empirical phenomena. A variant,
the displaced anti-lognormal, overcomes the slope constraint, but
its state space is bounded above and unbounded below. In light of
these limitations, we exploit the displaced (anti-)lognormal (DL),
not as a model, but as a control variate, to reduce variance in simulations
of CEV and SABR models. Moreover, we find an explicit formula for
the DL short-expiry limiting volatility skew, allowing direct calibration
of DL parameters.

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164

Dang, Ngoc Minh, (University Paris Dauphine)

**Optimal control of trading algorithms: a general impulse control
approach**

Authors: Bruno Bouchard, Ngoc Minh Dang, Charles-Albert Lehalle

We propose a general framework for intra-day trading based on the
control of trading algorithms. Given a generic parameterized algorithm,
we control the dates $(\tau_i)_i$ at which it is launched, the length
$(\delta_i)_i$ of the trading period and the value of the parameters
$(\mathcal{E}_i)_i$ kept during the time interval $[\tau_i,\tau_i\p
\delta_i[$. This gives rise to a non-classical impulse control problem
where not only the regime $\mathcal{E}_i$ but also the period $[\tau_i,\tau_i\p
\delta_i[$ has to be determined by the controller at the impulse time
$\tau_i$. We adapt the {\sl weak dynamic programming principle} of
Bouchard and Touzi (2009) to our context and provide a characterization
of the associated value function as a discontinuous viscosity solution
of a system of PDEs with appropriate boundary conditions, for which
we prove a comparison principle. We also propose a numerical scheme
for the resolution of the above system and show that it is convergent.
We finally provide an example of application to a problem of optimal
stock trading with a non-linear market impact function.

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167

Sonin, Isaac, (UNC at Charlotte)

**Optimal Stopping of Markov Chain and Three Abstract Optimization
Problems**

Authors::

It is well known that a connection exists between three problems,
all related to Optimal Stopping (OS) of Markov Chain (MC) and that
their key characteristics are equal. They are correspondingly: the
ratio (cycle) maximization with the classical Gittins index, the Kathehakis-Veinot
(KV) Restart Problem with the KV index, and the Whittle family of
Retirement Problems with the Whittle index. In a paper of author published
in 2008 in Statistics & Probability Letters these three problems and
corresponding indices were generalized in such a way that it is possible
to use the so called State Elimination (SE) algorithm developed earlier
by the author to solve OS of MC and to calculate this common index.
The main goal of our talk is to demonstrate that the equality of these
indices is a special case of a similar equality for three simple abstract
optimization problems.

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168

Itkin, Andrey, (Rutgers University)

**Using pseudo-parabolic and fractional equations for option pricing
in jump diffusion models**

Authors: Andrey Itkin, Peter Carr

In mathematical finance a popular approach for pricing options under
some Levy model is to consider underlying that follows a Poisson jump
diffusion process. As it is well known this results in a partial integro-differential
equation (PIDE) that usually does not allow an analytical solution
while numerical solution brings some problems. In this paper we elaborate
a new approach on how to transform the PIDE to some class of so-called
pseudo-parabolic equations which are known in mathematics but are
relatively new for mathematical finance. As an example we discuss
several jump-diffusion models which Levy measure allows such a transformation.

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169

Lee, Younhee, (Pohang University of Science and Technology)

**Numerical valuation for option pricing under jump-diffusion
models by finite differences**

Authors: YongHoon Kwon, Younhee Lee

We discuss formulating a numerical method for solving partial integro
differential equations which describe the option pricing under jump-diffusion
models. With localization to a bounded domain of the space variable,
these equations are discretized on uniform grid points over a finite
domain of time and space variables. The method based on three time
levels is reduced to an implicit method which can be solved by tridiagonal
systems of linear equations. In this paper the stability and the second-order
rate with respect to a discrete $\ell^{2}$-norm are proved. Numerical
results obtained with European call options under Merton and Kou models
show the behaviors of the stability and the second-order convergence
rate.

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170

Kou, Steven, (Columbia University)

**What Is a Good External Risk Measure: Bridging the Gaps between
Robustness, Subadditivity, and Insurance Risk Measures**

Authors: Steven Kou Xianhua Peng

Basel II Accord and its recent revision use Value-at-Risk (VaR) with
scenario analysis as the external risk measure for setting capital
requirement. Although the Basel II risk measures are of great importance,
there has been no axiomatic justification for their use. We propose
new data-based risk measures called natural risk statistics that are
characterized by a new set of axioms based on comonotonicity from
decision theory. Natural risk statistics include VaR with scenario
analysis, in particular Basel II risk measures, as special cases and
therefore provide axiomatic justification for their use in external
regulation.

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171

Kwon, Soonwon, (KAIST)

**A factor contagion model for portfolio credit derivatives with
interacting recovery rate**

Authors: Geon Ho Choe, Hyun Jin Jang, Soon Won Kwon

We propose the kth default time distributions in the semi-analytic
and analytic forms based on one factor contagion model with Marshall-Olkin
copulas for homogeneous underlying portfolios. In our model, the individual
default intensity processes are controlled by a systematic shock and
an idiosyncratic shock, and also jump by contagion effect. By using
proposed distributions we compute premiums of portfolio credit derivatives
and compare the estimated price with the existing results for accuracy
and efficiency tests.

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172

Overbeck, Ludger, (University of Giessen)

**Spectral Capital Allocation and Applications**

Authors:

Spectral risk measures provide the framework to formulate the risk
aversion of a firm specifically for each loss quantile of the firm.
More precisely the risk aversion is codified in a weight function,
weighting each quantile. Since spectral risk measures are coherent
there exists also a sensible capital allocation based on the notion
of derivatives or more in the light of the coherency approach as an
expectation under a generalized maximal scenario. We will present
the underlying theory for the capital alloction of spectral risk measure
and some examples of spectral risk measures as a finite combination
of expected shortfall allocations.

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173

Raval, Vimal, (Imperial College London)

**Arbitrage Bounds for Weighted Variance Swap Prices**

Authors: Vimal Raval, Mark Davis and Jan Obloj

Consider a frictionless market trading a \emph{finite} number of co-maturing
European call and put options written on a risky asset with continuous
price trajectories plus a weighted variance swap; an instrument with
path-dependent payoff. We ask: Do the traded prices admit an arbitrage
opportunity? We determine necessary and sufficient model-free conditions
for the price of a continuously monitored weighted variance swap to
be consistent with absence of arbitrage. We discuss in detail the
types of arbitrage that may arise when the determined conditions are
not satisfied. New results on smile asymptotics implied by variance
swap prices will also be presented.

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175

Cialenco, Igor, (Illinois Institute of Technology)

**Dynamic Coherent Acceptability Indices**

Authors: Tomasz R Bielecki, Igor Cialenco, Zhao Zhang

In this paper we present a theoretical framework of studying acceptability
indices from dynamic point of view. We establish a representation
type theorem for dynamic coherent acceptability indices and provide
several practical examples.

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178

Peng, Xianhua, (Fields Institute and York University)

**Default Clustering and Valuation of Collateralized Debt Obligations**

Authors: Xianhua Peng, Steven S.G. Kou

The recent financial crisis has witnessed the impact of the default
clustering effect (i.e., one default event tends to trigger more default
events in the future and cross-sectionally), especially on the market
of collateralized debt obligations (CDOs). We propose a model for
CDO pricing based on cumulative default intensities that can incorporate
the default clustering effect. The model is tractable enough to provide
a direct link between single-name and multi-name credit securities.
The result of calibration to the recent market data, when major financial
institutions collapsed and default correlation was substantially high,
shows that the model is promising.

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179

Roorda, Berend, (University of Twente)

**When Can a Risk Measure Be Updated Consistently?**

Authors: Berend Roorda and J.M. Schumacher

We aim at finding conditions under which risk measures can be consistently
updated. We consider notions of time consistency that are weaker than
the conventional notion of dynamic consistency, yet strong enough
to ensure uniqueness of updating. These notions better reflect the
dynamics of extreme risk underlying capital requirements. We give
conditions for the existence of consistent updates of a given risk
measure, and identify an update operator that must produce the consistent
update, if it exists. The theory is illustrated by examples of (non)existence
of consistent updates. A weakly time consistent version of entropic
risk measures is presented.

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182

Makhlouf, Azmi, (LJK)

**The tracking error rate of the Delta-Gamma hedging strategy**

Authors: Emmanuel GOBET, Azmi MAKHLOUF

We analyze the convergence rate of the quadratic tracking error, when
a Delta-Gamma hedging strategy is used at N discrete times. The fractional
regularity of the payoff function plays a crucial role in the choice
of the trading dates, in order to achieve optimal rates of convergence.

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185

Feehan, Paul, (Rutgers University)

**American-style options, stochastic volatility, and degenerate
parabolic variational inequalities**

Authors: Paul Feehan and Panagiota Daskalopoulos

Elliptic and parabolic partial differential equations arising in option
pricing problems involving the Cox-Ingersoll-Ross or Heston stochastic
processes are well-known to be degenerate parabolic. We provide a
report on our work on the existence, uniqueness, and regularity questions
for variational inequalities involving degenerate parabolic differential
operators and applications to American-style option pricing problems
for the Heston model. This is joint work with Panagiota Daskalopoulos
at Columbia University.

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189

Gerhold, Stefan, (Vienna University of Technology)

**On refined volatility smile expansion in the Heston model**

Authors: Peter Friz, Stefan Gerhold, Archil Gulisashvili, Stephan
Sturm

It is known that Heston's stochastic volatility model exhibits moment
explosion, and that the critical moment can be obtained by solving
(numerically) a simple equation. This yields a leading order expansion
for the implied volatility at large strikes (Roger Lee's moment formula).
Motivated by recent tail-wing refinements of this moment formula,
we first derive a novel tail expansion for the Heston density, and
then show the validity of a refined volatility expansion. Our methods
and results may prove useful beyond the Heston model: the entire analysis
is based on affine principles; at no point do we need knowledge of
the (explicit, but cumbersome) closed form expression of the Fourier
transform of log-spot. This is joint work with P. Friz, A. Gulisashvili,
and S. Sturm.

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190

Obloj, Jan, (University of Oxford)

**Utility theory front to back -- inferring utility from agents'
choices**

Authors: Alexander Cox, David Hobson and Jan Obloj

We pursue an inverse approach to utility theory and consumption/investment
problems. Instead of specifying agent's utility function and deriving
her actions, we assume we observe her actions (i.e. her consumption
and investment strategies) and derive utility function for which the
observed behaviour is optimal. This is done in a one-period model
and in continuous time both in a deterministic and stochastic setting.
In the setup of Black-Scholes market it turns out that the consumption
and investment strategies have to satisfy a consistency condition
(PDE) if they come from a classical utility maximisation problem.
We further show that agent's important characteristics such as attitude
towards risk (e.g. DARA) can be directly deduced from her consumption/investment
choices.

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191

Fabretti, Annalisa, (University of Rome, Tor Vergata)

**Delegated Portfolio Management with Investment Constraints**

Authors: A. Fabretti, S. Herzel

We consider the problem of how to set incentives for a portfolio manager
who is required to invest on a restricted set of assets, as it happens
when applying socially responsible screening rules. In the classic
framework of Delegated Portfolio Management we study the case where
restraining the investment opportunities to the subset of sustainable
assets involve a loss in expected earnings for the portfolio manager,
and hence the investor must offer an extra bonus to compensate the
loss. We compute the optimal bonus in a particular case and relate
it to the ability of the manager, that is the capacity of receiving
a private signal connected to asset's returns. We conclude by discussing
the problem of selecting the best managers when ability is not directly
observable.

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192

Yagi, Kyoko, (Akita Prefectural University)

**Convertible Subordinated Debt Financing and Optimal Investment
Timing**

Authors: Kyoko Yagi and Ryuta Takashima

In this paper, we examine the optimal investment policy of the firm
which is financed by issuing equity, straight debt and convertible
debt with the senior-sub structure. The senior-sub structure gives
preference to straight debt over convertible debt and to convertible
debt over equity when the default occurs. We investigate how the senior-sub
structure affects the optimal policies for default, conversion and
investment the values of equity, straight debt, convertible debt and
investment. In particular, we show that the senior-sub structure for
the equity, the straight debt and the convertible debt leads to the
accelerating conversion, decreases the values of convertible debt
and investment, and does not really affect the default and the investment.

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195

Crosby, John, (Glasgow University)

**Optimal Hedging of Variance Derivatives**

Authors: John Crosby

We examine the optimal hedging of variance derivatives, focussing
principally on variance swaps (but, en route, also considering skewness
swaps), when the underlying stock price has discontinuous sample paths.
We derive easily implementable formulae which give optimal (or nearly
optimal) hedges for variance swaps under very general dynamics for
the underlying stock which allow for multiple jump processes and (possibly,
multiple) stochastic time-changes. We illustrate how, for parameters
which are realistic for equity markets, our methodology gives significantly
better hedges than the standard log-contract replication approach
which assumes continuous sample paths.

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196

Melnikov, Alexander, (University of Alberta)

**Dynamic Hedging of Conditional Value-at-Risk**

Authors: A.Kuznetsov, I.Smirnov

Partial hedging is studied by constructing hedging strategies that
minimize conditional value-at-risk (CVaR). The problem is developed
in two aspects: minimization of CVaR with initial capital bounded
from above, and minimization of hedging costs subject to a CVaR constraint.
The Neyman-Pearson lemma is used to deduce semi-explicit solutions.
The results are illustrated by constructing CVaR-efficient hedging
strategies for a call option in the Black-Scholes model and in the
telegraph/regime-switching market model.

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197

Bentata, Amel, (Université Pierre et Marie Curie)

**Forward equations for option prices in semimartingale models**

Authors: Amel Bentata and Rama Cont

We derive a forward partial integro-differential equation for prices
of call options in a model where the dynamics of the underlying asset
under the pricing measure is described by a -possibly discontinuous-
semimartingale. This result generalizes Dupire's forward equation
to a large class of non-Markovian models with jumps and allows to
retrieve various forward equations previously obtained for option
prices in a unified framework.

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198

Jin, Lei, (University of Oxford)

**Credit Modelling by Particle Systems and Stochastic PDEs**

Authors: Ben Hambly, Lei Jin

We consider a structural credit model for a large basket of credit
risky assets. Using the particle representation with absorption for
the asset values of the firms, we assume interactive dynamics for
the particles and investigate the evolutionary behaviour of the limit
empirical measure of the particle system. Finally we derive Stochastic
PDEs which are satisfied by the limit measure itself and the density
of the limit measure. The loss function of the basket is then a function
of the density. In addition, we give estimations for the limit measure
behaviour near the absorbing boundary and prove the uniqueness of
the solution to the Stochastic PDE in some cases.

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199

Levendorskiy, Sergey, (University of Leicester)

**Convergence of price and sensitivities in Carr's randomization
approximation globally and near barrier**

Authors: Sergei Levendorskii

Barrier options under wide classes of L\'evy processes are studied.
The leading term of asymptotics of the option price and of Carr's
randomization approximation to the price are calculated, as the price
of the underlying approaches the barrier. We prove that the order
of asymptotics is the same in both cases, and the asymptotic coefficient
in the asymptotic formula for Carr's randomization approximation converges
to the asymptotic coefficient for the price. We justify Richardson
extrapolation of arbitrary order. Similar results are derived for
sensitivities. Convergence of prices and sensitivities is proved in
appropriate H\"older spaces.

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200

Vandaele, Nele, (Ghent University)

**Hedging of swaptions in the Lévy driven Heath-Jarrow-Morton
model**

Authors: Nele Vandaele, Kathrin Glau and Michèle Vanmaele

We study the pricing of forward swaptions and derive hedging strategies
for these on the basis of investments in zero-coupon bonds. As framework
we consider the Lévy driven Heath-Jarrow-Morton model for the term
structure and we determine the delta-hedge and the mean-variance hedge
which is a quadratic hedge. The pricing formula and the hedging strategies
are derived as closed-form expressions in terms of Fourier transforms.
Numerical comparison of the two hedging strategies is given at the
end.

