fm10 abstracts · in this talk, we present a recent methodology based on stochastic analysis to...

24 FM10 Abstracts

IP0

SIAG/FME Junior Scientist Prize: Proving Reg-ularity of the Minimal Probability of Ruin via aGame of Stopping and Control

We reveal an interesting convex duality relationship be-tween two problems: (a) minimizing the probability of life-time ruin when the rate of consumption is stochastic andwhen the individual can invest in a Black-Scholes financialmarket; (b) a controller-and-stopper problem, in which thecontroller controls the drift and volatility of a process inorder to maximize a running reward based on that pro-cess, and the stopper chooses the time to stop the runningreward and rewards the controller a final amount at thattime. Our primary goal is to show that the minimal proba-bility of ruin, whose stochastic representation does not havea classical form as does the utility maximization problem(i.e., the objective’s dependence on the initial values of thestate variables is implicit), is the unique classical solutionof its Hamilton-Jacobi-Bellman (HJB) equation, which isa non-linear boundary-value problem. We establish ourgoal by exploiting the convex duality relationship between(a) and (b). Joint work with Jenny Young. Available athttp://arxiv.org/pdf/0704.2244v13

Erhan BayraktarUniversity of MichiganDepartment of [email protected]

IP1

Title Not Available at Time of Publication

Abstract not available at time of publication.

Nicole El KarouiEcole Polytechnique, [email protected]

IP2

Does a Central Clearing Counterparty ReduceCounterparty Risk?

We show whether central clearing of a particular class ofderivatives lowers counterparty risk. For plausible cases,adding a central clearing counterparty (CCP) for a class ofderivatives such as credit default swaps reduces netting ef-ficiency, leading to an increase in average exposure to coun-terparty default. Clearing two or more different classes ofderivatives in separate CCPs always increases counterpartyexposures relative to clearing the combined set of deriva-tives in a single CCP.

Darrell DuffieStanford [email protected]

IP3

Singular Forward-Backward Stochastic DifferentialEquations and Emissions Derivatives

We introduce two simple models of forward-backwardstochastic differential equations with a singular terminalcondition and we explain how and why they appear nat-urally as models for the valuation of CO2 emission al-lowances. Single phase cap-and-trade schemes lead read-ily to terminal conditions given by indicator functions ofthe forward component, and using fine partial differentialequations estimates, we show that the existence theory of

these equations, as well as the properties of the candidatesfor solution, depend strongly upon the characteristics ofthe forward dynamics. Finally, we give a first order Taylorexpansion and show how to numerically calibrate some ofthese models for the purpose of CO2 option pricing.

Rene CarmonaPrinceton UniversityDpt of Operations Research & Financial [email protected]

IP4

On Quasiconvex Dynamic Risk Measures and onConvex Approximations

We introduce the notion of conditional quasiconvex riskmeasures and we provide their dual representation, whichgeneralizes the representation of quasiconvex real valuedrisk measures and of conditional convex risk measures.These results were inspired by the theory of dynamic mea-surements of risk and are applied in this context.

Marco FrittelliUniversita’ degli Studi di [email protected]

IP5

Stochastic Expansions Applied to Fast Pricing

In this talk, we present a recent methodology based onstochastic analysis to derive tractable approximations ofoption prices in various models. Regarding the models, ourresults cover the case of local volatility models, includingor not Gaussian jumps and Gaussian interest-rate models,Heston models. We also handle the case of stocks payingaffine dividends at discrete times, Asian or basket options...Error estimates are provided. Numerical results illustratethe relevancy of the expansions. Applications to real-timepricing/calibration are discussed as well.

