
ABSTRACTS  Thematic Speakers



Philippe
Balland, Bank of America Merrill Lynch 
Peter
Bank, Technische Universität Berlin 
Erhan
Bayraktar, University of Michigan 
Antje
Berndt, Carnegie Mellon University 
Mark
Broadie, Columbia University 
Peter
Carr, New York University 
Patrick
Cheridito, Princeton University 
Tahir
Choulli, University of Alberta 
Pierre
CollinDufresne, Columbia University 
Ernst
Eberlein, University of Freiburg 
Rüdiger
Frey, Universität Leipzig 
Kay
Giesecke, Stanford University 
Paul
Glasserman, Columbia University 
Christian
Gourieroux, University of Toronto 
Steven
R. Grenadier, Stanford University 
Jussi
Keppo, University of Michigan 
Haitao
Li, University of Michigan 
Bart
M. Lambrecht, Lancaster University 
Vadim
Linetsky, Northwestern University 
Dilip
Madan, University of Maryland 
Anis
Matoussi, University of Lemans 
Frank
Milne, Queens University 
Kristian
Miltersen, Copenhagen University 
Marek
Rutkowski, University of Sydney 
Walter
Schachermayer, University of Vienna 
Alexander
Schied, University of Mannheim 
Knut
Solna, UC Irvine 
Josef
Teichmann, ETH Zürich 
Nizar
Touzi, Ecole Polytechnique 
Johan
Tysk, Uppsala Universitet 

Philippe Balland, Bank of America Merrill Lynch
P. Balland, Q. Tran, G. Hodinic
Double
Mean Reversion in FX
In
this paper, we propose a new model for Foreign Exchange
rate that accounts for multiple time scale. We review
dynamic and calibration to Vanilla and Exotic shortdated
market. The effect of the ATM decorrelation on first
and second generation exotics is explored.
Peter
Bank, Technische Universität Berlin
Market
indifference prices
We
develop an equilibrium based model for the trades of
a large investor with a group of market makers at their
indifference prices. Using the theory of saddle functions
form convex duality, we show how to compute expansions
of derivative prices around their BlackScholes valuation,
illustrating how these depend on the market makers'
risk tolerances. This is joint work with Dmitry Kramkov.
Erhan Bayraktar,
University of Michigan
Authors:Erhan Bayraktar, Ioannis Karatzas,
Song Yao
Optimal
Stopping for Dynamic Convex Risk Measures
We use martingale and stochastic analysis
techniques to study a continuoustime optimal
stopping problem, in which the decision
maker uses a dynamic convex risk measure
to evaluate future rewards. We also find
a saddle point for an equivalent zerosum
game of control and stopping, between an
agent (the "stopper") who chooses
the termination time of the game, and an
agent (the "controller", or "nature")
who selects the probability measure.
Antje
Berndt, Carnegie Mellon University
Authors:Antje Berndt, Peter Ritchken and Zhiqiang Sun
On
Correlation and Default Clustering in Credit Markets
We
establish Markovian models in the HeathJarrowMorton
paradigm that permit an exponential affine representation
of riskless and risky bond prices while offering significant
flexibility in the choice of volatility structures.
Estimating models in our family is typically no more
difficult than in the workhorse affine family. Besides
diffusive and jumpinduced default correlations, defaults
can impact the credit spreads of surviving firms,
allowing for a greater clustering of defaults. Numerical
implementations highlight the importance of incorporating
interest ratecredit spread correlations, credit spread
impact factors, and the full credit spread curve when
building a unified framework for pricing credit derivatives.
Mark
Broadie, Columbia University
Authors: Mark Broadie, Yiping Du, Ciamac Moallemi
Effiicient
Risk Estimation via Nested Simulation
We analyze the computational problem of estimating financial
risk in a nested simulation. In this approach, an outer
simulation is used to generate financial scenarios and
an inner simulation is used to estimate future portfolio
values in each scenario. We propose a new algorithm
to estimate risk which sequentially allocates computational
effort in the inner simulation based on marginal changes
in the risk estimator in each scenario. Theoretical
and numerical results are given to show that the risk
estimator has a faster convergence order compared to
the conventional uniform inner sampling approach.