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201

Geissler, Johannes, (University of St Andrews)

**Inflation Linked Bonds: An incentive for lower inflation? Pricing
from a Central Bank's perspective**

Authors: Johannes Geissler and Christian-Oliver Ewald

We consider a continuous time framework in which the central bank
can dynamically adjust inflation similar as in a repeated Barro and
Gordon type model and in addition to that, can issue inflation linked
bonds, which it sells on the open market. The central banks objective
is to maximize a functional, which measures the classical trade-o
between output and inflation in Barro and Gordon style, but aggregated
in time, plus income from the sale of inflation linked bonds and payments
for the liability that the inflation linked bonds produce at maturity.
In this context we derive a pricing formula for inflation linked bonds
and study the consequences that the sales have on the observed inflation
rate and price level.

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202

Acciaio, Beatrice, (University of Perugia)

**Risk assessment for uncertain cash flows: Model ambiguity, discounting
ambiguity, and the role of bubbles**

Authors: Beatrice Acciaio, Hans Föllmer, Irina Penner

We study the risk assessment of uncertain cash flows in terms of dynamic
convex risk measures for processes. These risk measures take into
account not only the amounts but also the timing of a cash flow. We
discuss their robust representation in terms of suitably penalized
probability measures on the optional sigma-field. This yields an explicit
analysis both of model and discounting ambiguity. We focus on supermartingale
criteria for different notions of time consistency. In particular
we show how bubbles may appear in the dynamic penalization, and how
they cause a breakdown of asymptotic safety of the risk assessment
procedure.

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203

Boudreault, Mathieu, (UQAM)

**On the non-linear relationship between default intensity and
leverage**

Authors: Mathieu Boudreault, GeneviÃƒÂ¨ve Gauthier

This paper presents a hybrid credit risk model where default results
from an external source, highly correlated with leverage. A parametric
transformation of the debt ratio serves as an intensity process. Such
an approach provides for an endogenous recovery rate distribution
that is inversely proportional to the solvency of the company. The
model is fitted to each of the firms of the CDX NA IG and HY indices
using non-linear Kalman filters (EKF and UKF). An empirical study
is then conducted to understand the behavior of the model with real
data.

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205

Jena, Rudra, (Ecole Polytechnique)

**Arbitrage Opportunities in Misspecified Stochastic Volatility
Models**

Authors: rudra p. jena, peter tankov

There is vast empirical evidence that given a set of assumptions on
the real-world dynamics of an asset, the European options on this
asset are not efficiently priced in options markets, giving rise to
arbitrage opportunities. We study these opportunities in a generic
stochastic volatility model and exhibit the strategies which maximize
the arbitrage profit. In the case when the misspecified dynamics is
a classical Black-Scholes one, we give a new interpretation of the
classical butterfly and risk reversal contracts in terms of their
(near) optimality for arbitrage strategies. Our results are also illustrated
by a numerical example including transaction costs.

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209

Bäuerle, Nicole, (KIT)

**Control improvement for jump-diffusion processes with applications
to finance**

Authors: Nicole Bäuerle, Ulrich Rieder

We consider stochastic control problems for jump-diffusion processes
and formulate an algorithm which produces, starting from a given control
$\pi$, a new control with a better value. If no improvement is possible,
then $\pi$ is optimal. Such an algorithm is well-known for Markov
Decision Problems under the name Howard's policy improvement. Here
we show that such an algorithm also works for jump-diffusion problems.
As an application we characterize the optimality of certain portfolio
strategies, e.g. we show that it is optimal to invest a constant fraction
of the wealth in the stock iff the utility function is of CRRA type.

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210

Ledermann, Daniel, (Henley Business School)

**Exact Moment Simulation using Random Orthogonal Matrices**

Authors: Prof. Carol Alexander, Prof. Walter Ledermann, Mr. Daniel
Ledermann

We introduce a method for simulating multivariate samples with exact
means, covariances, multivariate skewness and kurtosis. A new class
of rectangular orthogonal matrices is fundamental to the methodology,
and these ``L-matrices'' can be deterministic, parametric or data
specific in nature. Infinitely many samples, with the same exact moments,
may be generated by multiplying L-matrices by random orthogonal matrices.
This methodology is thus termed ``ROM simulation''. We discuss the
sample characteristics associated with certain classes of random orthogonal
matrices. ROM simulation has applications to many problems that are
resolved using standard Monte Carlo methods. For illustration, we
apply ROM simulation to determine the value-at-risk of a stock portfolio.

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212

Arkin, Vadim, (Central Economics and Mathematics Institute)

**Real Options and Free-Boundary Problems: A Variational View**

Authors: V.I. Arkin, A.D. Slastnikov

The paper deals with optimal stopping problems which arise in real
options theory. We describe a variational approach to the solution
of optimal stopping problems for diffusion processes, as an alternate
to the traditional approach based on the solution of the Stefan (free-boundary)
problem. We study smooth pasting conditions from a variational point
of view. We present some examples where the solution to the Stefan
problem is not the solution to an optimal stopping problem. Using
the proposed approach, we obtain the solution to an optimal stopping
problem for a two-dimensional geometric Brownian motion with a non-linear
payoff function - a linear version of this problem is a base for real
option theory. As an application we consider an optimal investment
timing model taking into account tax exemptions.

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213

Huang, Yu-Jui, (University of Michigan)

**On Outperforming the Market Portfolio with a Given Probability**

Authors: Erhan Bayraktar, Yu-Jui Huang, And Qingshuo Song

Our goal is to resolve a problem stated by Karatzas and Fernholz 2008:
Finding the minimum amount of initial capital that would guarantee
the investor to beat the market portfolio with a certain probability.
We characterize the value function as the smallest supersolution of
a non-linear PDE. As in Karatzas and Fernholz 2008 we do not assume
the existence of an equivalent local martingale measure.

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214

Frittelli, Marco, (University of Milan)

**Dual Representation of Quasiconvex Conditional Maps**

Authors: Marco Frittelli, Marco Maggis

We provide a dual representation of quasiconvex maps between two lattices
of random variables, in terms of conditional expectations. This generalizes
the dual representation of quasiconvex real valued functions and the
dual representation of conditional convex maps. This results are applied
in the theory of dynamic quasiconvex risk measures.

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215

Meinerding, Christoph, (University of Muenster)

**Optimal Portfolio Choice with Contagion Risk and Restricted
Information**

Authors: Nicole Branger, Holger Kraft, Christoph Meinerding

This paper studies the impact of contagion risk and restricted information
on the portfolio decision of a CRRA investor. In a Poisson hidden
Markov model with two economic states and two assets, the investor
infers the probability of being in the riskier contagion state from
historical prices. We find that both contagion and learning significantly
affect the portfolio decision and, in particular, the reaction to
jumps. The investor overreacts to normal, noncontagious jumps and
underreacts to contagion-triggering jumps. The overreaction is most
pronounced in a complete market where derivatives are available, whereas
the underreaction is largest in an incomplete market.

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216

Xu, Zuoquan, (Oxford University)

**Optimal Stopping with Prospect Preference**

Authors: Zuo Quan Xu, Xun Yu Zhou

Prospect theory, featuring S-shaped utility (value) function and probability
distortion, proposed in Kahneman and Tversky (1979) has been widely
accepted as a successful supplement and extension of traditional expected
utility theory. In this paper, we study general optimal stopping with
prospect preference problems. The optimal stopping times turn out
to be highly depending on the shapes of the utility function and probability
distortion function. The main contribution of this paper is tackling
the time-inconsistency arising from the probability distortion in
the optimal stopping problems.

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217

Hu, Xueying, (University of Michigan)

**Minimizing the Probability of Lifetime Ruin under Stochastic
Volatility**

Authors: Erhan Bayraktar, Xueying Hu, Virginia R. Young

We assume that an individual invests in a financial market with one
riskless and one risky asset, with the latter's price following a
diffusion with stochastic volatility. In the current financial market
especially, it is important to include stochastic volatility in the
risky asset's price process. Given the rate of consumption, we find
the optimal investment strategy for the individual who wishes to minimize
the probability of going bankrupt. To solve this minimization problem,
we use techniques from stochastic optimal control

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220

Monoyios, Michael, (University of Oxford)

**Optimal Investment with Inside Information and Parameter Uncertainty**

Authors: A Danilova, M Monoyios, A Ng

An optimal investment problem is solved for an insider who has access
to noisy information related to a future stock price, but who does
not know the stock price drift. The drift is filtered from a combination
of price observations and the privileged information, fusing a partial
information scenario with enlargement of filtration techniques. We
apply a variant of the Kalman-Bucy filter to infer a signal, given
a combination of an observation process and some additional information.
This converts the combined partial and inside information model to
a full information model, and the associated investment problem for
HARA utility is explicitly solved via duality methods. We consider
the cases in which the agent has information on the terminal value
of the Brownian motion driving the stock, and on the terminal stock
price itself. Comparisons are drawn with the classical partial information
case without insider knowledge. The parameter uncertainty results
in stock price inside information being more valuable than Brownian
information, and perfect knowledge of the future stock price leads
to infinite additional utility. This is in contrast to the conventional
case in which the stock drift is assumed known, in which perfect information
of any kind leads to unbounded additional utility, since stock price
information is then indistinguishable from Brownian information.

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222

Glover, Kristoffer, (University of Technology, Sydney)

**The British Russian Option**

Authors: Kristoffer Glover, Goran Peskir and Farman Samee

We examine the British payoff mechanism (introduced in Peskir and
Samee, 2008) in the context of path dependent options. In particular,
we focus on the 'British Russian' option. Such options provide their
holder with an endogenous protection against unfavourable stock price
movements. The price of such options can be characterised as the unique
solution to a parabolic free-boundary problem, whose properties and
solution we investigate. Finally, we provide a preliminary financial
analysis of both options and conclude that in many circumstances these
options can be considered an attractive alternative to existing path
dependent options.

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226

Yamada, Tetsuya, (Bank of Japan)

**Accelerated Investment and Credit Risk under a Low Interest
Rate Environment: A Real Options Approach**

Authors: Tetsuya Yamada

Empirical studies have found that a low interest rate environment
accelerates firms' investment and debt financing, leading to subsequent
balance sheet problems in many countries in recent years. This paper
examines the mechanism whereby firm's debt financing and investment
become more accelerated and the credit risk rises under a low interest
rate environment from the perspective of a real options model. We
find that firms tend to increase debt financing and investment not
only under strong expectations of continued low interest rates but
also when there are expectations of future interest rate increases,
and such behavior causes higher credit risk. We also find that when
future interest rate rises are expected, the investment decisions
vary depending on how firms incorporate the possibility of future
interest rises. Specifically, myopic firms make "last-minute investments"
based on concerns over future interest rate hikes and this behavior
increases their credit risk. In contrast, economically rational firms
choose to decrease their investments, carefully considering the likelihood
of future interest rate hikes.

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229

Glau, Kathrin, (University of Freiburg)

**A new Feynman-Kac formula for option pricing in Lévy models**

Authors: Ernst Eberlein, Kathrin Glau

Feynman-Kac formulas provide a fundamental link between conditional
expectations and deterministic partial integro differential equations
(PIDEs). In the context of option pricing in L\'evy models, this relation
has recently led to the development of various numerical methods to
calculate prices via solving PIDEs. Among those wavelet-Galerkin methods
play an important role, since they provide efficient algorithms and
are applicable to a wide range of problems. To show that these numerical
solutions coincide with option prices, we give the precise link between
certain conditional expectations and weak solutions of the corresponding
PIDEs in Sobolev-Slobodeckii-spaces. Interpreting the equations as
pseudo differential equations provides an appropriate classification
of L\'evy processes according to their Fourier transform. We apply
the main result to price barrier and lookback options in L\'evy models
and illustrate this by numerical results using a wavelet-Galerkin
method.

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231

Dorn, Jochen, (ASB, Aarhus University)

**A CDO option market model for standardized CDS index tranches**

Authors:

We provide a market model which implies a dynamic for standardized
CDS index tranche spreads. This model is useful for pricing options
on tranches with future Issue Dates as well as for modeling emerging
options on structured credit derivatives. With the upcoming regulation
of the CDS market in perspective, the model presented here is also
an attempt to face the effects on pricing approaches provoked by an
eventual Clearing Chamber . It becomes also possible to calibrate
Index Tranche Options with bespoke tenors/tranche subordination to
market data obtained by more liquid Index Tranche Options with standard
characteristics.

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232

Keller-Ressel, Martin, (ETH Zurich)

**Pricing Options on Discrete Realized Variance**

Authors: Martin Keller-Ressel and Johannes Muhle-Karbe

We consider the pricing of derivatives written on the discrete realized
variance of an underlying security. For numerical valuation, realized
variance is usually approximated by its continuous-time limit, the
quadratic variation. We show that for options with short time-to-maturity
this approximation may produce considerably different prices than
the exact valuation. The difference strongly depends on whether or
not the stock price process has jumps. Moreover, to facilitate the
exact valuation of European-style options on the discrete realized
variance, we propose a novel approach that applies Fourier-Laplace
techniques.

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234

Shaikhet, Gennady, (Carnegie Mellon University)

**Optimal Execution in a General One-Sided Limit-Order Book**

Authors: Silviu Predoiu, Gennady Shaikhet, Steven Shreve

We construct an optimal execution strategy for the purchase of a large
number of shares of a financial asset over a fixed interval of time.
Purchases of the asset have a nonlinear impact on price, and this
is moderated over time by resilience in the limit-order book that
determines the price. The limit-order book is permitted to have arbitrary
shape. The optimal strategy has the following properties: it makes
three lump purchases, including one in the beginning and one in the
end of the time interval; between lumps it purchases continuously
at a rate equal to the order book resiliency.

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235

Kokholm, Thomas, (Aarhus University)

**A Consistent Pricing Model for Index Options and Volatility
Derivatives**

Authors: Rama Cont and Thomas Kokholm

We propose and study a flexible modeling framework for the joint dynamics
of an index and a set of forward variance swap rates written on this
index, allowing volatility derivatives and options on the underlying
index to be priced consistently. An affine specification using LÃ©vy
processes as building blocks leads to analytically tractable pricing
formulas for options on the VIX as well as efficient numerical methods
for pricing of European options on the underlying asset. We show that
our model can simultaneously fit prices of European options on S&P
500 across strikes and maturities as well as options on the VIX volatility
index.

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236

Ludkovski, Mike, (UC Santa Barbara)

**Stochastic Switching Games and Duopolistic Competition in Emissions
Markets**

Authors: Michael Ludkovski

We study optimal behavior of energy producers under a CO_2 emission
abatement program. We focus on a two-player discrete-time model where
each producer is sequentially optimizing her emission and production
schedules. The game-theoretic aspect is captured through a reduced-form
price-impact model for the CO_2 allowance price. Such duopolistic
competition results in a new type of a non-zero-sum stochastic switching
game on finite horizon. Existence of game Nash equilibria is established
through generalization to randomized switching strategies. Since there
is no uniqueness, we consider correlated equilibrium mechanisms. A
simulation-based recursive algorithm to solve for the game values
is constructed and a numerical example is presented.

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237

Taschini, Luca, (London School of Economics and Political Science)

**Flexibility Premium in Marketable Permits**

Authors: Luca Taschini

We study the market for emission permits in the presence of reversible
abatement measures characterized by delay in implementation. Assuming
that the new operating profits follow a one-dimensional geometric
Brownian motion and that the company is risk-neutral, we derive an
analytic solution of the premium for flexibility embedded in marketable
permits. Numerical results are presented to illustrate the likely
magnitude of the premium and how it is affected by uncertainty and
delays in implementation.

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239

Fukasawa, Masaaki, (Osaka University)

**Asymptotic Analysis for Stochastic Volatility: Edgeworth expansion**

Authors: Masaaki Fukasawa

The validity of an approximation formula for European option prices
under general stochastic volatility models is proved in the light
of the Edgeworth expansion for ergodic diffusions. The asymptotic
expansion is around the Black-Scholes price and is uniform in bounded
payoff functions. The result provides a validation of, in particular,
an existing singular perturbation expansion formula for the so-called
fast mean reverting stochastic volatility model.