Emmanuel GobetEcole [email protected]

IP6

Constant Proportion Debt Obligations: A Post-Mortem Analysis of Rating Models

In its complexity and its vulnerability to market volatil-ity, the CPDO might be viewed as the poster child forthe excesses of financial engineering in the credit market.This paper examines the CPDO as a case study in modelrisk in the rating of complex structured products. Wedemonstrate that the models used by S&P and Moody’sfail standard in-sample specification tests even during thepre-crisis period, and in particular understate the kurtosisof spread changes. Model-implied probabilities of attaininghigh spread levels were biased downwards, which in turnbiased the rating upwards. We conclude with larger lessonsfor the rating of complex products and for modeling creditrisk in general.

Michael GordyFederal Reserve [email protected]

FM10 Abstracts 25

IP7

Variation Swaps on Time-Changed Levy Processes

For a family of functions G, we define the G-variation,which generalizes power variation; G-variation swaps,which pay the G-variation of the returns on an underly-ing share price F; and share-weighted G-variation swaps,which pay the integral of F with respect to G-variation. Forinstance, the case G(x) = x2 reduces these notions to, re-spectively, quadratic variation, variance swaps, and gammaswaps. We prove that a multiple of a log contract pricesa G-variation swap, and a multiple of an F log F contractprices a share-weighted G-variation swap, under arbitraryexponential Levy dynamics, stochastically time-changed byan arbitrary continuous clock having arbitrary correlationwith the Levy driver, under integrability conditions. Wesolve for the multipliers, which depend only on the Levyprocess, not on the clock. Depending on the choice of G,these multipliers relate to other quantities of interest, suchas jump skewness and various notions of hedge-risk.

Roger LeeUniversity of [email protected]

IP8



Jin MaUniversity of Southern [email protected]

IP9

Market Impact Modeling and Optimal Order Exe-cution

Market impact refers to the adverse feedback effect on theprice of a stock caused by one’s own trading. It can leadto significant costs for the execution of sufficiently largeorders. Due to the transience of market impact, the associ-ated costs can be reduced by slicing the order in a sequenceof small orders that are then distributed over a certaintime interval. In practice the size of the individual slicesis computed by optimizing a cost criterion within a math-ematical model for market impact. In this talk, we discussseveral market impact models that have been proposed inthe literature. A particular question, which is similar tothe question of characterizing the absence of arbitrage in astandard asset pricing model, is how one can exclude theoccurence of certain model irregularities that can arise inmarket impact models. We also discuss optimization prob-lems for order execution strategies with respect to variouscost criteria.

Alexander SchiedUniversity of [email protected]

IP10

An Approximation Scheme for Investment Perfor-mance Processes in Incomplete Markets

An approximation scheme for the maximal expected utilityin an incomplete market will be presented. The market in-completeness comes from a stochastic factor affecting thedynamics of the stock price. The scheme yields an intu-itively pleasing decomposition of the value function process

at each splitting step. Specifically, in the first sub-step, thecurrent utility is being adjusted while the component ofthe investment opportunity set that is perfectly correlatedwith the stock remains unchanged. In the second sub-stepthe reverse happens. This orthogonal decomposition high-lights how dynamic preferences and investment decisionsbehave in terms on the imperfect correlation and, more-over, explains some effects of the stochastic factors on therisk preferences and the investment decisions. This is jointwork with Sergey Nadtochiy (University of Oxford).

Thaleia ZariphopoulouUniversity of Texas at [email protected]

CP1

American-Style Options, Stochastic Volatility, andDegenerate Parabolic Variational Inequalities

Elliptic and parabolic partial differential equations arisingin option pricing problems involving the Cox-Ingersoll-Rossor Heston stochastic processes are well-known to be degen-erate parabolic. We provide a report on our work on theexistence, uniqueness, and regularity questions for varia-tional inequalities involving degenerate parabolic differen-tial operators and applications to American-style optionpricing problems for the Heston model. This is joint workwith Panagiota Daskalopoulos (Department of Mathemat-ics, Columbia University).

