BACHELIER FINANCE SOCIETY











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 Collin-Dufresne, Columbia University
Ernst Eberlein, University of Freiburg
Rudiger 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 short-dated 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 Black-Scholes 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 continuous-time 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 zero-sum 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 Heath-Jarrow-Morton 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 jump-induced 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 rate-credit 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.



Peter Carr, New York University
Authors: Peter Carr and Roger Lee
Pricing Variance Swaps on Time Changed Lévy Processes
We generalize to time-changed Lévy processes (including a wide range of jump dynamics) the "model-free'' 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 Marie-Amelie 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 horizon-unbiased 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 entropy-Hellinger martingale density (MEHM density hereafter) and its variations. The third contribution discusses the mathematical structures of the horizon-dependence 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 tailor-made to deal with the horizon's effect in exponential hedging.


Pierre Collin-Dufresne, 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 path-dependent options such as one-touch 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.

Rudiger 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 non-negligible 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 quasi-variational 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.

Kay Giesecke, Stanford University
Authors: Kay Giesecke and Dmitry Smelov
Exact Simulation of Jump-Diffusion Processes
This paper develops a method for the exact simulation of a one-dimensional jump-diffusion 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 asset-based 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.

 


Steven R. Grenadier, Stanford University



Christian Gourieroux, University of Toronto
Granularity Adjustment in Dynamic Multiple Factor Models: Systematic vs Unsystematic Risks


Jussi Keppo,
University of Michigan
Authors: Stein-Erik 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 2000-2006, 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
Co-author: 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 risk-averse, and their utility function allows for habit formation. We show that dividends follow Lintner's (1956) target-adjustment model. We provide closed-form, 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 multi-dimensional 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.


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
Co-authors : 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 exponential-quadratic BSDE with jumps and non bounded final condition. We use a new point of view based on entropic-semimartingale 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

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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 intensity-based 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 intensity-based setup, specifically, the CIR default intensity model. The main results furnish semi-analytical 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), 2495-2529.
[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 CDS-calibrated 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. Kohatsu-Higa, N. Privault and
S.-J. Sheu, eds., Birkhauser, 2010.

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Walter Schachermayer, University of Vienna

TBA


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.

Knut Solna, UC Irvine

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 arbitrage-free 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.


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Nizar Touzi, Ecole Polytechnique

Johan Tysk, Uppsala Universitet
Presenting author: Johan Tysk
Co-author: Erik Ekström

Forward is backward for time-homogeneous 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 time-homogeneous 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 non-negative 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 blow-up 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.