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Peter
Carr, New York University
Authors: Peter Carr and Roger Lee
Pricing
Variance Swaps on Time Changed Lévy
Processes
We generalize to timechanged Lévy
processes (including a wide range of jump
dynamics) the "modelfree'' valuation
of variance swaps previously investigated
only in the case of continuous underlying
dynamics.
Patrick
Cheridito, Princeton University
Authors:P. Cheridito, A. Nikeghbali, E.
Platen
Processes
of class Sigma, last passage times and drawdowns
We propose a general framework to study
last passage times, suprema and drawdowns
of a large class of stochastic processes.
Our approach is based on processes of class
Sigma. We provide three general representation
results that allow to deduce the laws of
a variety of interesting random variables
such as running maxima, drawdowns and maximum
drawdowns of suitably stopped processes.
As an application we discuss the pricing
and hedging of options that depend on the
running maximum of an underlying price process.
Tahir
Choulli, University of Alberta
Authors: T. Choulli, Junfeng Ma, and MarieAmelie
Morlais
Exponential
Hedging under Variable Horizons
This
paper addresses four main issues intimately
related to the exponential hedging when
the horizon may vary in the set of bounded
stopping times. The first contribution deals
with explicit and complete characterization/parametrization
of the class of exponential forward performances.
The second main contribution focuses on
the horizonunbiased exponential hedging
problem. Precisely, for a given dynamic
payoff B = (B_t, t>0), this problem consists
of finding an admissible optimal strategy
that minimizes the risk in the exponential
utility framework up to any stopping time
bounded by a constant T. Here, our goal
is to explicitly describe the optimal strategy
when it exists, and fully describe the payoff
B for which this problem admits solution.
The effect of the change of numeraire on
this problem as well as its relationship
to the exponential forward performances
are illustrated. Both contributions (the
first and the second) rely heavily on the
concept of minimal entropyHellinger martingale
density (MEHM density hereafter) and its
variations. The third contribution discusses
the mathematical structures of the horizondependence
in the optimal portfolio and strategy for
an exponential hedging problem. This extends
the work of Choulli and Schweizer (2009)
to the case of exponential utilities. The
last contribution analyzes the optimal sale
problem for the exponential utility and
the semimartingale framework. Again, here
the MEHM density concept plays a crucial
role in our methodology and this enhances
once more our belief that this Hellinger
tool is tailormade to deal with the horizon's
effect in exponential hedging.
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Pierre
CollinDufresne, Columbia University
On
the Relative Pricing of long Maturity S&P
500 Index Options and CDX Tranches
Ernst
Eberlein, University of Freiburg
Authors: Ernst Eberlein, Kathrin Glau, Antonis
Papapantoleon
Analysis
of Fourier transform valuation in Lévy
models
A
systematic analysis of the conditions such
that Fourier transform valuation formulas
are valid is provided. The interplay between
the conditions on the payoff function and
the driving process is investigated. Plain
vanilla as well as exotic pathdependent
options such as onetouch or lookback options
and equity default swaps are considered.
A number of results are extended to the
multidimensional setting to include basket
products and calculation of Greeks by Fourier
transform methods is discussed.
Rüdiger
Frey,
University of Leipzig
Authors: Ruediger Frey, Roland Seydel
Optimal
Securitization of Credit Portfolios via Impulse Control
We study the optimal loan securitization policy of a commercial
bank which is mainly engaged in lending activities. For this we
propose a stylized dynamic model which contains the main features
affecting the securitization decision. In line with reality we
assume that there are nonnegligible fixed and variable transaction
costs associated with each securitization. The fixed transaction
costs lead to a formulation of the optimization problem in an
impulse control framework. We prove viscosity solution existence
and uniqueness for the quasivariational inequality associated
with this impulse control problem. Iterated optimal stopping is
used to find a numerical solution of this PDE, and numerical examples
are discussed.
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Kay
Giesecke, Stanford
University
Authors: Kay Giesecke and Dmitry Smelov
Exact
Simulation of JumpDiffusion Processes
This paper develops a method for the exact
simulation of a onedimensional jumpdiffusion
process. The drift, diffusion coefficient and
intensity are arbitrary functions of the state.
We illustrate the effectiveness of the method
with examples from credit/equity, including the
analysis of options on defaultable stocks.