Paul FeehanRutgers [email protected]

CP1

Efficient Time Differencing Schemes for Pricing Ex-otic Options with Transaction Cost

A new second order exponential time differencing (ETD)scheme is developed to price exotic options using aBlack-Scholes equation which incorporates transaction costthrough a HWW nonlinear function. The scheme is com-pared with the ETD Crank-Nicolson method which doesnot incur unwanted oscillations. This will be demonstratedin numerical examples for a Butterfly Spread, and Digitalcall options. We also investigate American options using apenalty approach with transaction cost.

Abdul Q.M. KhaliqMiddle Tennessee State UniversityDepartment of Mathematical [email protected]

Britta JanssenBrandenburg Technical UniversityCottbus, [email protected]

CP1

Smoothing Effect of the Greens Function Ap-proach to Terminal-Boundary Value Problems forthe Black-Scholes Equation

A number of terminal-boundary value problems are con-sidered for the Black-Scholes equation. A semi-analyticalGreens function-based algorithm is developed for their so-lution. Closed analytical representations are obtained forrequired Greens functions. The procedure, which is im-

26 FM10 Abstracts

plemented for construction of the Greens functions, usesa combination of the Laplace integral transform with themethod of variation of parameters. The latter is applied tothe construction of Greens functions for resulting ordinarydifferential equations. Numerous graphical illustrations arepresented justifying high accuracy level for settings withnon-smooth and even discontinuous terminal and bound-ary data. The high accuracy is attained due to the inte-gral feature of the approach where numerical differentia-tion is completely avoided. The proposed semi-analyticalapproach can be employed to accurately solve either Eu-ropean or American option problems simulated with theBlack-Scholes equation. In the first case, our algorithmdirectly solves the problem, whereas for American optionsettings, an iteration procedure can readily be developed.

Max MelnikovCumberland [email protected]

CP1

Efficient Price Sensitivity Estimation of FinancialDerivatives by Weak Derivatives

We present the stochastic gradient estimation method ofweak derivatives (WD) with the aim of constructing effi-cient algorithms for the ”Greeks” estimation of financialderivatives. The key idea is to replace the derivative of theprobability measure of the underlying model by its WD.The WD method has the advantageous property that theform of the estimator does not depend on the details of thepayoff but only on the density of the underlying model.

Carlos Sanz ChaconGoethe University [email protected]

Peter KloedenJohann Wolfgang Goethe UniversityFrankfurt am Main, [email protected]

CP1

A Toolbox for Option Pricing with Theta-CalculusBased on Sparse Grids

Theta-calculus is a mathematical modeling language forthe description of sequential processes, financial contracts,and multi-period strategies. With the Theta-notation, itis possible to model financial products as sequences of op-erators. We combined the idea of Theta-calculus with anapproach based on partial differential equations, such asthe Black-Scholes equation, discretized with locally adap-tive sparse grids. With this, we can handle various typesof multi-dimensional option pricing problems numericallywith one general technique, in a straightforward way.

Stefanie SchraufstetterTechnische Universitat MunchenInstitute for Scientific [email protected]

CP1

Exact Sampling of Jump-diffusions

Jump-diffusion processes are ubiquitous in finance and eco-nomics. They arise as models of security, energy andcommodity prices, exchange and interest rates, and de-

fault timing. This paper develops a method for the exactMonte Carlo simulation of a skeleton and a hitting timeof a one-dimensional jump-diffusion with state-dependentdrift, volatility, jump intensity and jump size. The methodrequires the drift function to be C1, the volatility func-tion to be C2, and the jump intensity function to be lo-cally bounded. No further structure is imposed on thesefunctions. The method leads to unbiased simulation es-timators of derivatives prices, transition densities, hittingprobabilities, and other quantities. Numerical experimentsdemonstrate its advantages over a conventional discretiza-tion scheme.