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240

Mnif, Walid, (University of Western Ontario)

**Pricing and Hedging Strategies for Contingent Claims in an Incomplete
Hybrid Emissions Market**

Authors: Walid Mnif, Matt Davison

We propose a stochastic approach for trading and pricing emission
permits under an incomplete hybrid system in which credits are partially
fungible from one period to another. We show that it is essential
for a market to have multiple trading periods in order to promote
efficient price signals and effective hedging strategies. In order
to price exotic options in such markets, we present a flexible approach
based on the filtering theory proposed by Follmer and Schweizer (1991).
Within the resulting pricing framework, exotic options can easily
be priced with the use of Monte Carlo simulation.

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241

Kan, Kin Hung (Felix), (University of Western Ontario)

**Optimized Least-squares Monte Carlo for Measuring Counterparty
Credit Exposure of American-style Options**

Authors: Kin Hung (Felix) Kan, Mark Reesor

Building on the least-squares Monte Carlo (LSM) method that was originally
proposed by Longstaff and Schwartz (2001) to price American options,
we develop a new version of the LSM method, which we term "optimized
least-squares Monte Carlo" (OLSM), to measure the counterparty credit
exposure of American-style options. The main advantage of OLSM is
that it prevents the use of nested simulations. In order to enhance
its performance, OLSM is integrated with the following three techniques:
variance reduction, initial state dispersion and multiple bucketing
(piecewise linear regression). Numerical results demonstrate the power
of the OLSM method.

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242

Beiglböck, Mathias, (University of Vienna)

**Is the minimum value of an option on variance generated by local
volatility?**

Authors: M. Beiglböck, P. Friz, S. Sturm

We discuss the possibility of obtaining model-free bounds on volatility
derivatives, given present market data in the form of a calibrated
local volatility model. A counter-example to a wide-spread conjecture
is given.

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243

Vargiolu, Tiziano, (University of Padova)

**Optimal portfolio for HARA utility functions where risky assets
are exponential additive processes**

Authors: Laura Pasin, Tiziano Vargiolu

In this paper we analyse a market where the risky assets follow exponential
additive processes, which are time-inhomogeneous generalisations of
geometric Levy processes. In this market we show that, when an investor
wants to maximize a HARA utility function, the optimal strategy consists
in keeping proportions of wealth in the risky assets which depend
only on time but not on the current wealth level or on the prices
of the risky assets: in the time-homogeneous case we extend the classical
Merton's result to this market. While the one-dimensional case has
been extensively treated and the multidimensional case has been treated
only in the time-homogeneous case, to the Authors:' knowledge this
is the first time that such results are obtained for exponential additive
processes in the multidimensional case. We conclude with four examples.

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244

Seifried, Frank, (University of Kaiserslautern)

**Optimal Investment for Worst-Case Crash Scenarios: A Martingale
Approach**

Authors: Frank Seifried

One of the inherent hazards of investing in financial markets is the
risk of a sudden and sharp decrease in asset prices, possibly affecting
future investment opportunities. We investigate the optimal portfolio
problem under the threat of a financial market crash in a multi-dimensional
jump-diffusion framework. We set up a non-probabilistic crash model
and consider an investor that seeks to maximize CRRA utility in the
worst possible crash scenario. We recast the problem as a stochastic
differential game; with the help of the fundamental notion of indifference
strategies, we completely solve the portfolio problem using martingale
arguments.

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245

Cui, Xiangyu, (The Chinese University of Hong Kong)

**Better than Dynamic Mean-Variance Policy in Market with ALL
Risky Assets**

Authors: Xiangyu Cui and Duan Li

As the dynamic mean-variance portfolio selection formulation does
not satisfy the principle of optimality of dynamic programming, phenomena
of time inconsistency occur, i.e., investors may have incentives to
deviate from the pre-committed optimal mean-variance portfolio policy
during the investment process under certain circumstances. By introducing
the concept of time inconsistency in efficiency and defining the induced
trade-off, we further demonstrate in this paper that investors behave
irrationally under the pre-committed optimal mean-variance portfolio
policy when their wealth is above certain threshold during the investment
process in a market with all risky assets. By relaxing the self-financing
restriction to allow withdrawal of money out of the market, we develop
a revised mean-variance policy which dominates the pre-committed optimal
mean-variance portfolio policy in the sense that, while the two achieve
the same mean-variance pair of the terminal wealth, the revised policy
enables the investor to receive a free cash flow stream during the
investment process.

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247

Pistorius, Martijn, (Imperial College London)

**CONTINUOUSLY MONITORED BARRIER OPTIONS UNDER MARKOV PROCESSES**

Authors: A MIJATOVIC & M R PISTORIUS

In this talk we present an algorithm for pricing barrier options in
one-dimensional Markov models. The approach rests on the construction
of an approximating continuous-time Markov chain that closely follows
the dynamics of the given Markov model. We illustrate the method by
implementing it for a range of models, including a local Levy process
and a local volatility jump-diffusion. We also provide a convergence
proof and error estimates for this algorithm.

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249

Schmutz, Michael, (University of Bern)

**Multivariate extension of put-call symmetry**

Authors: Michael Schmutz in joint work with Ilya Molchanov

Multivariate analogues of the put-call symmetry can be expressed as
certain symmetry properties of basket options and options on the maximum
of several assets with respect to some (or all) permutations of the
weights and the strike. It is shown how to characterise distributions
that feature these symmetries and important closely related quasi-symmetry
properties. A particular attention is devoted to the case of asset
prices driven by Lévy processes. Based on this, semi-static hedging
techniques for certain multi-asset barrier options are suggested.

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251

Rometsch, Mario, (Ulm University)

**Hedging Under Model Uncertainty - Efficient Computation Of The
Hedging Error Using The Proper Orthogonal Decomposition**

Authors: Michael Monoyios And Mario Rometsch And Till Schröter
And Karsten Urban

We examine the hedging performance of the Black-Scholes, Heston and
SABR models in simulated market environments that are characterised
by (i) a three-dimensional It\^{o} diffusion, (ii) a stochastic volatility
model with jumps, and (iii) the CGMYe model. The performance is measured
in terms of the distribution of the terminal hedging error when a
path-dependent option is hedged. Based upon a FEM solver for the pricing
PDE, we make use of a Proper Orthogonal Decomposition (POD) in order
to enhance the computational efficiency.

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252

Danilova, Albina, (London School of Economics)

**Dynamic markov bridges motivated by models of insider trading**

Authors: Luciano Campi, Umut Cetin, Albina Danilova

Given a Markovian Brownian martingale $Z$, we build a process $X$
which is a martingale in its own filtration and satisfies $X_1 = Z_1$.
We call $X$ a dynamic bridge, because its terminal value $Z_1$ is
not known in advance. We compute explicitly its semimartingale decomposition
under both its own filtration $\cal{F}^X$ and the filtration $\cal{F}^{X,Z}$
jointly generated by $X$ and $Z$. Our construction is heavily based
on parabolic PDE's and filtering techniques. As an application, we
explicitly solve an equilibrium model with insider trading, that can
be viewed as a non-Gaussian generalization of Back and Pedersen's
(1998), where insider's additional information evolves over time.

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254

Dias, Jose Carlos, (ISCTE-IUL - NIF: 501510184)

**Double Barrier Options Valuation under Multifactor Pricing Models**

Authors: Joao Pedro Vidal Nunes and Jose Carlos Dias

There exists a vast literature on the pricing of barrier options.
However, the literature is mainly focused on the valuation of European-style
contracts under single-factor option pricing models (such as the geometric
Brownian motion and the CEV processes). This paper extends the literature
in two directions. First, European-style (double) barrier options
are priced under a multifactor and Markovian financial model that
is able to accommodate stochastic volatility, stochastic interest
rates and endogenous bankruptcy. Second and more importantly, quasi-analytical
pricing solutions are also proposed for American-style (double) barrier
option contracts under the same general financial model. The proposed
pricing solutions are shown to be accurate, easy to implement, and
efficient.

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258

Maggis, Marco, (University of Milan)

**Conditional Certainty Equivalent**

Authors: Marco Frittelli, Marco Maggis

In a dynamic framework, we study the conditional version of the classical
notion of the certainty equivalent when the preferences are described
by a stochastic dynamic utility satisfying natural conditions. We
point out the need of an Orlicz space approach for the time consistency
of the conditional certainty equivalent. This conditional map turns
out to be quasiconcave, regular and well defined on an appropriate
Orlicz space: thus a robust dual represantation can be proved.

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260

Paulsen, Michael, (HU Berlin/QPL)

**Averaging Principle for an order book model**

Authors: Ulrich Horst, Michael Paulsen

One approach to analyzing stochastic fluctuations in market prices
is to model the complex dynamics of order arrivals on the microscopic
level, with the aim of extracting consequences in the aggregate on
the macroscopic level. In this work we prove an averaging principle
for key quantities (best bid/ask price and standing buy/sell volume
densities) of a random state-dependent order book model by taking
scaling limits when the tick size approaches zero. The averaging principle
states that the scaled quantities converge in probability to the solution
of a coupled functional ODE containing the input parameters of the
model.

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262

Wiktorsson, Magnus, (Lund University)

**On the Convergence of Higher Order Hedging Schemes**

Authors: Mats Broden and Magnus Wiktorsson

Hedging errors induced by discrete rebalancing of the hedge portfolio
of a delta-gamma hedging strategy is investigated. The rate of convergence
of the expected squared hedging error as the number of adjustments
of the hedge portfolio goes to infinity is analyzed. It is found that
the delta-gamma strategy produces higher convergence rates than the
usual delta strategy.

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263

Zhou, Xunyu, (University of Oxford)

**Greed, Leverage, and Potential Losses: A Prospect Theory Perspective**

Authors: Hanqing Jin and Xunyu Zhou

Partly motivated by a deeper understanding of the role human greed
has played in the current financial crisis, this paper quantifies
the notion of greed, and explores its connection with leverage and
potential losses, in the context of a continuous time behavioral portfolio
choice model under (cumulative) prospect theory. We argue that the
reference point is the critical parameter in defining greed. An asymptotic
analysis on optimal trading behaviors when the pricing kernel is lognormal
and the S-shaped utility is a two-piece CRRA shows that both the level
of leverage and the magnitude of potential losses will grow unbounded
if the greed grows uncontrolled. However, the probability of ending
with gains does not diminish to zero even as the greed approaches
infinity. This explains why a sufficiently greedy behavioral agent,
despite the risk of catastrophic losses, is still willing to gamble
on potential gains because they have a positive probability of occurrence
whereas the corresponding rewards are huge. As a result an effective
way to contain human greed, from a regulatory point of view, is to
impose a priori bounds on leverage and/or potential losses.

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264

Krühner, Paul, (Christian-Albrechts-Universität zu Kiel)

**On a Heath-Jarrow-Morton approach for stock options**

Authors: Jan Kallsen and Paul Krühner

The purpose of financial models is, among other things, pricing and
hedging derivates. Most of them model the dynamics of an underlying
instrument on which the derivatives are written on. However, if the
derivates are traded liquidly, it appears reasonable to model them
directly. This was first advocated by Heath, Jarrow and Morton for
the interest rate markets. We adopt this approach, but contrary to
a related contribution by Carmona and Nadtochiy, the key parametrisation
of our setup involves time-inhomogeneous Levy processes instead of
local volatility models. This talk is based on joint work with Prof.
Dr. Jan Kallsen.

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266

Tobelem, Sandrine, (London School of Economics)

**Robust Decision Under Model Uncertainty**

Authors: Pauline Barrieu & Sandrine Tobelem

In the present paper, we propose a robust portfolio optimization methodology
under model ambiguity, when there is some ambiguity concerning the
dynamics leading asset prices. The decision maker considers several
priors for the asset price dynamics measure and displays an ambiguity
aversion against those priors. We have developed a two steps robust
methodology that offers the advantage to be more tractable and easier
to implement than the methodologies proposed in the literature. This
methodology decomposes the ambiguity aversion into a model specific
ambiguity aversion, where the optimal weights inferred by each prior
are transformed through a generic function psi. Then, the optimal
transformed weights are mixed through a measure pi that reflects the
relative ambiguity aversion of the investor for the different priors
considered.

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267

Law, Sebastian, (University of Manchester)

**Monsoon options: early-exercise Asian tail using fast & accurate
hybrid numerical techniques**

Authors: Sebastian Law, Peter Duck, David Newton

We introduce a new class of option that nests several vanilla contracts,
including European, fixed-strike (average rate) Asian, and American
options, depending on the contract parameters. Specifically, this
contract is an early-exercise Asian tail option, where 'exercise'
initiates the start of the averaging period (of predetermined length).
We christen this the Monsoon option, and describe efficient numerical
techniques to value the contract (and its simpler sibling, the Asian
tail option) for both geometric and arithmetic averaging, with particular
reference to commodity futures contracts as the underlying asset.apr

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268

Jin, Hanqing, (University of Oxford)

**Behavioral Portfolio Selection with Loss Control**

Authors: H. Jin, Xun Yu Zhou, Song Zhang

In this paper we formulate a continuous-time behavioural (a la cumulative
prospect theory) portfolio selection model where the losses are constrained
by a pre-specified upper bound. Economically the model is motivated
by the previously proved fact that the losses occurring in a bad state
of the world can be catastrophic for an unconstrained model. Mathematically
solving the model boils down to solving a concave Choquet minimization
problem with an additional upper bound. We derive the optimal solution
explicitly for such a loss control model. The optimal terminal wealth
profile is in general characterized by three pieces: the agent has
gains in the good states of the world, gets a moderate, endogenously
constant loss in the intermediate states, and suffers the maximal
loss (which is the given bound for losses) in the bad states. Examples
are given to illustrate the general results.

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270

Hadjiliadis, Olympia, (City University of New York, Brooklyn College)

**Insuring Against Maximum Drawdown and Drawing Down Before Drawing
Up**

Authors: Peter Carr, Hongzhong Zhang, Olympia Hadjiliadis

We introduce two new digital options whose payoff depends on a well-known
risk measure, namely maximum drawdown, and the corresponding reward
measure known as maximum drawup. The payoff of the former is contingent
upon the event that the underlying has incurred a drawdown of $K by
maturity, while the payoff of the latter is contingent upon the event
that a $K drawdown has preceded a $K drawup. In this work we provide
static and semi-static hedges of these options in terms of one-touch
knock outs, one touches and vanillas under arithmetic and geometric
models.

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271

Wiese, Anke, (Heriot-Watt University)

**Positive Stochastic Volatility Simulation**

Authors: Simon J.A. Malham and Anke Wiese

In the Heston stochastic volatility model, the transition probability
of the variance process can be represented by a non-central chi-square
density. We focus on the case when the number of degrees of freedom
is small, typical in foreign exchange markets. We prove a new representation
for this density based on the generalized Gaussian density. We prove
Marsaglia's polar method extends to this distribution, providing an
exact method for generalized Gaussian sampling. The advantages are
that for the mean-reverting square-root process in the Heston model
and Cox-Ingersoll-Ross model, we can generate samples from the true
transition density simply, efficiently and robustly.

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272

Borovkova, Svetlana, (VU Amsterdam)

**American basket and spread option pricing by a simple binomial
tree**

Authors: Borovkova, Permana, v.d. Weide

We address the problem of valuing and hedging American options on
baskets and spreads. We adopt the main ideas of the Generalized Lognormal
(GLN) approach introduced in Borovkova et al. (2007) and extend them
to the case of American options. We approximate the basket price process
by a suitable Geometric Brownian motion, shifted by an arbitrary parameter
and reflected over the x-axis. We construct a simple binomial tree,
by matching the basket's volatility, and evaluate our approach by
comparing the binomial tree option prices to those obtained by other
methods. We evaluate the delta-hedging performance of our method and
show that it performs remarkably well. The main advantages of our
method are that it is simple, computationally extremely fast and efficient,
while providing accurate option prices and deltas.

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275

Czichowsky, Christoph, (ETH Zurich)

**Time-consistent Mean-Variance Portfolio Selection in Discrete
and Continuous Time**

Authors:

It is well known that mean-variance portfolio selection is a time-inconsistent
control problem in the sense that the dynamic programming principle
fails. We present a time-consistent formulation of this problem which
is based on local mean-variance efficiency. We start in discrete time,
where the formulation is straightforward, and then find the natural
extension to a general continuous-time semimartingale setting. This
generalises recent results by Basak and Chabakauri (2009) and Björk
and Murgoci (2008) where the treatment relies on an underlying Markovian
framework. As a new feature we justify the continuous-time formulation
by showing that it coincides with the continuous-time limit of the
discrete-time formulation. The proof of this convergence exploits
a global characterisation of the locally optimal strategy in terms
of the Föllmer-Schweizer decomposition of the mean-variance tradeoff
process.