Paul Glasserman, Columbia University
Authors:Paul Glasserman and Behzad Nouri
Pricing Contingent Capital with Continuous Conversion
Among the solutions proposed to the problem of banks "too big to fail" is contingent capital in the form of debt that converts to equity when the firm's capital ratio falls below a threshold.
We analyze the dynamics of such a security with continuous conversion and derive closed form expressions for its value when the firm's assets are modeled as geometric Brownian motion and the conversion trigger is an assetbased capital ratio. A key step in the analysis is an explicit formula for the fraction of equity held by the original holders of the contingent capital debt.
Christian Gourieroux, University of Toronto
Granularity Adjustment in Dynamic Multiple Factor Models: Systematic vs Unsystematic Risks
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Jussi Keppo, University
of MichiganAuthors: SteinErik Fleten, Jussi Keppo, Helga Lumb, Johan Sollie, Vivi Weiss
Hydro
Scheduling Powered by Derivatives
Hydropower
producers maximize the value of the
water in their reservoirs under uncertain
future electricity price and reservoir
inflow. Using weekly data from thirteen
Norwegian power plants during 20002006,
we find that electricity derivative
prices affect significantly the scheduling
decisions. Hence, consistent with
recommendations by several theoretical
Operations Management studies, financial
market information is used in the
everyday production planning practice.
Further, since our empirical model
explains about 78% of the realized
variation in the power plant scheduling,
the model can be used to simplify
the scheduling in practice.
Bart M. Lambrecht, Lancaster University
Coauthor: Stewart Myers (MIT Sloan School of Management)
A Linter Model of Dividends and Managerial Rents
We
develop a model where dividend payout, investment
and financing decisions are made by managers who attempt
to maximize the rents they take from the firm. But
the threat of intervention by outside shareholders
constrains rents and forces rents and dividends to
move in lockstep. Managers are riskaverse, and their
utility function allows for habit formation. We show
that dividends follow Lintner's (1956) targetadjustment
model. We provide closedform, structural expressions
for the payout target and the partial adjustment coefficient.
Risk aversion causes managers to underinvest, but
habit formation mitigates the degree of underinvestment.
Changes in corporate borrowing absorb fluctuations
in earnings and investment.
Vadim Linetsky, Northwestern University
Modeling Dependent Jumps: A Time Change Approach
We show how to construct multidimensional Markov processes with dependent jumps via time changes, how to solve the resulting models via the spectral method, and discuss a range of applications
in mathematical finance.
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Dilip Madan, University of Maryland
Joint
Risk Neutral Laws and Hedging
Complex positions on multiple underliers are hedged
using the options surface of all underliers. Hedging
objectives follow Cherny and Madan (2010) by minimizing
ask prices for which post hedge residual risks are acceptable
at prespeci.ed levels. It is shown that such hedges
require one to use a risk neutral law on the set of
underlying risks. We propose a joint risk neutral law
for multiple underliers and estimate it from multiple
option surfaces. Under our joint law asset returns are
a linear mixture of independent Lévy components.
Data on the independent components are estimated by
an application of independent components analysis on
time series data for the underlying returns. A comparison
of the the risk neutral law with the statistical law
shows that risk neutral correlations dominate their
statistical counterparts. Hedges signicantly reduce
ask prices.
Anis Matoussi, University of Maine (Le Mans) and Ecole Polytechnique
Coauthors : N. El Karoui, M. Jeanblanc and A. Ngoupeyou
Quadratic BSDE's with jumps and exponential utility maximization problem for portfolio with defaults
We
study a class of exponentialquadratic BSDE with jumps
and non bounded final condition. We use a new point of
view based on entropicsemimartingale estimates and stability
theorem for semimartingales. Moreover, we apply this result
to solve a exponential utility indifference price of a
contingent claim in incomplete market involving credit
derivatives.
Kristian Miltersen, Copenhagen Business School
Real Investments and their Financing: a real options approach
How (and how much) does the firm's capital structure influences its optimal investment strategies? The main finding
of this project is that the existing debt in the firm and the fact that the new investment project can be partly financed by debt both influences the optimal
investment strategy. However, the existing debt and issue of new debt influence the optimal investment strategy in different directions. Hence, it is not obvious whether
the firm's capital structure will accelerate or delay the launch of an investment project.