Dmitry Smelov, Kay GieseckeStanford [email protected], giesecke @ stanford.edu

CP1

A Projected Algebraic Multigrid Method for Pric-ing American Options

We adapt an algebraic multigrid (AMG) method for solv-ing linear complementarity problems (LCPs) resulting frompricing American options using implicit finite differencediscretizations. As an example we consider pricing Ameri-can options under Heston’s stochastic volatility model.

Jari ToivanenStanford [email protected]

Cornelis W. OosterleeCWI, Centrum Wiskunde & Informatica, [email protected]

CP1

Some Non-arbitrage Properties in Numerical Solu-tions for American Options

We first give a brief overview of American option pricingmodels and numerical methods. We treat American op-tion models as a special class of obstacle problems. Fi-nite element formulation is introduced together with erroranalysis of numerical solutions. Some interesting arbitrageproperties about sensitivity of the option price to the pay-off function are proved. We also give a criterion for theconvergence of numerical free boundaries (optimal exerciseboundaries) under mesh refinement. Some future researchplans will be discussed.

Yongmin ZhangXi’an Jiaotong - Liverpool [email protected]

CP2

Controlling Portfolio Allocation Using a KalmanFilter and Multi-Factor Model Framework

Multi-factor models are developed and implemented intoa Kalman filter to estimate portfolio states. The analyt-ical framework of the state estimates combines the leastsquares models with classic mean-variance optimization.The multi-factor models include the CAPM, Fama-French,and other more diverse models to describe the behavior ofvarious segments of the capital markets. A framework forfilter tuning against expected process and plant noise isdefined, and numerical results demonstrate effectiveness of

FM10 Abstracts 27

the approach.

James DilellioPepperdine [email protected]

CP2

Risk Preferences and Their Robust Representation

To address the plurality of risk notions, we concentrate onsetting invariant features: diversification and monotonic-ity. We introduce and study three key concepts, risk or-der, risk measure and risk acceptance family which allowsus to provide a general robust representation of lower semi-continuous risk orders on convex subsets of locally convextopological vector spaces. This general approach is then il-lustrated in different setups (random variables, probabilitydistributions, consumption streams...) allowing for differ-ent interpretations of risk.

Samuel Drapeau, Michael KupperHumboldt University [email protected], [email protected]

CP2

Entropy Approach to Incorporate Heavy TailedConstraints in Financial Models

In the existing financial literature, entropy based ideas havebeen proposed in portfolio optimization and in model cal-ibration for options pricing. The abstracted problem es-sentially corresponds to finding a probability measure thatminimizes Kullbach- Leibler (KL) distance with respect toa known measure and satisfies certain moment constraintson functions of underlying assets. In this paper, we showthat under KL distance, the optimal solution may not ex-ist when constraints involve fat tailed distributions ubiqui-tous in financial practice. We note that this drawback maybe corrected if ‘polynomial-divergence’ entropy distance isused. We discuss existence and uniqueness issues relatedto this new optimization problem as well as the nature ofthe optimal solution under different objectives. We alsoidentify the optimal solution structure under KL distanceas well as polynomial divergence when the associated con-straints include those on marginal distribution of functionsof underlying assets. These results are applied to portfo-lio modeling in Markowitz framework where we note thata reasonable view that a particular portfolio of assets hasheavy tailed losses may lead to a more realistic tail distri-bution model of all assets.

Sandeep JunejaTata Institute of Fundamental ResearchSchool of Technology and Computer [email protected]

Santanu DeyTata Institute of Fundamental [email protected]

CP2

Portfolio Selection in a Market with TransactionCosts

In this paper we solve a portfolio optimization problemwhere the investor must pay transaction costs proportionalto the size of the trade whenever the portfolio is reallo-cated. The risky asset is modeled as a geometric Brownian

motion. There are no restrictions on short selling or bor-rowing. Despite this, the trading strategy is found analyti-cally. The proof of our method relies on several conditionsfor the optimality of a portfolio choice problem.