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**276**

**Ostaszewski** , **A.J **( London School of Economics)

*Inference of Managerial Precision from Voluntary Disclosure
Intensity*

Authors:M.B. Gietzmann, A.J Ostaszewski

The Dye model of corporate communication gives only a qualitative
explanation for optimal disclosure of voluntary information in a stylized
risk-neutral valuation procedure in which with some probability management
receives a noisy signal of firm value. Working in a general framework
including both standard utility approaches and a broad class of trading
mechanisms (with public observation), we operationalize Dye’s
model by endogenizing and optimizing its stylized

parameter. We determine the resulting intensity of voluntary disclosure
flow; subject to a recognition of investor risk preferences, we find
that the intensity is montonic in managerial precision. In the general
framework we conclude that higher disclosure intensity

(greater information sharing) typically follows from poorer managerial
information precision and thus provide an econometrically testable
mathematical link between cost-of-capital and observable corporate
disclosure behaviour.

278

Reesor, Mark, (University of Western Ontario)

**Enhanced Convergence Results for Stochastic Tree Estimators**

Authors: Tyson Whitehead, Matt Davison and Mark Reesor

The stochastic tree method for valuing American-style options yields
Monte Carlo estimators of option value that are biased and consistent.
Assuming the existence of an absolute first-plus-epsilon moment, Broadie
and Glasserman (1997) show that the stochastic tree estimators converge
in probability. In this work we show the almost sure convergence of
the high-biased stochastic tree estimator assuming only the existence
of the first absolute moment. This yields a stronger convergence result
under weaker conditions.

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279

Davison, Matt, (University of Western Ontario)

**Correcting the Optimal Stopping bias in Monte Carlo evaluation
of early exercise options**

Authors: Matt Davison, Mark Reesor, Tyson Whitehead

We present a method for reducing the bias present in Monte Carlo estimators
of the discrete finite-time horizon optimal stopping problem. At each
time step we subtract a large-sample theory derived asymptotic bias
expression to produce bias-corrected estimators. We show these corrected
estimators to be consistent under finite second-moment conditions
and that the bias has reduced order under finite fourth moment condition
plus a region in which sampling density is continuous and variance
is bounded. The simple closed form of the correction, easily evaluated
in the context of a simulation, makes this work of practical significance.

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280

Marshall, James, (University of Western Ontario)

**Forest of Stochastic Trees: A New Method for Valuing High Dimensional
Swing Options**

Authors: T. James Marshall and R. Mark Reesor

Swing options are generalizations of American-style options as they
allow the holder more than one exercise right and typically some control
over the exercise amounts. For a low-dimensional underlying, valuation
of these contracts can be done using the forest of trees algorithm;
a generalization of the standard tree method for pricing American-style
claims. As with pricing American-style claims, this tree method breaks
down in high dimensions, implying a simulation approach is required.
The stochastic tree algorithm is a Monte Carlo method for valuing
American-style options that depend on a high-dimensional underlying.
In this work, we replace the standard (binomial) trees in the forest
of trees algorithm with stochastic trees, yielding the forest of stochastic
trees; a simulation-based method for valuing high-dimensional swing
options.

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285

Lutz, Matthias, (University of Ulm)

**Efficient Pricing of CMS Spread Options in a Stochastic Volatility
LMM**

Authors: Ruediger Kiesel, Matthias Lutz

The calibration of Libor market models with stochastic volatility
to quoted CMS spread option prices requires fast yet accurate approximation
methods for pricing such options. In the present paper we develop
a new method for the fast evaluation of the density of an integrated
Cox-Ingersoll-Ross (CIR) process. Combined with approximations for
the swap-rate dynamics, this results in a semi-analytical formula
for CMS spread option prices. The effectiveness of this formula is
demonstrated by comparison with Monte Carlo values. We also present
some examples of calibration to real market data.

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288

Tashman, Adam, (University of California, Santa Barbara)

**Portfolio Optimization Under a Stressed-Beta Model**

Authors: Jean-Pierre Fouque, Adam P Tashman

This paper presents a closed-form solution to the portfolio optimization
problem where an agent wishes to maximize expected terminal wealth,
trading continuously between a risk-free bond and a risky stock following
Stressed-Beta dynamics specified in Fouque and Tashman (2010). The
agent has a finite horizon and a utility of the Constant Relative
Risk Aversion type. The model for stock dynamics is an extension of
the Capital Asset Pricing Model (CAPM); it is expressed in continuous-time,
and the slope relating excess stock returns to excess market returns
switches between two values. This mechanism reflects the fact that
the slope may steepen during periods of stress, a feature which has
been demonstrated to better model stock dynamics than CAPM. An asymptotic
expansion technique is used to write an explicit expression for the
agent's optimal strategy. Lastly, the optimization approach is illustrated
with market data, and its outperformance versus the Merton approach
is demonstrated.

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**284**

**Nguyen Huu, Adrien** (R33, Market Risk Management & Pricing

EDF R&D )

**Industrial Arbitrage in Markets with Transaction Costs **

Authors: Bruno Bouchard, Adrien Nguyen Huu

We consider a market with proportional transaction costs in discrete
time, with production possibilities. When the production function
is linear, we study two natural extensions of the robust no-arbitrage
and no-arbitrage of the second kind conditions introduced by Schachermayer
and Rasonyi respectively. We show that both conditions imply the closedness
of the set of attainable claims and are equivalent to the existence
of a strictly consistent price system extended to production possibilities.
This allows to discuss the closedness of the set of terminal wealth
in models with non-linear production functions which may allow arbitrage
with low production regimes but not asymptotically.

291

de Innocentis, Marco, (University of Leicester)

**Prices and sensitivities of barrier and first-touch digital
options in Lévy-driven models, near barrier**

Authors: Mitya Boyarchenko, Marco de Innocentis and Sergei Levendorskii

We calculate the asymptotics of the prices of barrier options and
first-touch digitals near the barrier for wide classes of Lévy processes
with exponential jump densities. In the case of processes of infinite
activity and finite variation, with the drift pointing from the barrier,
we prove that the price is discontinuous at the boundary. We extend
Carr's randomization approach to the calculation of the option's delta
without making use of numerical differentiation. By comparing the
exact asymptotic results for prices and deltas with those of Carr's
randomization approximation, we conclude that the latter is very accurate
near the barrier.

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292

Leung, Siu Tang (Tim), (Johns Hopkins University)

**Forward Indifference Valuation of American Derivatives**

Authors: Tim Leung, Ronnie Sircar, Thaleia Zariphopoulou

We study an indifference valuation methodology based on the forward
investment performance measure introduced by Musiela and Zariphopoulou.
In particular, we consider hedging a long position of a finite-maturity
American option in an incomplete diffusion market. The option holder
selects an admissible trading strategy and exercise time in order
to maximize the expected forward performance from trading wealth plus
the option payoff upon exercise. This leads to a combined stochastic
control and optimal stopping problem. The holder's forward indifference
price for the American option is determined by comparing his optimal
expected forward investment performance with and without the derivative.
We investigate the holder's optimal hedging and exercising strategies
through the analytic and numerical studies of the associated variational
inequality. In the case of exponential forward performance, the holder's
forward indifference price admits a dual representation that involves
relative entropy penalization with respect to the minimal martingale
measure over a random horizon. We show that higher risk aversion reduces
the indifference price and shortens the optimal exercise time. We
also apply the forward performance criterion to model early exercises
of employee stock options using. Finally, we introduce the concept
of marginal forward performance price. In contrast to the classical
marginal utility price, the marginal forward performance is independent
of the holder's wealth and risk preferences, and is simply the risk-neutral
price under the minimal martingale measure.

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294

Sircar, Ronnie, (Princeton University)

**Games with Exhaustible Resources**

Authors: C. Harris, S. Howison, R. Sircar

We study N-player continuous-time Cournot games in an oligopoly where
firms choose production quantities. These are nonzero-sum differential
games, whose value functions may be characterized by systems of nonlinear
Hamilton-Jacobi partial differential equations. When resources are
in finite supply, such as oil, exhaustibility enters as boundary conditions
for the PDEs. We analyze the problem when there is an alternative,
but expensive, technology (for example solar power for energy production),
and give an asymptotic approximation in the limit of small exhaustibility.
We illustrate the two-player problem by numerical solutions, and discuss
the impact of limited oil reserves on production and oil prices in
the duopoly case.

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298

Yam, Phillip, (The Hong Kong Polytechnic University)

**A unified "Bang-Bang" Principle with respect to a class of nonanticipative
benchmarks**

Authors: S. C. P. Yam, S. P. Yung and W. Zhou

In recent years, there has been a number of work on finding the optimal
selling time of a stock so that the expected ratio of its selling
price to certain benchmark (e.g., its ultimate highest price) over
a finite time horizon is maximized. Even though being formulated in
different settings, they all result in a "bang-bang" type optimal
solution which can literally be interpreted as Â'Buy-And-Hold or Sell-At-OnceÂ'
depending on the quality of the stock. In this paper, we first provide
three algebraic conditions on a class of benchmarks and show that
for any benchmark satisfying the three conditions the corresponding
optimal stopping problem has a "bang-bang" type optimal solution.
Our work here provides a unified proof of all similar problems considered
in the existing literature and also implies results complementary
to certain existing work.

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302

Mijatovic, Aleksandar, (Imperial College London)

**Deterministic criteria for the absence of arbitrage in diffusion
models**

Authors: Aleksandar Mijatovic, Mikhail Urusov

We describe a deterministic characterisation of the no free lunch
with vanishing risk (NFLVR), the no generalised arbitrage (NGA), and
the no relative arbitrage (NRA) conditions in the one-dimensional
diffusion setting and examine how these notions of no-arbitrage relate
to each other.

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304

Bayer, Christian, (TU Berlin)

**A Donsker theorem for cubature on Wiener space**

Authors: Christian Bayer and Peter K. Friz

Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc.~R.~Soc.~Lond.~A
8 January 2004 vol. 460 no.~2041 169-198] provides a powerful alternative
to Monte Carlo simulation for the integration of certain functionals
on Wiener space. More specifically, and in the language of mathematical
finance, cubature allows for fast computation of European option prices
in generic diffusion models. We give a random walk interpretation
of cubature and similar (e.g.~the Ninomya--Victoir) weak approximation
schemes. By using rough path analysis, we are able to establish weak
convergence for general path-dependent option prices.

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307

Sass, Jörn, (University of Kaiserslautern)

**The Numeraire Portfolio under Proportional Transaction Costs**

Authors: Jörn Sass and Manfred SchÃ¤l

We study existence of a numeraire portfolio for a general discrete
time financial market with proportional transaction costs. In an incomplete
market without frictions, consistent prices for financial derivatives
can be obtained by taking expectation of the claim with respect to
some martingale measure. The numeraire portfolio allows to replace
this change of measure by a change of numeraire. A well known approach
is to find the growth optimal portfolio as candidate for the numeraire
portfolio, but the numeraire portfolio in the strict sense might not
exist. With transaction costs, these concepts have to be modified.
Using methods of dynamic programming we show that the same approach
essentially works.

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308

Mackie, Ewan, (Imperial College London)

*Rational Term Structure Models with Geometric Levy Martingales*

Authors::Dorje Brody, Lane Hughston

In the "positive interest" models of Flesaker & Hughston (1996) the
nominal discount bond system is represented by a one-parameter family
of positive martingales. In the present paper we extend this analysis
to include a variety of distributions for the martingale family, parameterised
by a function f(x) that determines the behaviour of the market risk
premium. We consider cases for which the martingale families are (a)
exponential Brownian, (b) exponential gamma, and (c) exponential VG.
Our findings lead to semi-analytical and Fourier-inversion style solutions
for the prices of bond options and other derivatives. (Authors::
D.C. Brody, L.P. Hughston).

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309

Tankov, Peter, (Ecole Polytechnique)

**Jump-adapted discretization schemes for Levy-driven SDEs**

Authors: Arturo Kohatsu-Higa, Peter Tankov

We present new algorithms for weak Monte Carlo approximation of stochastic
differential equations driven by pure jump LÃ©vy processes. The method
is built upon adaptive non-uniform discretization based on the times
of large jumps of the driving process. To approximate the solution
between these times we replace the small jumps with a Brownian motion.
Our technique avoids the simulation of the increments of the LÃ©vy
process, and in many cases achieves better convergence rates than
the traditional Euler scheme with equal time steps. To illustrate
the method, we discuss an application to option pricing in the Libor
market model with jumps.

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310

Grasselli, Martino, (University of Padova and ESILV Paris)

**Riding on the smiles**

Authors: José Da Fonseca and Martino Grasselli

We investigate the calibration performance of several multifactor
stochastic volatility models, including Heston (1993), Double-Heston,
and Wishart Affine Stochastic Correlation proposed by Da Fonseca et
al. (2007). Finally, we provide some price approximations for vanilla
options that are very useful to speed up the pricing process thus
leading to reasonable calibration time.

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311

De Franco, Carmine, (Université Paris 7, Denis Diderot)

**Portfolio Insurance under a risk-measure constraint**

Authors: Carmine De Franco and Peter Tankov

We study optimal strategies for portfolio insurance. We consider the
problem of a fund manager who wants to structure a portfolio insurance
product where the investors pay the initial value x0 and are guaranteed
to receive at least the amount z at maturity. If, at maturity, the
value of the portfolio X is smaller than z, a third party pays back
the shortfall amount z-X. This guarantee may indeed be provided by
the bank which owns the fund. In exchange, the third party imposes
a limit on the risk exposure z-X, represented by a law invariant convex
risk measure.

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316

Schmidt, Thorsten, (Chemnitz University of Technology)

**Market Models for CDOs driven by time-inhomogeneous Levy processes**

Authors: Ernst Eberlein, Zorana Grbac and Thorsten Schmidt

his paper considers a top-down approach for CDO valuation and proposes
a market model. We extend previous research on this topic in two directions:
on the one side, we use as driving process for the interest rate dynamics
a time-inhomogeneous Levy process, and on the other side, we do not
assume that all maturities are available in the market. Only a discrete
tenor structure is considered, which is in the spirit of the classical
Libor market model. We create a general framework for market models
based on multi- dimensional semimartingales. This framework is able
to capture dependence between the default-free and the defaultable
dynamics, as well as contagion effects. Conditions for absence of
arbitrage and valuation formulas for tranches of CDOs are given.

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317

Strong, Winslow, (University of California, Santa Barbara)

**Regulation, Diversity, and Arbitrage**

Authors: Winslow Strong and Jean-Pierre Fouque

In 1999 Robert Fernholz observed an inconsistency between the normative
assumption of existence of an equivalent martingale measure (EMM)
and the empirical reality of diversity in equity markets. We explore
a method of imposing diversity on market models by a type of antitrust
regulation that is compatible with EMMs. The regulatory procedure
breaks up companies that become too large, while holding the total
number of companies constant by imposing a simultaneous merge of other
companies. As an example, regulation is imposed on a market model
in which diversity is maintained via a log-pole in the drift of the
largest company.

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320

Rayee, Gregory, (Universite Libre de Bruxelles)

**Local Volatility Pricing Models for Long-dated FX Derivatives**

Authors: Gregory Rayee and Griselda Deelstra

We study the local volatility function in the FX market where both
domestic and foreign interest rates are stochastic. We derive the
local volatility function and obtain several results that can be used
for the calibration of this local volatility on the FX option's market.
Then, we study one extension which allows the volatility of the spot
FX rate to have stochastic behavior. More precisely, the extension
is obtained by multiplying the FX spot local volatility with a stochastic
volatility. Thanks to the Gyöngy's mimicking property, we obtain a
calibration method for the local volatility associated to this model.

