6th World Congress of the Bachelier Finance Society

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.

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.

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.

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."

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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}

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.

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.

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.

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.

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]

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.

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.

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.

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.

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.

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).

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.

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.

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.

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 $\lambda^{\frac13}.$

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

465
Chun, Albert Lee, (Copenhagen Business School)
A Forward-looking Model of the Term Structure of Interest Rates
Authors:

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.

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.

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.

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.

470
Yildirim, Yildiray, (Syracuse University)
Subprime Default Contagion
Authors: Yildiray Yildirim, Marius Ascheberg, Robert A. Jarrow, Holger Kraft

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.

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.

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.

BACHELIER FINANCE SOCIETY