Thomas LeirvikPhD student, University of [email protected]

CP2

Optimal Investing with Reaping Losses in a Tax-able Portfolio

Just as investors are best off deferring gains as long aspossible, they are also best off realizing losses as soon aspossible. We develop a PDE that corresponds to activelyexploiting losses, but being passive otherwise. The PDEis determined from the adjoint of the formulation withthe value function for the optimal expected utility at thetime of portfolio liquidation. We show that finite differencemethods for our PDE yield the optimal investing strategyin a fraction of the time needed by Monte Carlo methods,and with significantly more precision. Finally, we show howto account for wash sale constraints, transaction costs, andthe $3000 annual limit on losses in the American tax code.

Dan Ostrov, Tom WongSanta Clara [email protected], [email protected]

CP2

Portfolio Management with Hyperbolic Discount-ing

This paper considers the Merton portfolio managementproblem. We are concerned with non-exponential discount-ing of time, which has received much attention lately, es-pecially in the area of behavioural ?nance. It is a bet-ter description of the behaviour of investors, but it leadsto problems of time inconsistency, so that the notion ofoptimal strategy no longer is appropriate. We introducethe notion of subgame perfect strategies, henceforth calledpolicies, and for CARA preferences we characterize themby an integral equation.

Traian A. PirvuMcMaster [email protected]

CP2

Market Models with a Stochastic Number of Assets

In equity markets the number of companies whose stock istradeable changes over time as existing companies mergeand split and new companies offer IPOs. To properly studythe diversity and stability of equity markets over time, thenumber of assets being modeled must be allowed to varystochastically in time. We present a mathematical frame-work for these models and study some of their basic prop-erties.

Winslow C. StrongUniversity of California Santa [email protected]

CP2

On a Hybrid Uncertain Market Model with Ran-

28 FM10 Abstracts

dom Interval Payoffs

A new hybrid uncertain market model, in which securitiesare modeled by random intervals, is proposed. New con-cepts, such as strong arbitrage opportunity, acceptable riskneutral measure, and weighted expected utility are pro-posed. Based on no strong arbitrage argument, the pricingrule for contingent claim and the problem of utility max-imization are discussed, where weighted expected utilitymodel is used to measure the utility towards random inter-val wealth.

Surong YouCollege of Science, Donghua [email protected]

CP3

A Novel Modelling of Stochastic Skewness with Ap-plications to Fitting and Hedging

[Carr, Geman, Madan and Yor, 2003] and [Carr and Wu,2007] modelled stochastic skewness using a time-change,which corresponds to having stochastic intensity parame-ters of the Levy measure. By calibrating to liquid vanillaoptions, we found evidence that a model with stochasticsteepness parameters may be more appropriate. We de-velop a fast pricing algorithm for barrier options understochastic steepness parameters by using an approxima-tion with a regime-switching model, compare performanceof the two models, and analyze implications for hedging.

Marco De InnocentisDepartment of MathematicsUniversity of [email protected]

Sergei LevendorskiiUniversity of [email protected]

CP3

Asymptotic Approximations to Deterministic andStochastic Volatility Models with Applications toHigh Frequency Trading

Asymptotic pricing formulas are derived for equity deriva-tives based on deterministic and stochastic volatility mod-els. The formulas are valid near expiry and are derivedusing the ray method to first construct the density func-tion. Next the risk-neutral integrals in the pricing formulasare expanded to obtain a uniform asymptotic approxima-tion. The accuracy of the new formulas is demonstratedalong with their usefulness for hedging and calibration inhigh frequency trading.