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322

Kühn, Christoph, (Goethe-University Frankfurt)

**Large Traders and Illiquid Options: Hedging vs. Manipulation**

Authors: Holger Kraft and Christoph Kühn

We study the effects on derivative pricing arising from price impacts
by large traders. When a large trader issues a derivative and (partially)
hedges his risk, he influences the price process of the underlying
and thus the derivative's payoff. In a Black-Scholes model with price
impact on the drift, we explicitly solve the arising utility maximization
problem. The seller's indifference price becomes a concave function
of the claim (in frictionless markets it is convex). Furthermore,
it tends to the minimum payoff if the position size tends to infinity
and to the Black-Scholes price if the risk aversion tends to infinity.

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323

Wang, Tai-Ho, (Baruch College, CUNY)

**Asymptotics of implied volatility in local volatility models**

Authors: Jim Gatheral, Elton P. Hsu, Peter Laurence, Cheng Ouyang,
Tai-Ho Wang

Using an expansion of the transition density function of a 1-dimensional
time inhomogeneous diffusion, we obtain the short time asymptotics
of European call option prices. We then use these option prices approximations
to calculate the first order and second order deviation of the implied
volatility from its leading value and obtain approximations which
we numerically demonstrate to be highly accurate. We shall also briefly
show the corresponding results in the case of stochastic volatility
models.

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324

Zhong, Yifei, (University of Oxford)

**Optimal Stock Selling Based on the Global Maximum**

Authors: Min Dai, Zhou Yang and Yifei Zhong

We aim to determine an optimal stock selling time to minimize the
expectation of the square error between the selling price and the
global maximum price over a given period. Assuming that stock price
follows the geometric Brownian motion, we formulate the problem as
an optimal stopping time problem, or equivalently, a variational inequality
problem. We provide a partial differential equation (PDE) approach
to characterize the resulting free boundary that corresponds to the
optimal selling strategy. The monotonicity and smoothness of the free
boundary are addressed as well.

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326

Englezos, Nikolaos, (University of Piraeus Research Center)

**Utility Maximization With Habit Formation: Dynamic Programming
and Stochastic PDE's**

Authors: Nikolaos Englezos, Ioannis Karatzas

This paper studies the habit-forming preference problem of maximizing
total expected utility from consumption net of the standard of living,
a weighted-average of past consumption. Exploiting the interplay between
dynamic programming and Feynman-Kac results concerning random fields,
the value random field of the optimization problem satisfies a non-linear,
backward stochastic partial differential equation (BSPDE) of parabolic
type, widely referred to as the stochastic Hamilton-Jacobi-Bellman
equation. The dual value random field is characterized further in
terms of a parabolic BSPDE which is linear. Progressively measurable
versions of stochastic feedback formulae for the optimal portfolio
and consumption choices are obtained as well.

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328

Grasselli, Matheus, (McMaster University)

**Calibration of Chaos Models for Interest Rates**

Authors: M. R. Grasselli and T. Tsujimoto

The Wiener chaos approach to interest rates was introduced a few years
ago by Hughston and Rafailidis as an axiomatic framework to model
positive interest rates, continuing a line of research started by
the seminal Flesaker and Hughston model and including the elegant
potential approach of Rogers and others. Apart from ensuring positivity,
one appealing feature of the chaotic approach is its hierarchical
way to introduce randomness into a model through different orders
of chaos expansions. We propose a systematic way to calibrate Wiener
chaos models to market data, and compare the performance of chaos
expansions of different orders with popular short rate models in the
presence of interest rate derivatives of increased complexity.

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329

Lyasoff, Andrew, (Boston Univ./School of Management)

**New Algorithm for Equilibrium Asset Pricing in Incomplete Financial
Markets**

Authors: Bernard Dumas and Andrew Lyasoff

We develop a method that allows one to compute incomplete-market equilibria
routinely for Markovian equilibria (when they exist). The main difficulty
that we overcome arises from the set of state variables. There are,
of course, exogenous state variables driving the economy but, in an
incomplete market, there are also endogenous state variables, which
introduce path dependence. We write on an event tree the system of
all .rst-order conditions of all times and states and solve recursively
for state prices, which are dual variables. We illustrate this "dual"
method and show its many practical advantages by means of several
examples.

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330

Espinosa, Gilles-Edouard, (Ecole Polytechnique)

**Optimal Investment Under Relative Performance Concerns **

Authors: GE Espinosa and Nizar Touzi

Since the works of Merton, the problem of optimal investment has been
widely studied in order to generalize the original framework. However
in all those works, the agent only takes into account his absolute
wealth, without any consideration with respect to his peers. We introduce
here interactions between N particular agents, the criterion for each
investor being a convex combination of his absolute wealth and of
the difference between his wealth and the average wealth of the others.
We study the existence and uniqueness of Nash equilibria in this context
and derive some economical implications.

http://www.megavideo.com/?d=YP6NB050

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331

Baurdoux, Erik, (LSE)

**The Shepp-Shiryaev stochastic game driven by a spectrally negative
Lévy process**

Authors: Erik Baurdoux and Andreas Kyprianou

In [2] a callable version of the Russian option (cf. [3]) was considered
driven by an exponential Brownian motion. We consider the same optimal
stopping game but driven by a spectrally negative Lévy process instead.
While the Russian option leads to reduced regret on the buyer's part,
the possibility for the seller to terminate the option leads to reduced
regret on the seller's part in case market conditions turn out to
be unfavorable. We make use of a mixture of techniques including fluctuation
theory and reduction of the stochastic game to an optimal stopping
problem. Based on joint work with Andreas Kyprianou (University of
Bath). References: [1] A.E. Kyprianou. Some calculations for Israeli
options. Finance and Stochastics, 2004 [2] L.A. Shepp and A.N. Shiryaev.
The Russian option: reduced regret. Ann. Appl. Probab., 1993.

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334

Kervarec, Magali, (Université d'Evry)

**Risk measure in non dominated models**

Authors: M. Kervarec

In this paper, we provide a framework in which we can set the problem
of risk measure, taking into account the model uncertainty and encompassing
the case of the UVM model. The uncertainty is specified by a family
of orthogonal martingale laws which is typically non-dominated. We
define coherent and convex risk measure in this framework, prove some
representations Theorem and give some examples for those kind of measures

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335

Lorig, Matthew, (University of California - Santa Barbara)

**Spectral Decomposition of Option Prices in Fast Mean-Reverting
Stochastic Volatility Models**

Authors: Matthew Lorig

Using spectral decomposition techniques and singular perturbation
theory, we develop a systematic method to price a variety of options
in a fast mean-reverting stochastic volatility setting. Four examples
are provided in order to demonstrate the versatility of our method.
These include: European options, up-and-out options, double-barrier
knock-out options, and options which pay a rebate upon hitting a boundary.

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336

Packham, Natalie, (Frankfurt School of Finance & Management)

**Correlation under stress in normal variance mixture models**

Authors: Michael Kalkbrener, Natalie Packham

We investigate correlations of asset returns in stress scenarios where
a common risk factor is truncated. Our analysis is performed in the
class of normal variance mixture (NVM) models, which encompasses many
distributions commonly used in financial modelling. For the special
cases of jointly normally and t-distributed asset returns we derive
closed formulas for the correlation under stress. For the NVM distribution,
we calculate the asymptotic limit of the correlation under stress,
which depends on whether the variables are in the maximum domain of
attraction of the Frechet or Gumbel distribution. It turns out that
correlations in heavy-tailed NVM models are less sensitive to stress
than in medium- or light-tailed models. Our analysis sheds light on
the suitability of this model class to serve as a quantitative framework
for stress testing, and as such provides important information for
risk and capital management in financial institutions, where NVM models
are frequently used for assessing capital adequacy.

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338

Lasak, Katarzyna, (Aarhus University)

**Maximum likelihood estimation of fractionally cointegrated systems**

Authors: Katarzyna Lasak

In this paper we consider a fractionally cointegrated error correction
model and investigate asymptotic properties of the maximum likelihood
(ML) estimators of the matrix of the cointegration relations, the
degree of fractional cointegration, the matrix of the speed of adjustment
to the equilibrium parameters, and the variance-covariance matrix
of the error term. We show that by using ML principles to estimate
jointly all parameters of the fractionally cointegrated system, consistent
estimates are obtained. Their asymptotic distributions are provided.
The cointegration matrix is asymptotically mixed normal distributed,
while the degree of fracional cointegration and the speed of adjustment
to the equilibrium matrix have a joint normal distribution, which
proves the intuition that the memory of the cointegrating residuals
affects the speed of convergence to the long-run equilibrium, but
does not have any influence on the long-run relationship. The rate
of convergence of the estimators of the long-run relationships depends
on the cointegration degree but it is optimal for the strong cointegration
case considered. We also prove that misspecification of the degree
of fractional cointegation does not affect the consistency of the
estimators of the cointegration relationships, although usual inference
rules are not valid. The findings are illustrated for finite samples
by Monte Carlo analysis. We also apply the developed methodology in
a study of the term structure of interest rates.

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345

Metzler, Adam, (University of Western Ontario)

**A Multiname First-Passage Model for Credit Risk**

Authors: Adam Metzler, Don L. McLeish

In multiname extensions of the seminal Black-Cox model, dependence
is typically introduced by correlating the Brownian motions driving
firm values. Despite its significant intuitive appeal such a framework
is simply not capable of describing market data. In this paper we
propose a novel multiname framework by altering the location of systematic
risk in the Black-Cox model. This is accomplished by introducing common
``systematic risk'' processes which govern the trend and volatility
in credit qualities. We are able to calibrate several versions of
the model to market quotes for CDX index tranches, including quotes
from the current distressed environment.

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347

Hamel, Andreas, (Princeton University)

**Duality for set-valued measures of risk**

Authors: Andreas Hamel, Frank Heyde

Extending previous approaches we define set-valued (convex) measures
of risk and their acceptance sets, and we give dual representation
theorems. Using primal and dual descriptions, we introduce new examples
for set-valued measures of risk, e.g. set-valued upper expectations,
Value at Risk, Average Value at Risk. Moreover, a link to super-hedging
prices for conical market models is given.

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349

Perez, Leonel, (CIMAT)

**On the dual problem associated to the robust utility maximization
in a market model driven by a Levy process**

Authors: Daniel Hernández-Hernández and Leonel Pérez-Hernández

We derive the dual value function for a robust utility maximization
problem subject to uncertainty in the beliefs. In order to achieve
this goal we characterize the set of absolutely continuous and equivalent
local martingale measures associated with a market model, which prices
are driven by an exogenous process, determined by an underlying Levy
process. The necessary tools to make the connection with robust measures
of risk are also developed.

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350

Li, Lingfei, (Northwestern University)

**Commodity Derivative Models with Mean-Reverting Jumps and Stochastic
Volatility: A Time Change Approach**

Authors: Lingfei Li, Vadim Linetsky

We propose a new class of commodity models with state-dependent mean-reverting
jumps and stochastic volatility by applying time changes to the classical
commodity models based on mean-reverting Ornstein-Uhlenbeck diffusion
processes. We obtain analytical solutions for commodity futures options
in terms of the eigenfunction expansion of the Ornstein-Uhlenbeck
transition semigroup and the Laplace transform of the time change.
The models are flexible enough to capture a wide variety of implied
volatility smile patterns observed in energy, metals, and agricultural
commodities futures options.

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351

Lee, Kyungsub, (KAIST)

**A GARCH Intensity Model for Asset Price and Its Application
to Option Pricing**

Authors: Geon Ho Choe

We introduce intensity models for asset price movement and adapt the
idea of GARCH to incorporate empirical features such as volatiliy
clustering, leverage effect and volatility smile. In the model the
frequencies of up and down movements of asset price in each time period
are assumed to have Poisson distributions, and corresponding intensities
are time varying. When applied to option pricing, our model yields
an explicit formula for equivalent martingale measures. We employ
maximum likelihood estimation to calibrate the parameters in GARCH
intensity model using S\&P 500 data.

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352

Cai, Ning, (The Hong Kong University of Science and Technology)

**Option Pricing under a Mixed-Exponential Jump Diffusion Model**

Authors: Ning Cai and S. G. Kou

We propose a jump diffusion model for asset prices whose jump sizes
are mixed-exponentially distributed. The mixed-exponential distribution
can approximate any distributions arbitrarily closely, including various
heavy tail distributions. We demonstrate the mixed-exponential jump
diffusion model (MEM) can lead to closed-form Laplace transforms of
option prices and deltas for lookback and barrier options, which can
be inverted easily via the Euler inversion algorithm. In addition,
an interesting numerical example is provided to illustrate that approximating
Merton's lognormal jump diffusion model with the MEMs may result in
accurate lookback and barrier option prices and deltas for Merton's
model.

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354

Badescu, Alex, (University of Calgary)

**Esscher Transforms and Consumption-Based Models**

Authors: Robert J. Elliott, Tak Kuen Siu

The Esscher transform is an important tool in actuarial science. Since
the pioneering work of Gerber and Shiu (1994), the use of the Esscher
transform for option valuation has also been investigated extensively.
However, the relationships between the asset pricing model based on
the Esscher transform and some fundamental equilibrium-based asset
pricing models, such as consumption-based models, have so far not
been well-explored. In this paper we attempt to bridge the gap between
consumption-based models and asset pricing models based on Esscher-type
transformations in a discrete-time setting. Based on certain assumptions
for the distributions of asset returns, changes in aggregate consumptions
and returns on the market portfolio, we construct pricing measures
that are consistent with those arising from Esscher-type transformations.
Explicit relationships between the market price of risk and the risk
preference parameters are derived for some particular cases.

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357

Faria, Gonçalo, (Fundação da Universidade do Porto, Faculdade
de Economia)

**Dynamic Consumption and Portfolio Choice with Ambiguity about
Stochastic Volatility**

Authors: Gonçalo Faria, João Correia-da-Silva, Cláudia Ribeiro

Ambiguity about stochastic variance of the risky asset's return is
introduced in a model for dynamic consumption and portfolio choice.
When investors are able to update their portfolio continuously, as
a function of the instantaneous variance, ambiguity has no impact.
When continuous portfolio updating is not possible, investors must
use their expectation of future variance for their portfolio decision.
In this scenario, we find that ambiguity may have a very significant
impact (in contrast with the low impact from variance risk). Stochastic
variance can therefore be very relevant for portfolio choice, essentially
due to investors' ambiguity about it.

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358

Wong, Hoi Ying, (Chinese University of Hong Kong)

**Mean-Variance Portfolio Selection of Co-Integrated Assets**

Authors: Mei Choi CHIU, Hoi Ying WONG

This paper considers the continuous-time mean-variance portfolio selection
problem in a financial market in which asset prices are co-integrated.
The asset price dynamics are then postulated as the diffusion limit
of the corresponding discrete-time error correction model of co-integrated
time series. The problem is completely solved in the sense that solutions
of the continuous-time portfolio policy and the efficient frontier
are obtained as explicit and closed-form formulas. The analytical
results are applied to pair trading using co-integration techniques.
Numerical examples show that identifying a co-integrated pair with
a high mean reversion rate can generate significant statistical arbitrage
profits once the current state of the economy sufficiently departs
from the long-term equilibrium. We propose an index to simultaneously
measure the departure level of a co-integrated pair to equilibrium
and the mean-reversion speed based on the mean-variance paradigm.

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359

Owari, Keita, (Hitotsubashi University)

**On the Duality for Robust Utility Maximizaiton with Unbounded
Random Endowment**

Authors: Keita Owari

We address the convex duality method for robust utility maximization
with random endowment. When the underlying price process is a locally
bounded semimartingale, we show that the fundamental duality equality
holds true for a wide class of utility functions and unbounded random
endowment. To obtain this duality, we prove a robust version of Rockafellar's
theorem on convex integral functionals in a sufficiently general situation.
The duality then follows from Fenchel's general duality theorem.

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362

Gruber, Peter, (Università della Svizzera Italiana)

**Three make a dynamic smile - unspanned skewness and interacting
volatility components in option valuation**

Authors: Peter H. Gruber, Claudio Tebaldi, Fabio Trojani

We propose a new modeling approach to option valuation, in which volatility
and skewness of returns are functions of three distinct, but dependent,
stochastic components. Two components modeling short and long run
volatility risk and a third component capturing shocks to return skewness
that are unspanned by shocks to volatility. The model state dynamics
follows a matrix jump diffusion and nests a number of existing affine
models. We estimate our model using S&P 500 index option data and
find that models with unspanned skewness components and dynamic interactions
provide better pricing performance and a more accurate description
of the joint dynamics of the implied volatility surface.