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Frank Milne, Queens University
General Approaches for Modelling Liquidity Effects in Asset Markets and their Application to Risk Management Systems
Marek Rutkowski, University of Sydney
Hedging of Credit Default Swaptions
An important issue arising in the context of modeling credit default
swap spreads is the construction of an appropriate model in which
a family of options written on credit default swaps, that is, credit
default swaptions, can be valued and hedged. The solution to the hedging
problem is readily available in market models of forward CDS spreads
(see, for instance, Brigo [3] or Li and Rutkowski [4]) in which a
credit default swaption can be valued through a variant of the Black
formula. By contract, it is a challenging problem when working within
a commonly used intensitybased framework. The present talk is based
on the paper by Bielecki et al. [2]. The main goal of the paper was
to exemplify the usefulness of some abstract hedging results, which
were obtained previously in Bielecki et al. [1], for the valuation
and hedging of the credit default swaption in a particular intensitybased
setup, specifically, the CIR default intensity model. The main results
furnish semianalytical formulae for the price and the replicating
strategy for credit default swaptions.
References
[1] T.R. Bielecki, M. Jeanblanc and M. Rutkowski: Pricing and trading
credit default swaps in a hazard process model. Annals of Applied
Probability 18 (2008), 24952529.
[2] T.R. Bielecki, M. Jeanblanc and M. Rutkowski: Hedging of a credit
default swaption in the CIR default intensity model. Forthcoming in
Finance and Stochastics.
[3] D. Brigo: CDS options through candidate market models and the
CDScalibrated CIR++ stochastic intensity model. In: Credit Risk:
Models, Derivatives and Management, N. Wagner, ed., Chapman &
Hall/CRC Financial Mathematics Series, 2008, pp. 393–426.
[4] L. Li and M. Rutkowski: Market models of forward CDS spreads.
Forthcoming in: Progress in Probability, Stochastic Analysis with
Financial Applications, A. KohatsuHiga, N. Privault and
S.J. Sheu, eds., Birkhauser, 2010.
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Alexander Schied, University of Mannheim Authors:Aurélien Alfonsi, Jim Gatheral, Alexander Schied, Alla
Slynko
Aspects of market impact modeling and optimal trade execution
Research on market impact has shown that the price
impact of trades is mainly transient and often nonlinear.Several
mathematical models have been proposed to describe
these features quantitatively. In this talk we will
discuss some of these models and their properties.
In particular we will see that small changes in
the description of transience can have significant
effects on the qualitative behavior of the model.
Derivative Time Scale Perturbations
We analyze the role of stochastic volatility from the point of view of time scale perturbations.
We discuss how a separation of time scales can be used to obtain parsimonious approximations and the interpretation of these. We discuss briefly
application in credit markets.
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Josef Teichmann, ETH Zürich
Risk management, Arbitrage and Scenario generation for interest rates
We present a general framework for the arbitragefree generation of scenarios for the purposes of risk management.
We give arguments why NA matters, how to estimate the characteristics of SPDEs from time series data, and how to solve the obtained equations numerically.
This is based on joint work with R. Pullirsch, J.P. Ortega and J. Wergieluk.
Johan Tysk, Uppsala Universitet
Presenting author: Johan Tysk
Coauthor: Erik Ekström
Forward
is backward for timehomogeneous diffusions
The transitional densities for Brownian motion are symmetric
in the backward and forward spatial variables. We show in the
present paper that by multiplying the transitional probabilities
for timehomogeneous processes by a suitable explicit function
of the diffusion and drift coefficients, we also obtain a function
that is symmetric in the spatial variables. This enables us
to reduce the study of forward equations to backward equations.
We consider for instance diffusions on the nonnegative real
axis with a diffusion coefficient tending to zero at zero. Under
very general conditions the backward equation has a solution
differentiable up to zero, whereas the density, which solves
the forward equation, might tend to infinity there. The blowup
of the solution of the forward equation is then reflected by
the function mentioned above symmetrizing the transitional densities.
In this way we derive new results on the asymptotic behaviour
of the density at boundary points where the diffusion degenerates.
These results are applied to processes occuring in finance,
both for short rate models and for option pricing models.
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