Richard A. JordanIntercontinental Exchange [email protected]

Charles TierDepartment of Applied MathematicsIllinois Institute of [email protected]

CP3

The Contribution of Trader Interaction to Market

Noise

We use limit theorems and the Cucker-Smale flocking ideato construct a dynamic asset price model that captures ex-plicitly the impact of communication among market partic-ipants. Our results provide insights to various puzzling em-pirical properties (sometimes known as ”stylized facts’) ofasset returns that have been observed in the market. Thisbuilds on work of Rama Cont, Jean-Philippe Bouchaud,Andrew Lo, and others. By modelling rates of communi-cation among active traders in the spirit of Darrell Duffiefor example, we are able to derive a mathematical structureexisting in the limit that explains the inevitability of thesestylized facts. In particular, among other things, we showthat while asset returns over a longer period are indeednormally distributed, one can still observe leptokurtic dis-tributions when the returns are calculated on smaller timescales.

Sophia Liu, Philip ProtterCornell [email protected], [email protected]

CP3

Efficient Valuation of Discrete Realized VarianceContracts

We value arbitrary contracts on discrete realized vari-ance. The underlying follows a conditionally Gaussian pro-cess modulated by autonomous stochastic volatility. Eulerschemes of the Heston, Hull-White and SABR models arespecial cases. We show that uncertainty in realized vari-ance arises largely from the norm of the Gaussian shocksand the time average of volatility. We combine determinis-tic integration along privileged directions with exact MonteCarlo sampling in an algorithm that generates significantspeed gains.

Nicolas MerenerSchool of BusinessUniversidad Torcuato Di [email protected]

Leonardo VicchiUniversidad de Buenos [email protected]

CP3

On Refined Volatility Smile Expansion in the Hes-ton Model

It is known that Heston’s stochastic volatility model ex-hibits moment explosion, and that the critical moment s∗

can be obtained by solving (numerically) a simple equa-tion. This yields a leading order expansion for the impliedvolatility at large strikes: σBS(k, T )2T ∼ Ψ(s∗ − 1) × k(Roger Lee’s moment formula). Motivated by recent “tail-wing’ refinements of this moment formula, we first derivea novel tail expansion for the Heston density, sharpeningprevious work of Dragulescu and Yakovenko [Quant. Fi-nance 2, 6 (2002), 443–453], and then show the validity of

a refined expansion of the type σBS(k, T )2T = (β1k1/2 +

β2+ . . .)2, where all constants are explicitly known as func-tions of s∗, the Heston model parameters, spot vol andmaturity T . In the case of the “zero-correlation’ Hestonmodel such an expansion was derived by Gulisashvili andStein [Appl. Math. Opt., DOI: 10.1007/s002450099085].Our methods and results may prove useful beyond the He-ston model: the entire quantitative analysis is based on

FM10 Abstracts 29

affine principles; at no point do we need knowledge of the(explicit, but cumbersome) closed form expression of theFourier transform of log ST (equivalently: Mellin transformof ST ). Secondly, our analysis reveals a new parameter(‘critical slope’), defined in a model free manner, whichdrives the second and higher order terms in tail- and im-plied volatility expansions.

Stephan SturmORFE DepartmentPrinceton [email protected]

Peter FrizTU and WIAS [email protected]

Stefan GerholdTU [email protected]

Archil GulisashviliOhio [email protected]

CP3

Potential PCA interpretation problems for Volatil-ity Smile Dynamics

Abstract Principal Component Analysis (PCA) is a com-mon procedure for the analysis of financial market data,such as implied volatility smiles or interest rate curves. Re-cently, Pelsser and Lord [11] raised the question whetherPCA results may not be facts but artefacts. We extendthis line of research by considering an alternative matrixstructure which is consistent with foreign exchange optionmarkets. For this matrix structure, PCA effects which areinterpreted as shift, skew and curvature can be generatedfrom unstructured random processes. Furthermore, we findthat even if a structured system exists, PCA may not beable to distinguish between these three effects. The contri-bution of the factors explaining the variance in the originalsystem are incorrect. Finally, for a special case, we providean analytic correction that recovers correct factor variancesfrom those incorrectly estimated by PCA.