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364

Jacquier, Antoine, (Imperial College London)

**Implied volatility asymptotics of affine stochastic volatility
models with jumps**

Authors: Antoine Jacquier and Aleksandar Mijatovic

In this paper, we propose a unified approach for the implied volatility
asymptotic under the general class of affine stochastic volatility
models with jumps. Under mild conditions on the jump measures, we
derive semi-closed form formulae for the implied volatility as the
maturity gets large or small.

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365

Macrina, Andrea, (King's College London)

**Credit Risk, Market Sentiment and Randomly-Timed Default**

Authors: Dorje C. Brody, Lane P. Hughston, Andrea Macrina

We propose a credit model in which the default times of bonds are
assumed to be functions of one or more independent market factors.
Market participants have partial information about the market factors,
represented by the values of a set of information processes. The filtration
is generated jointly by the information processes and by the default
indicator processes of the bonds. The value of a discount bond is
the discounted expectation of the value of the default indicator function
at maturity, conditional on the information provided by the market
filtration. Explicit expressions are derived for bond price processes
and the associated default hazard rates. The latter are not given
a priori as part of the model but rather are deduced and shown to
be functions of the values of the information processes. Thus the
perceived hazard rates, based on the available information, determine
bond prices, and as perceptions change so do the prices.

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366

Cuchiero, Christa, (ETH Zürich)

**Affine processes on positive semidefinite matrices**

Authors: Christa Cuchiero, Damir Filipovic, Eberhard Mayerhofer, Josef
Teichmann

We study stochastically continuous affine processes on the cone of
positive semi-definite symmetric matrices. This analysis has been
motivated by a large and growing use of matrix-valued affine processes
in finance, including multi-asset option pricing with stochastic volatility
and correlation structures, and fixed-income models with stochastically
correlated risk factors. We completely characterize this class of
Markov processes through a detailed parameter specification of the
infinitesimal generator.

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369

Muromachi, Yukio, (Tokyo Metropolitan University)

**Yukio Muromachi**

Authors: An application of the implied copula model to the risk evaluation
of a portfolio

We propose a simple application of the implied copula model, proposed
by Hull and White (2006), to the risk evaluation of a portfolio. In
the implied copula model, the hazard rates of the entities have a
distribution, and the default times are conditionally independent.
Additionally we assume that the normalized hazard rates under the
risk neutral probability measure and the physical measure have the
same distribution. Then, the risk calculated by our model can reflect
the latent fear of the major market participants. We will show a practical
and simple example.

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373

Coculescu, Delia, (Swiss Banking Institute)

**From the decompositions of a stopping time to risk premium decompostions**

Authors: Delia Coculescu

We build a general model for pricing defaultable claims. In addition
to the usual absence of arbitrage assumption, we assume that one defaultable
asset (at least) looses value when the default occurs. We prove that
under this assumption, in some standard market filtrations, default
times are totally inaccessible stopping times; we therefore proceed
to a systematic construction of default times with particular emphasis
on totally inaccessible stopping times. This abstract mathematical
construction, reveals a very specific and useful way in which default
models can be built, using both market factors and idiosyncratic factors.
We then provide all the relevant characteristics of a default time
(i.e. the Az\'ema supermartingale and its Doob-Meyer decomposition)
given the information about these factors. We also provide explicit
formulas for the prices of defaultable claims and analyze the risk
premiums that form in the market in anticipation of losses which occur
at the default event. The usual reduced-form framework is extended
in order to include possible economic shocks, in particular jumps
of the recovery process at the default time. This formulas are not
classic and we point out that the knowledge of the default compensator
or the intensity process is not anymore a sufficient quantity for
finding explicit prices, but we need indeed the Az\'ema supermartingale
and its Doob-Meyer decomposition.

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376

Fabre, Emilie, (Ecole Polytechnique)

**Optimal Liquidation of an Indivisible Asset with Independant
Investment**

Authors: Emilie Fabre and Nizar Touzi

We consider a portfolio which contains, among other assets, one unit
of an asset known at any dates but which can only be sold at a convenient
stopping time. This asset participates to the optimization problem
but can not be hedged by the market. The aim of the agent is to maximize
the expected utility of total wealth at the sell time. We obtain by
dynamic programming equation the value function then we construct
the optimal strategy and sell time. Our results show that this mixed
investment/sale problem involves an original concavity structure and
a pure jump strategy process.

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378

Herzel, Stefano, (University of Rome "Tor Vergata")

**Evaluating Discrete Dynamic Strategies in Affine Models**

Authors: Flavio Angelini, Stefano Herzel

We consider the problem of measuring the performance of a dynamic
strategy, re-balanced at a discrete set of dates, whose objective
is that of replicating a claim in an incomplete market driven by a
general multi-dimensional affine process. Our purpose is to propose
a method to efficiently compute the expected value and variance of
the hedging error of the strategy. Representing the payoff of the
claim as an inverse Laplace transform, we are able to get semi-explicit
formulas for strategies satisfying a certain property. The result
is quite general and can be applied to a very rich class of models
and strategies, including Delta hedging. We provide illustrations
for the cases of interest rate models and Heston's stochastic volatility
model.

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379

Werner, Ralf, (Hochschule München)

**Comparison and robustification of Bayes and Black-Litterman
models**

Authors: Schöttle, Werner, Zagst

For determining an optimal portfolio allocation, parameters representing
the underlying market - characterized by expected asset returns and
the covariance matrix - are needed. Traditionally, these point estimates
for the parameters are obtained from historical data samples, but
often approaches to combine sample information and experts' views
are sought for. The focus of this presentation is on the two most
popular of these frameworks - the Black-Litterman model and the Bayes
approach. We will show that the Black-Litterman is just a special
case of the Bayes approach. In contrast to this, we will show that
the extensions of both models to the robust portfolio framework yield
two rather different robustified optimization problems.

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381

Xia, Lihong, (University of North Carolina at Charlotte)

**On ?-Quantile Dependent Convex Risk Measures**

Authors: Lihong Xia, Mingxin Xu

In this paper we will observe a class of convex measures of risk whose
values depend on the random variable only up to the ?-quantile for
some given constant ? in the interval (0,1]. For this class of convex
risk measures, the assumption of the Fatou property can be weakened
and we provide the robust representation theorem via convex duality
method. As an example, Weighted Value-of-Risk, which includes Value-at-Risk
and Conditional Value-at-Risk as special cases, will be discussed.
The ?-quantile uniform preference (?-quantile second order stochastic
dominance) of two probability distribution measures will be defined
to describe the set of probability measures that represents the Weighted
Value-of-Risk in the ?-quantile dependent case.

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384

Tashiro, Yusuke, (University of Tokyo)

**Dual Pricing of Swing Options with Bang-bang Control**

Authors: Yusuke Tashiro

A dual approach for pricing options gives an upper bound of the true
value. However, for swing options with bang-bang control, it is difficult
to directly apply existing duality methods, because the pricing problem
includes the decision of buying or selling. We decompose the price
of swing options into the sum of second-order differences of the price,
and show that the sum of single stopping problems corresponding to
the second-order differences provides an upper bound for the price.
A numerical example indicates that our method gives an appropriate
upper bound for the price of swing options.

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385

Jaimungal, Sebastian, (University of Toronto)

**Ambiguity Aversion in Real Options**

Authors:

Real option valuation has traditionally been concerned with investment
under project value uncertainty while assuming the agent has perfect
confidence in a specific model. However, agents do not generally have
perfect confidence in their model and this model uncertainty affects
their decisions. In this work, we introduce a simple model for real
option valuation to account for the agent's aversion to model ambiguity
through the notation of robust indifference prices. We derive analytical
results for the perpetual option to invest and the linear complementarity
problem that the finite time problem satisfies.

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388

Herbertsson, Alexander, (University of Gothenburg)

**Pricing index-CDS options in a nonlinear filtering model**

Authors: Alexander Herbertsson and RÃ¼diger Frey

We derive practical formulas for forward starting index-CDS spreads
in the filtering model of Frey & Schmidt 09. We also outline a novel
approach for estimating the parameters in the filtering models by
using time-series data of index-CDS spreads and classical maximum-likelihood
algorithms. The calibration-approach incorporates the Kushner-Stratonovich
SDE for the dynamics of the filtering probabilities. The convenient
formula for the forward starting index-CDS is a prerequisite for our
estimation algorithm. Furthermore, a systematic study is performed
in order to understand the impact of various model parameters on credit
index options (and on the index itself).

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390

Golbeck, Steven, (Northwestern University)

**Asset Financing with Default Risk**

Authors: Steven Golbeck and Vadim Linetsky

We develop a stochastic model for assets of depreciating value that
generate a service flow over the course of a finite useful lifetime.
We give particular attention to financial transactions, including
loans, leases, forward contracts and securitization vehicles, which
are collateralized by aircraft, and calibrate the stochastic model
to a time series of aircraft current market value appraisals. The
concept of a Risk-Adjusted Residual Value Curve (RA-RVC) is introduced
as an illustration of how the expected depreciation of the asset is
faster under the risk-neutral $\mathbb{Q}$ -measure compared to under
the physical $\mathbb{P}$-measure. Investors interested in financial
assets collateralized by the aircraft require a risk-premium as compensation
for taking on the risks associated with not only the credit-worthiness
of the counterparty, in this case the airline, but also for the collateral
price risk due to depreciation and market volatility as well as the
risk of incurring transaction, repair and remarketing costs in the
event of the counterparty default. This risk-premium is introduced
through a change of measure from the $\mathbb{P}$ to the $\mathbb{Q}$
-measure, and then is shown to be the prime component of the faster
rate of depreciation observed in the RA-RVC. Thus, the Risk-Adjusted
Residual Value Curve, a tool used by practioners, is seen to be perfectly
consistent with modern asset pricing theory.

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391

Pommier, David, (Ecole des Ponts ParisTech)

**About equity models based on Independent Increment processes**

Authors: F.Russo D.Pommier

This paper provides a new approach for financial applications based
on the use of the Independent Increments (II) or Additive Process
for the pricing, hedging. We study the properties of the characteristic
exponent, well-known for Levy processes, associated to the II process.
In the first part we discuss about the pricing and hedging problem.
In the second part, we will be interested in the computation of prices
by numerical methods. We give a complete characterization of the corresponding
partial-integro differential equation (PIDE) in term of weak formulation.
We prove existence and uniqueness for this equation. Then we introduce
a new approach based on Galerkin methods. This approach is close to
classical Finite Difference method, so many tools based on PDE formulation
can be generalized to the II process. The independent increments property
guarantees a toeplitz form for the rigidity matrix in the Galerkin
method.

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394

Robertson, Scott, (Carnegie Mellon University)

**Sample Path Large Deviations and Optimal Importance Sampling
for Stochastic Volatility Models**

Authors: Scott Robertson

Sample path Large Deviation Principles (LDP) of the Freidlin-Wentzell
type are derived for a class of diffusions which govern the price
dynamics in common stochastic volatility models from Mathematical
Finance, including the models of Heston and Hull and White. Using
the sample path LDP for the Heston model, the problem is considered
of selecting an importance sampling change of drift, for both the
price and the volatility, which minimize the variance of Monte Carlo
estimators for path dependent option prices. The case of the arithmetic
average Asian put option is solved in detail.

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398

Tsukahara, Hideatsu, (Seijo University)

**Comparative Analysis of VaR and Some Distortion Risk Measures**

Authors: Hideatsu Tsukahara

Several families of distortion risk measures has been proposed in
the literature, and we will give a conprehensive comparative study
of these families as an attempt to understand the main features of
each family. Comparison will be made in terms of statistical estimation
and simulation, backtesting procedures, and capital allocation, emphasizing
numerical aspects.

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400

Emmerling, Thomas, (University of Michigan)

**Perpetual Cancellable American Call Option**

Authors: Thomas J. Emmerling

We examine the valuation of a generalized American-style option known
as a Game-style call option in an infinite time horizon setting. The
specifications of this contract allow the writer to terminate the
call option at any point in time for a fixed penaltyamount paid directly
to the holder. Valuation of a perpetual Game-style put option was
addressed by Kyprianou (2004) in a Black-Scholes setting on a non-dividend
paying asset. We undertake a similar analysis for the perpetual call
option in the presence of dividends and find qualitatively different
explicit representations for the value function depending on the relationship
between the interest rate and dividend yield. Specifically, we find
that the value function is not convex when $r>d$. Numerical results
show the impact this phenomenon has upon the vega of the option.

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402

Cox, Alexander, (University of Bath)

**Robust pricing and hedging of options on variance**

Authors: Alexander M G Cox, Jiajie Wang

Recent work of Dupire [2005] and Carr and Lee [2010] has emphasised
the importance of understanding the Skorokhod embedding originally
proposed by Root [1969] for applications in the model-free hedging
of variance options. Root's work shows that there exists a barrier
from which one may define a stopping time which solves the Skorokhod
embedding problem. This construction has the remarkable property,
proved by Rost [1976], that it minimises the variance of the stopping
time among all solutions. In the financial setting, this construction
should give rise to a lower bound on the price of a call on the variance
given the prices of call options on the underlying at the same maturity.
Unfortunately, the results of Root [1969] and Rost [1976] are not
explicit, and so calculating the correct pricing and hedging bounds
is not explicit from their results. In this work, we prove that Root's
problem is equivalent to a free-boundary problem given by Dupire [2005],
and give a novel proof of the optimality of the construction, which
gives in turn allows us to derive the optimal sub-hedging strategy.

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403

Kaila, Ruth, (Aalto University)

**The integrated correlated variance as a statistical inverse
problem**

Authors:

We consider the inverse problem of integrated variance when the stock
price and volatility processes are correlated. Instead of regularization,
we apply a Bayesian approach to this ill-posed inverse problem. We
show how the integrated correlated variance can be estimated from
option prices by means of statistical inference and marginalization.
We use a stripe of option prices, very general prior assumptions,
and a hyperprior, defined by the data, to fit the skewness of the
density. We obtain estimates of the density of interest and of its
moments, as well as information on the reliability of these estimates.

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404

Mohamed, Mrad, (Ecole Polytechnique)

**An Exact Connection between two Solvable SDEs and a Non Linear
Utility Stochastic PDEs**

Authors: Nicole El Karoui ; Mohamed M'Rad

The paper proposes a new approach to consistent stochastic utilities,
also called forward dynamic utility, recently introduced by M. Musiela
and T. Zariphopoulou. These utilities satisfy a property of consistency
with a given incomplete financial market which gives them properties
similar to the function values of classical portfolio optimization.
First, we derive a non linear stochastic PDEs that satisfy consistent
stochastic utilities processes of Itô type and their dual convex conjugates.
Then, under some assumptions of regularity and monotony on the stochastic
flow associated with the optimal wealth as function of the initial
capital, and on the optimal state price dual process, we characterize
all consistent utilities for a given increasing optimal wealth process
from the composition of the dual optimal process and the inverse of
the optimal wealth. This allows us to reduce the resolution of fully
nonlinear second order utility SPDE to the existence of monotone solutions
of two stochastic differential equations. We also, express the volatility
of consistent utilities as an operator of the first and the second
order derivatives of the utility in terms of the optimal primal and
dual policies.

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405

Hoyle, Edward, (Imperial College London)

**Stable-1/2 Bridges and Insurance: a Bayesian approach to non-life
reserving**

Authors: E. Hoyle, L.P. Hughston and A. Macrina

We develop a non-life reserving model using a stable-1/2 random bridge
to model the accumulation of paid claims. This allows for an arbitrary
choice of \emph{a priori} distribution (on the positive half-line)
for the ultimate loss. Taking a Bayesian approach to the reserving
problem, we derive the process of conditional distribution functions
for the ultimate loss. The `best-estimate ultimate loss process' is
given by the conditional expectation of the ultimate loss, and is
a martingale. We derive explicit expressions for the best estimate
ultimate loss process, and for expected recoveries arising from aggregate
excess-of-loss reinsurance treaties. Use of a deterministic time-change
allows for the matching of any initial (increasing) development pattern
for the paid-claims. We show that these methods are well-suited to
the modelling of claims where there is a non-trivial probability of
catastrophic loss. The generalized inverse Gaussian (GIG) distribution
is shown to be a natural choice for the \emph{a priori} ultimate loss
distribution. Indeed, for particular parameter choices of the GIG
distribution, the best-estimate ultimate loss process can be written
as a rational function of the paid-claim process. We extend the original
model to include a second paid-claim process, and allow the two paid-claim
processes to be dependent. The results we obtain can be applied to
the modelling of multiple lines of business or multiple origin years.
The multidimensional model we present has the attractive property
that the dimensionality of calculations remains low, regardless of
the number of paid-claims processes under consideration. We also provide
algorithms for the simulation of the paid-claim processes.