Robert G. TompkinsFrankfurt School of Finance and [email protected]

Dimitri ReiswichFrankfurt School of Finance & [email protected]

CP3

Most-Likely-Path Approximation of Option Priceson the Arithmetic Average in Local Volatility Mod-els

We address the problem of approximating the price of op-tions on the discrete arithmetic average of the underlyingin local volatility models, specifically Asian options andvariance options. We assume that such options are writtenon the average of the underlying sampled at equally spaceddiscrete time points before expiry. The application of theheat kernel expansion for the transition density betweenconsecutive sampling time points with the aid of Laplaceasymptotic formula leads to a “path-integral” type expres-

sion for option prices. In the limit as the sampling timewindow approaches zero under this formalism, we end upwith a constrained variational problem of finding an opti-mal path in time-price space; an approximation of the op-tion price is obtained once the variation problem is solved.This optimal path is reminiscent of, and actually inspiredby, earlier most-likely-path approximations such as the onepresented in Gatheral’s book “The Volatility Surface”. Wewill conclude by presenting results of numerical tests of ourapproximation.

Tai-Ho WangBaruch College, [email protected]

Jim GatheralBaruch [email protected]

CP3

Fx Volatility Smile Construction

The foreign exchange options market is one of the largestand most liquid OTC derivative markets in the world. Sur-prisingly, very little is known in the academic literatureabout the construction of the most important object in thismarket: The implied volatility smile. The smile construc-tion procedure and the volatility quoting mechanisms areFX specific and differ significantly from other markets. Wegive a detailed overview of these quoting mechanisms andintroduce the resulting smile construction problem. Fur-thermore, we provide a new formula which can be used foran efficient and robust FX smile construction.

Uwe WystupFrankfurt School of Finance & ManagementMathFinance [email protected]

Dimitri ReiswichFrankfurt School of Finance & [email protected]

CP4

Fair Value of Equity-Linked Polices with StochasticInterest Rate

Pricing of an equity linked policy with surrender optionbefore maturity date under stochastic interest rate is stud-ied here by computation of a derived PDE model. Thesurrender option makes the policy American style. Pricingis conducted by method of lines with spatial discretizationthrough finite difference and integration in time by ODEsolver RK23. Early exercise of surrender option can be de-tected in the ODE solver and price can be evaluated then.

Tzyy-Leng HorngDepartment of Applied MathematicsFeng Chia [email protected]

CP4

Minimizing the Probability of Lifetime Ruin underStochastic Volatility

We assume that individuals invest in a financial market

30 FM10 Abstracts

with one riskless and one risky asset, with the latter’s pricefollowing a diffusion with stochastic volatility. In currentfinancial market especially, including stochastic volatilityin the risky asset’s price process is important. Given therate of consumption, we find optimal investment strategyfor individuals who wish to minimize the probability ofgoing bankrupt. To solve this minimization problem, weuse techniques from stochastic optimal control.

Xueying Hu, Erhan Bayraktar, Virginia YoungUniversity of MichiganDepartment of [email protected], [email protected], [email protected]

CP4

Bringing Focus to Fuzzy Real Options

Fuzzy numbers have recently been introduced in the realoptions literature as a simple alternative to option valu-ation. However, so far the assumption that the projectvalue is a fuzzy number has not been put on solid theoret-ical ground. Here, we demonstrate how projects which aredriven by a Geometric Brownian motion can lead to trian-gular profiles. The GBM acts as a market indicator is notdirectly traded, however, it is assumed strongly correlatedto a tradable index. By utilizing the minimal entropy mar-tingale measure, we value the real option in a theoreticallysound manner.

Sebastian JaimungalUniversity of Toronto, [email protected]

Yuri LawryshynUniversity of [email protected]

CP4

No-remorse Principles for Real Options

We give short proofs of general theorems about optimal en-try and exit problems in Levy models, when payoff streamsmay have discontinuities and be non-monotone. As appli-cations, we consider exit and entry problems in the theoryof real options, entry problem with an embedded option toexit, and problems with ambiguity and strategic interac-tions. We demonstrate a non-trivial impact of jump un-certainty and ambiguity on the investment threshold.