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407

Ferrando, Sebastian (Olivares, Pablo), (Ryerson University)

**Non-Probabilistic Hedging and Pricing. Applications to Probabilistic
Models**

Authors: Alexander Alvarez, Sebastian Ferrando, Pablo Olivares

The paper studies several aspects of a non-probabilistic approach
to hedging and pricing. In order to illustrate some of the differences
with the classical probabilistic approach, we use our setup to derive
new hedging and pricing results in probabilistic models. Besides dealing
with classes of continuous paths, we also incorporate jumps; for some
of our deterministic classes this leads to incompleteness and, in
order to achieve perfect replication of options in such a setting,
we allow hedging with options to take place. In this setup, our results
provide a path-wise and discrete approach, with explicit expressions
for the hedging portfolio, to a result of Mancini on perfect hedging
with European calls in a Poisson-Gaussian model.

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408

Grbac, Zorana, (University of Freiburg)

**Rating based Lévy Libor model**

Authors: Ernst Eberlein, Zorana Grbac

In this work we consider modeling of credit risk within the Libor
market models. We extend the classical definition of the default-free
forward Libor rate to defaultable bonds with credit ratings and develop
the rating based Libor market model. We use time-inhomogeneous Lévy
processes to model the dynamics of the default-free and the pre-default
term structure of Libor rates. Credit migration is modeled by a conditional
Markov process with finite state space, constructed in a doubly stochastic
setting. We show that its properties are preserved under all forward
Libor measures. Conditions for absence of arbitrage in the model are
derived and valuation formulae for some common credit derivatives
in this setup are presented.

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409

Reisinger, Christoph, (Oxford University)

**Calibrating Financial Models Using Consistent Bayesian Estimators**

Authors: Alok Gupta and Christoph Reisinger

We consider a general calibration problem for derivative pricing models.
We reformulate the problem into a Bayesian framework to attain posterior
distributions for calibration parameters. We give conditions on the
value function under which the corresponding Bayesian estimator is
consistent. Finally we apply our results to a discrete local volatility
model and work through numerical examples to clarify the construction
of Bayesian posteriors and its uses.

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410

Surkov, Vladimir, (The Fields Institute for Research in Mathematical
Science)

**Efficient Construction of Robust Hedging Strategies under Jump
Models**

Authors: Matt Davison and Vladimir Surkov

Markets where asset prices follow processes with jumps are incomplete
and any portfolio hedging against large movements in the price of
the underlying asset must include other instruments. This paper generalizes
the approach of minimizing the price variance of the hedging portfolio
to include minimization of the Greeks variances as well. The new approach
yields improved hedging portfolios over long horizons and for non-stationary
model parameters. From the computational perspective, this paper develops
a new Fourier transform-based numerical method for computing the Greeks
of European options with arbitrary payoffs. The new computational
method allows to rapidly compute the hedging portfolio weights of
the generalized hedging approach.

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412

Sabanis, Sotirios, (University of Edinburgh)

**A class of stochastic volatility models and the q-optimal martingale
measure**

Authors: Sotirios Sabanis

This paper proposes a framework under which the q-optimal martingale
measure, for the case where continuous processes describe the evolution
of asset price and its stochastic volatility, exists for all finite
time horizons. More precisely, it is assumed that while the ``mean-variance
trade-off process" is uniformly bounded, volatility and asset are
imperfectly correlated. As a result, under some regularity conditions
for the parameters of the corresponding Cauchy problem, one obtains
that the $q$th moment of the corresponding Radon-Nikodym derivative
does not explode in finite time.

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414

Liebmann, Thomas, (Ulm University)

**When are path-dependent payoffs suboptimal?**

Authors: Stefan Kassberger, Thomas Liebmann

We discuss when risk-averse investors with fixed planning horizon
prefer path-independent payoffs. The answer is not tied to a specific
type of model for the underlying or knowledge of the investor's utility
function, but to the pricing kernel. If we assume that the pricing
kernel is a function of the underlyingÂ's price at the end of the
planning horizon, every path-dependent payoff can be replaced by a
more attractive path-independent alternative. Moreover, if the pricing
kernel is a decreasing function of the underlying, increasing payoff
functions are preferred.

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416

Gapeev, Pavel, (London School of Economics)

**Pricing of perpetual American options in a model with partial
information**

Authors: Pavel Gapeev

We present a solution to the perpetual American call option pricing
problem in a model of a financial market in which the dividend rate
of a risky asset switches between two constant values at the times
at which certain unobservable external events occur. The asset price
dynamics are described by a geometric Brownian motion with random
drift rate modeled by a continuous time Markov chain with two states.
The optimal time of exercise is found as the first time at which the
asset price hits a stochastic boundary depending on the current state
of the filtering dividend rate estimate. The proof is based on embedding
of the initial problem into a two-dimensional optimal stopping problem
and the analysis of the associated parabolic-type free-boundary problem.
We also provide several closed form estimates for the rational option
value and optimal exercise boundary.

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417

Wunderlich, Ralf, (Zwickau University of Applied Sciences)

**Portfolio optimization under partial information with expert
opinions**

Authors: Ralf Wunderlich, Rüdiger Frey and Abdelali Gabih

We investigate optimal portfolio strategies for utility maximizing
investors in a market with an unobservable drift which is modelled
by finite-state Markov chain. Information on the drift is obtained
from the observation of stock prices. Furthermore, expert opinions
are incorporated. They are modelled by a marked point process with
jump-size distribution depending on the current state of the hidden
Markov chain. Using nonlinear filters the problem is transformed into
a completely observable problem. For power utility the associated
Hamilton-Jacobi-Bellman equation is derived. We adopt a policy improvement
method to obtain an approximation of the optimal strategy.

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418

Veerman, Enno, (University of Amsterdam)

**Affine diffusions with non-canonical state space**

Authors: Peter Spreij, Enno Veerman

Multidimensional affine diffusions have been studied in detail for
the case of a canonical state space. We extend known results for canonical
to general state spaces. In particular we validate the exponential
affine formula for exponential moments for general affine diffusions
by proving the martingale property of an exponential local martingale,
using existence and uniqueness of strong solutions to the associated
stochastic differential equations. Next we present a complete characterization
of all possible affine diffusions with polyhedral and quadratic state
space. We give necessary and sufficient conditions on the behavior
of drift and diffusion on the boundary of the state space in order
to obtain invariance and to prove strong existence and uniqueness.

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419

Dang, Duy Minh, (University of Toronto)

**GPU Pricing of Cross-Currency Interest Rate Derivatives under
a FX Volatility Skew Model**

Authors: Duy Minh Dang, Christina C. Christara, Kenneth R. Jackson

We present a GPU parallelization of the computation of exotic cross-currency
interest rate derivatives, namely Bermudan cancelable Power Reverse
Dual Currency (PRDC) swaps. We consider a three-factor pricing model
with FX volatility skew which results in a 3-D time-dependent parabolic
PDE. Uniform finite difference methods and the ADI technique are employed
for the space and time discretization of the PDE, respectively. Over
each period of the tenor structure, we divide the pricing of a Bermudan
cancelable PRDC swap into two independent pricing subproblems, each
of which can efficiently be solved on a GPU via a parallelization
of the ADI technique. Numerical results showing the efficiency of
the parallel methods and a discussion of the impact of the FX skew
are provided.

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421

Feng, Liming, (University of Illinois at Urbana-Champaign)

**Pricing Bermudan Options in Levy Process Models**

Authors: Liming Feng, Xiong Lin

This paper presents a Hilbert transform method for pricing Bermudan
style vanilla, knock-out barrier and floating strike lookback options
in Levy process models. The corresponding optimal stopping problem
is reduced to a backward induction that involves taking Hilbert transforms
of certain analytic functions or integrating such functions. The Hilbert
transforms and integrals can be discretized using very simple schemes.
The resulting discrete approximation can be efficiently implemented
using the fast Fourier transform. The computational cost is linear
in the number of monitoring times, and O(Mlog(M)) in the number of
points used to approximate the Hilbert transforms and integrals. The
method is very accurate. The pricing error decays exponentially in
terms of the computational cost M for many popular Levy process models.
The early exercise boundary is obtained as a by-product.

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426

Kupper, Michael, (Humboldt University Berlin)

**Risk Preferences and their Robust Representation**

Authors: Samuel Drapeau and Michael Kupper

Due to the plurality of interpretations of risk, we concentrate on
context invariant features related to this notion: diversification
and monotonicity. We define and study general properties of three
key concepts, risk order, risk measure and risk acceptance family
and their one-to-one relations. Our main result is a uniquely characterized
dual robust representation of lower semi continuous risk orders. We
then illustrate this approach in different settings. In the setup
of random variables, where risk perception can be interpreted as a
model risk, we give a robust representation for numerous risk measures:
various certainty equivalents, or a general version of Aumann and
Serrano's economic index. It is based on joint work with Samuel Drapeau.

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427

Mendoza-Arriaga, Rafael, (The University of Texas at Austin)

**Modeling Default Correlation and Clustering: A Multivariate
Time Change Approach**

Authors: Vadim Linetsky and Rafael Mendoza-Arriaga

We present a reduced-form modeling framework that provides far reaching
extensions of the multivariate intensity. This can be viewed as a
multivariate stochastic time-change of the multivariate intensity
framework. The integrated default hazard processes are time-changed
with an n-dimensional subordinator so that the resulting default hazard
processes are processes with jumps. Having jumps in default hazard
processes allows us to model simultaneous defaults and default clustering.
We extend the application of multivariate subordination to general
Markov processes. We obtain analytical solutions for the joint multivariate
distribution of default times, the distribution of portfolio losses,
and the value of credit derivatives.

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430

Drapeau, Samuel, (Humboldt University Berlin)

**Risk Preferences: Further Developments beyond Random Variables**

Authors: Samuel Drapeau Michael Kupper

In a recent work, we defined risk preferences by the core characteristics
of diversification and monotonicity, aside any commitment to some
or other settings. Since this notion for random variables, which can
be interpreted as model risk, is quite understood, we address here
other underlying. For the setting of lotteries (probability distributions),
the risk will be interpreted as a distributional risk, and we illustrate
the robust representation there by the Value@Risk which is on this
setting (not on random variables) a risk measure. We further provide
automatic continuity results due to monotonicity. On the setting of
consumption streams where risk will be interpreted as discounting
risk, we show an explicit dual representation of the intertemporal
utility functional of Hindy, Huang and Kreps. We end with the setting
of stochastic kernels which allow us to explicit the interplay between
model risk and distributional risk. We illustrate their use in the
context of long term contracts depending on the temperature evolution.

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431

Sarais, Gabriele, (Imperial College)

**Inflation-Linked pricing in the Presence of a Central Bank Reaction
Function**

Authors: Lane P. Hughston, Gabriele Sarais

We propose a pricing model for inflation-linked derivatives based
on the premise that, to be successful, an inflation model has to take
into account the central bank reaction function to explain the co-movement
of interest rates and inflation. To achieve this, we adapt elements
of a mainstream macroeconomic model (the DSGE model with a Taylor
rule) and price derivatives in a no-arbitrage setting. We formally
prove that the no-arbitrage conditions hold in the inflation market
and verify that the chosen macroeconomic model dynamics are consistent
with the no-arbitrage framework. The proposed approach is more ambitious
than those currently most used in the industry (i.e. the Jarrow-Yildirim
and the BGM-I modelling strategies) since the co-movement of interest
rates and inflation is not taken as a given in our approach but is
the result of central bank policy. We propose a parsimonious strategy
to calibrate the model to nominal interest rates, inflation term structures
and smiles. We calibrate the model to recent market data and show
that the calibration scheme is satisfactory.

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433

López Cabrera, Brenda, (Humboldt University)

**Localizing temperature residuals**

Authors: Brenda López Cabrera, Wolfgang Karl Härdle, Weining Wang

On the temperature derivative market, modeling temperature volatility
is an important issue for pricing and hedging. In order to apply financial
mathematics, one needs to isolate a Gaussian risk factor. A conventional
model for temperature dynamics is a stochastic model with seasonality
and inter temporal autocorrelation. Empirical work based on seasonality
and autocorrelation correction reveals that the obtained residuals
are heteroscedastic with a periodic pattern. The object of this research
is to estimate this heteroscedastic function so that after scale normalization
a pure standardized Gaussian variable appears. Earlier work investigated
this temperature risk in different locations and showed that neither
parametric component functions nor a local linear smoother with constant
smoothing parameter are flexible enough to generally describe the
volatility process well. Therefore, in this paper, we consider a local
adaptive modeling approach to find at each time point, an optimal
smoothing parameter to locally estimate the volatility. Our approach
provides a more flexible and accurate fitting procedure of temperature
volatility processes by achieving excellent normal risk factors.

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434

Xie, Jiayao, (University of Leicester)

**Fast Pricing of Out-of-The-Money Options under Levy Processes**

Authors: Sergei Levendorskii, Jiayao Xie

FFT method, a standard tool for pricing options, produces large errors
in many situations, such as pricing deep OTM options. We propose a
fast and accurate method, which explicitly controls the error. For
one strike, the speed is hundreds times faster than FFT; and if prices
for many strikes are needed, our method, together with the quadratic
interpolation, is still faster and more accurate than FFT and the
refined and enhanced versions of FFT suggested recently by Boyarchenko
and Levendorski\v{i}. The method is applicable to NIG, VG, and KoBoL
(CGMY including) in finite variation case.

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435

Cosma, Antonio, (Université du Luxembourg)

**Valuing options using fast recursive projections**

Authors: Antonio Cosma, Stefano Galluccio, Olivier Scaillet

This paper introduces a new numerical option pricing method by fast
recursive projections. The projection step consists in representing
the pay- off with a fast discrete transform based on a simple grid
sampling. The recursive step consists in transmitting coefficients
of the representation from one date to the previous one by an explicit
recursion formula. Numerical illustrations with different Bermudan
payoffs and on dividend paying stocks in the Black-Scholes and Heston
models show that the method is fast, accurate, and general.

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438

Levental, Shlomo, (Michigan State University)

**The Continuous-Time Principal-Agent Problem with Moral Hazard
and Recursive Preferences**

Authors: Mark Schroder, Sumit Sinha and Shlomo Levental

We study the principal-agent problem with moral hazard in a continuous-time
Brownian filtration with recursive preferences on the part of both
principal and agent, and pay over the lifetime of the contract. Previous
work has considered only additive utility, which, as is well known,
arbitrarily links intertemporal substitution and risk aversion. Yet
time-additivity offers essentially no advantage in tractability because
agent optimality induces recursivity to the principal's preferences
even in the additive case. We show that the (necessary and sufficient)
first-order conditions for the principal's problem take the form of
a forward-backward stochastic differential equation. If the agent's
first-order condition satisfies an invertibility condition, the principal's
problem can be rewritten with the agent's utility satisfying a forward
equation. The problem then becomes analogous to the optimal portfolio/consumption
problem. Under translation-invariant preferences (a class that includes
time-additive exponential utility) or scale-invariant (homothetic)
preferences, the system uncouples and dramatically simplifies to the
solution of a single backward stochastic differential equation. We
obtain closed-form solutions for some parametric examples, including
one with constant cash flow volatility and subjective beliefs that
differ between principal and agent, and another with square-root cash-flow
dynamics. Linear sharing rules are obtained only under very special
conditions.

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439

Kang, Lening, (Michigan State University)

**Optimal Contracting and Nash Equilibria in the Continuous-Time
Principal-Agent problem with Multiple Principles**

Authors: Mark Schroder, Lening Kang, Shlomo Levental

We study the principal-agent problem with moral hazard in continuous
time with a Brownian filtration, recursive preferences, and multiple
principals (one agent for each principal). The innovations in our
paper are to allow for multiple principals (which can also be interpreted
as competing firms), each employing their own agent, and to allow
for more general preferences. Recursive preferences are essentially
as tractable as additive utility because the agency problem induces
recursivity in the principal's utility even in the time-additive case.
Furthermore, recursive preferences allow more flexible modelling of
risk aversion. We express each principal's solution as a forward backward
stochastic differential equation and then find a Nash equilibrium
among the principals. The resulting solution is also a Nash equilibrium
among the agents. This provides a general framework for examining
the impact of competition or collusion on optimal contracts.

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441

Hughston, Lane, (Imperial College)

**Implied Density Models for Asset Pricing**

Authors: Damir Filipovic, Lane Hughston and Andrea Macrina

We model the dynamics of asset prices by consideration of the conditional
probability density process for the value of an asset at some specified
time in the future. We derive a master equation for the dynamics of
the conditional probability density, and express this equation in
integral form. By a model for the density we mean a solution to the
master equation with a specification of the initial density and the
volatility structure for the density, which is assumed at any given
time and for each value of the argument of the density to take the
form of a functional that depends on the history of density. In practice
one specifies the functional modulo sufficient parametric freedom
to allow for the input of additional option data. Various specific
examples are studied in detail, with exact solutions in some cases.

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**442**

**Murgoci, Agatha** (Copenhagen Business School)

Authors::Tomas Björk; Agatha Murgoci; Xunyu Zhou

**Mean Variance Optimization with State Dependent Risk Aversion**

The object of this paper is to study the mean variance portfolio
op- timization in continuous time. Since this problem is time inconsistent
we attack it by placing the problem within a game theoretic framework
and look for subgame perfect Nash equilibrium strategies. This particular
problem has already been studied in Basak-Chabakauri(2009) where the
Authors: assumed a constant risk aversion parameter. This assumption
leads to an equilibrium control where the dollar amount invested in
the risky asset is independent of current wealth, and we argue that
this result is unrealistic from an economic point of view. In order
to have a more realistic model we instead study the case when the
risk aversion is allowed

to depend dynamically on current wealth. This is a substantially more
complicated problem than the one with constant risk aversion but,
using the general theory of time inconsistent control developed in
Björk-Murgoci (2008), we provide a fairly detalied anaysis on
the general case. We also study the particular case when the risk
aversion is inversely proportional to wealth, and for this case we
provide an analytic solution where the equilibrium dollar amount invested
in the risky asset is proportional to current wealth. The equilibrium
for this model is thus much more realistic than the one for the model
with constant risk aversion.

444

Lacerda, Ana, (Banco de Portugal)

**Credit Risk and Capital Requirements under Basel II**

Authors: Ana Lacerda ; Paula Antão

This work studies the hypothesis of lower capitalization of banks
under the rules defined in Basel II. In this sense, an assessment
of the impact of Basel II rules on the capital requirements for non-financial
firms' credit risk is performed. A comparison of capital requirements
under Basel I and Basel II is presented and intervals of variation
for the risk drivers such that capital requirements under Basel II
exceed capital requirements under Basel I are established. Data for
a European country supports the hypothesis of a smaller capitalization
of banks under Basel II, as far as credit risk in concerned.

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446

Han, CH Sean, (National Tsing-Hua University)

**An improved procedure for VaR/CVaR estimation under stochastic
volatility models**

Authors: C.-H. Han, W.-H. Liu, T.-Y. Chen

This paper proposes an improved procedure for stochastic volatility
model estimation with an application in risk management. This procedure
is composed of the following instrumental components: Fourier transform
method for volatility estimation with a price correction scheme, and
importance sampling for extreme event probability estimation with
applications to estimation of value-at-risk and conditional value-at-risk.
Then we conduct a value-at-risk backtesting for some foreign exchange
data and the S&P 500 index data. In comparison with empirical results
obtained from RiskMetrics, historical simulation, and the GARCH(1,1)
model, we find that our improved procedure outperforms on average.

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449

Zubelli, Jorge, (IMPA)

**A Convex-Regularization Framework for Local-Volatility Calibration
in Derivative Markets: The Connection with Convex Risk Measures and
Exponential Families**

Authors: Jorge P. Zubelli, Otmar Scherzer and Adriano De Cezaro

We present a unified framework for the calibration of local volatility
models that makes use of recent tools of convex regularization of
ill-posed Inverse Problems. The unique aspect of the present approach
is that it address in a general and rigorous way the key issue of
convergence and sensitivity of the regularized solution when the noise
level of the observed prices goes to zero. In particular, we present
convergence results that include convergence rates with respect to
noise level in fairly general contexts and go well beyond the classical
quadratic regularization.

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**451**

**Boyarchenko, Mitya **(University of Michigan)

*Carr-Wiener-Hopf method and refined fast Fourier transforms
for pricing *

barrier options

Authors:: Mitya Boyarchenko, Svetlana Boyarchenko, Sergei
Levendorskii

We present an overview of a general option pricing technique based
on Carr's randomization combined with the operator form of the Wiener-Hopf
factorization method developed by the second two Authors:. The practical
implementation of our method involves fast Fourier transforms, and
we use two techniques for improving its speed and accuracy: the finite
element

method (introduced in option pricing by Eydeland) and the "refined
FFT." We will explain how all these ideas combine to yield fast
and accurate algorithms for pricing barrier options in Levy models
and regime-switching Levy models.

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452

Kassberger, Stefan, (Ulm University)

**Importance sampling and Monte Carlo-based calibration for time-changed
Lévy processes**

Authors: Stefan Kassberger, Thomas Liebmann

We consider the use of structure preserving measure transforms for
the Monte Carlo simulation of subordinated Lévy processes. Applying
Esscher transforms to the subordinator and the subordinated process
separately provides additional flexibility in a variety of different
applications. Typical applications include variance reduction via
importance sampling, calculating sensitivities to model parameters
via likelihood ratios, but also modifying process parameters while
keeping the same set of paths.

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**454**

**Chellaboina, Vijaysekhar** (Tata Consultancy Services)

*Discrete-Time, Minimum-Variance Hedging of European Contingent
Claims*

Authors:Sanjay Bhat, Vijaysekhar Chellaboina, and Anil Bhatia

This paper addresses minimum-variance hedging of European contingent
claims (ECC) in the case where changes to the hedging portfolio can
be made only at discrete, pre-decided times. A simple derivation of
the minimum-variance hedging strategy is first given in a general
setting. The strategy is then applied to a general class of European
contingent claims written on an underlying asset whose price process
is a martingale modeled by a geometric Brownian motion. A Wiener space
setting is used to show that the minimum-variance strategy requires
the asset holding to equal the ratio of conditional expectations of
the changes in the ECC payoff and the underlying asset price that
occur when sample paths of the Wiener process are modifed in a certain
manner. In the case of speci?c claims, the minimum-variance hedging
strategy can be further expressed in terms of pricing functions. Unlike
previous work, the results of this paper apply equally well to simple
as well as path-dependent claims.

455

Hamrick, David, (Rhodes College)

**Contagion and Confusion in Credit Default Swap Markets**

Authors: Jeff Hamrick and Murad S. Taqqu

We model the relationship between credit default swap (CDS) premia
with a nonlinear regression model. Just as the linear correlation
coefficient characterizes the strength of the dependence between two
variables Y and X in a linear regression model, a local correlation
function captures the strength of the conditional dependence of Y
given X = x in a nonlinear regression model. We use the local correlation
function to define spatial contagion between two credit default swap
markets or two credit default swap indices. We find little empirical
evidence of contagion. Instead, we define a notion of confusion and
find, for example, that Countrywide Financial CDS and a financial
services sector CDS index were subject to confusion rather than contagion
during a time period including the Panic of 2008-2009.

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456

Muthuraman, Kumar, (University of Texas at Austin)

**Commodity Storage Valuation**

Authors: K. Muthuraman and S. Tompaidis

We present a general valuation framework for commodity storage facilities,
for non-perishable commodities. We consider the case of a storage
facility small enough so that injections and withdrawals do not influence
the price of the underlying commodity. We allow for mean-reversion
and seasonality in the price of the commodity, and allow for injection
and withdrawal costs. To find the optimal actions for the storage
owner we present an iterative numerical algorithm and prove its convergence.
We illustrate our framework with numerical examples for the case of
storage facilities for oil, natural gas, and water.

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457

Rubisov, Dmitri, (BMO Capital Markets)

**Pricing of Options Exposed to Cross-Currency Rates**

Authors: S. Jaimungal and D. Rubisov

In this article we are interested in cross-currency options which
are exposed to both currency and equity/commodity risk. The main challenge
is to consistently match market implied Black volatility smiles while
simultaneously capturing the correlation of forwards and currency.
To this end, we introduced a parsimonious five factor model which
allows for jumps in forward prices and diffusive stochastic volatility
in exchange rates. Closed form formulae for options on forwards, currency
and options on the equity/commodity struck in foreign currency are
derived and we calibrate the model to market data. Finally, we assess
the stability of the model by performing daily re-calibrations of
the at-the-money implied volatility while keeping other parameters
held fixed.

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461

Cebiroglu, Gökhan, (Humboldt-Universität zu Berlin)

**Hidden Liquidity and Optimal Display Strategies in US Markets**

Authors: Gökhan Cebiroglu, Prof. Ulrich Horst

Most electronic stock exchange markets provide traders the opportunity
to shield their orders from public view. Thus, the question arises
to what extend should a trader hide his trading intentions? For that,
we construct a sequential trading model for the execution process
of a partly hidden order - the so called Iceberg order - submitted
at some time at a prespecified price level. We consider randomly arriving
market and limit orders that execute and compete against the traders
Iceberg order. Considering a risk-neutral setting, we define the optimal
display size, as the size that maximizes the iceberg orders expected
execution volume within the given trading time horizon. We answer
the question, how the optimal choice of the display size relates to
the state of the orderbook. Calibration results indicate, that the
choice of the display size depends critically on the prevailing order
book imbalance and the order size. In particular, we find that traders
should display their trading intentions so as to avoid too large order
book imbalances, especially in the presence of wide spreads. Using
standard nonlinear regression and model reduction techniques, we also
provide significant explanatory variables for the presence of hidden
liquidity in order books.

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464

Dos Reis, Goncalo, (Ecole Polytechnique)

**On securitization, market completion and equilibrium risk transfer**

Authors: Ulrich Horst, Traian Pirvu, Goncalo dos Reis

We propose an equilibrium framework within which to price financial
securities written on non-tradable underlyings such as temperature
indices. We analyze a financial market with a finite set of agents
whose preferences are described by a convex dynamic risk measure generated
by the solution of a backward stochastic differential equation. The
agents are exposed to financial and non-financial risk factors. They
can hedge their financial risk in the stock market and trade a structured
derivative whose payoff depends on both financial and external risk
factors. We prove an existence and uniqueness of equilibrium result
for derivative prices and characterize the equilibrium market price
of risk in terms of a solution to a non-linear BSDE.

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465

Chun, Albert Lee, (Copenhagen Business School)

**A Forward-looking Model of the Term Structure of Interest Rates**

Authors:

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466

Maalaoui Chun, Olfa, (KAIST)

**Detecting Regime Shifts in Corporate Credit Spreads**

Authors: Olfa Maalaoui Chun, Georges Dionne, Pascal Francois

Switching regimes in credit spreads are thought to correlate with
macroeconomic factors. However, episodes of high credit spreads as
identified from the data are characterized by a high degree of persistence
so as to uncouple them from the underlying economic cycle. Using an
innovative regime detection technique, we focus on separately detecting
two distinct effects in the dynamics of credit spreads: a level effect
and a volatility effect. We show that patterns of level and volatility
regimes in credit spreads are surprisingly different. Specifically,
volatility regimes appear to be contemporaneously related to NBER
recessions but are also detected during significant economic shocks
occurring outside recessions. However, level regimes have long-lasting
patterns around NBER recessions and prove to be linked to Federal
Reserve policy and credit market conditions. Our findings also suggest
that level regimes contain predictive information about economic downturns
and act in response to tightening standards. These results are supported
by three widely used databases on corporate bond data - Warga, NAIC,
and TRACE and cover the last three economic recessions.

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467

Zhou, Zhuowei, (McMaster University)

**Two-factor capital structure models for equity and credit**

Authors: Thomas Hurd and Zhuowei Zhou

We extend the structural credit modelling approach of Black and Cox
to a unification of equity products (written on the stock price),
and credit products like bonds and credit default swaps (CDS). This
'hybrid' model is capable of reproducing well known equity models
such as the variance gamma model, at the same time producing the stylized
facts about default stemming from structural models of credit.

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468

Kuznetsov, Alexey, (York University)

**Wiener-Hopf factorization and distribution of extrema for a
family of Levy processes**

Authors: Alexey Kuznetsov

We introduce a ten-parameter family of Levy processes for which we
obtain Wiener-Hopf factors and distribution of the supremum process
in semi-explicit form. This family allows an arbitrary behavior of
small jumps and includes processes similar to the generalized tempered
stable, KoBoL and CGMY processes. Analytically it is characterized
by the property that the characteristic exponent is a meromorphic
function, expressed in terms of beta and digamma functions. As an
illustration of numerical efficiency that can be achieved with this
family of processes we discuss computation of various distributions
related to one-sided and two-sided exit problems.

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469

Valov, Angel, (Scotiabank)

**Generalyzed Shiryaev's Embedding and Skorohod Problem**

Authors: S. Jaimungal, A. Kreinin, A. Valov

We consider a connection between the famous Skorohod stopping problem
and an inverse problem for the first hitting time distribution for
the Brownian motion: given a probability distribution, F, find a boundary
such that the first hitting time distribution is F. We show that randomization
of the initial state of the process makes the inverse problem analytically
tractable. The idea of randomization of the initial state allows us
to significantly extend the class of distribution in the case of a
linear boundary and helps to establish connection with the Skorohod
stopping problem.

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470

Yildirim, Yildiray, (Syracuse University)

**Subprime Default Contagion**

Authors: Yildiray Yildirim, Marius Ascheberg, Robert A. Jarrow, Holger
Kraft

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471

Pan, Xuhui (Nick), (McGill University)

**State Price Density Estimated from Commodity Derivatives and
Its Relevant Economic Implications**

Authors: Xuhui Pan

I nonparametrically estimate the risk neutral probability densities
and state price densities (SPDs) of crude oil derivatives conditional
on the slope and volatility of futures. I find that risk neutral densities
in the crude oil market significantly deviate from lognormal distribution
and can be either negatively or positively skewed depending on maturities.
I also find SPDs display a U-shape and significantly depend on the
volatility level of the futures rather than the slope of futures price:
During the periods of low volatility, the U-shape is tighter, market
participants assign higher values to extreme returns than in high
volatility periods.

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472

Song, Yong, (University of Toronto)

**Components of bull and bear markets: bull corrections and bear
rallies**

Authors: John Maheu; Thomas McCurdy; Yong Song

Existing methods of partitioning the market index into bull and bear
regimes do not identify market corrections or bear market rallies.
In contrast, our probabilistic model of the return distribution allows
for rich and heterogeneous intra-regime dynamics. We focus on the
characteristics and dynamics of bear market rallies and bull market
corrections, including, for example, the probability of transition
from a bear market rally into a bull market versus back to the primary
bear state. A Bayesian estimation approach accounts for parameter
and regime uncertainty and provides probability statements regarding
future regimes and returns. A Value-at-Risk example illustrates the
economic value of our approach.

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474

Anand, Kartik, (Abdus Salam ICTP)

**Financial crises and the evaporation of trust**

Authors: Kartik Anand, Prasanna Gai and Matteo Marsili

Trust lies at the crux of most economic transactions, with credit
markets being a notable example. Drawing on insights from the literature
on coordination games and network growth, we develop a simple model
to clarify how trust breaks down in financial systems. We show how
the arrival of bad news about a financial agent can lead others to
lose confidence in it and how this, in turn, can spread across the
entire system. Our results emphasize the role of hysteresis - it takes
considerable effort to regain trust once it has been broken. Although
simple, the model provides a plausible account of the credit freeze
that followed the global financial crisis of 2007/8, both in terms
of the sequence of events and the measures taken (and being proposed)
by the authorities.

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