Svetlana BoyarchenkoUniversity of Texas at [email protected]

Sergei LevendorskiiUniversity of [email protected]

CP4

Worst Case Scenario Portfolio Optimisation andOptimising Reinsurance

The worst–case scenario portfolio problem which has beenintroduced by Korn and Wilmott (2002) will be consid-ered in this presentation. First, the portfolio optimisationproblem will be introduced and the main results will begiven. Second, the idea of the worst–case scenario will beapplied to an insurance company who wants to optimiseits reinsurance level. Usually, the reinsurance level will be

determined by a ruin probability constraint. It will be dis-cussed to which extend this constraint can be replaced bythe worst–case scenario approach. This research is jointwork with Ralf Korn (Kaiserslautern) and Mogens Stef-fensen (Copenhagen).

Olaf A. MenkensDublin City UniversitySchool of Mathematical [email protected]

CP4

Gambling When Broke: Optimal Risk-Taking Un-der Financial Distress

In this economy, it is anathema to say that is optimal formanagers to undertake risky investments under financialdistress. We show this by including distress costs into cashreserves represented by two different Brownian processes.Under arithmetic Brownian motion, it is optimal when dis-tress costs are extremely high. Under a mixed geometric-arithmetic Brownian process, it is optimal when productiv-ity of financial capital gets sufficiently large. Capital pro-ductivity is represented by an exponent to the multiplica-tive term appended to geometric Brownian motion.

Arnav ShethSaint Mary’s College of [email protected]

Larry Shepp, Oded PalmonRutgers [email protected], [email protected]

CP4

Maximizing the Utility of Consumption with Re-versible Annuities

The purpose of this paper is to reveal the relation betweenthe reversibility of annuities and retirees’ reluctance to an-nuitize. To this end, we assume the existence of reversibleannuities, whose surrender charges are a fixed proportionof their purchasing values. We model a retiree as a utility-maximizing economic agent who can invest in a marketwith a risky and a riskless asset and who can purchaseand surrender reversible annuities. We define the wealthof an individual as the total value of her risky and risk-less assets; this value is required to be non-negative dur-ing her lifetime. We solve this incomplete market utilitymaximization problem via duality arguments and obtainsemi-analytical solutions. We find that the optimal annu-itization strategy depends on the size of the proportionalsurrender charge and that a lower proportional surrendercharge encourages annuitization. We also find that full an-nuitization is optimal when there is no surrender chargeor when the retiree is very risk averse. More surprisingly,we find that in the case when the proportional surrendercharge is larger than a critical value, an individual behavesas if annuities are not reversible at all. Numerical examplesare given to illustrate our results.

Ting WangUniversity of [email protected]

CP4

Optimal Non-Proportional Reinsurance Control

FM10 Abstracts 31

and Stochastic Differential Games

We study stochastic differential games between two insur-ance companies who employ reinsurance to reduce risk ofexposure. We consider competition between two compa-nies and construct a single payoff function of two compa-nies surplus processes. We describe the Nash equilibriumof the game and prove a verification theorem for a generalpayoff function. For the payoff function being the proba-bility that the difference between two surplus reaches anupper bound before it reaches a lower bound, the game issolved explicitly.

Xudong ZengShanghai University of Finance and [email protected]

CP5

Controlling Cascades on Dynamic Financial Net-works

The network of financial exposures that arise among finan-cial institutions is an important determinant of systemicrisk. Real and idealized network structures can be ana-lyzed to produce cascade statistics which quantify systemicrisk, and to estimate the effects of certain mitigations inlimiting the size of cascades. Such analyses take the net-work of institutional exposures as given: this assumption isespecially limiting when evaluating the effectiveness of po-tential mitigations, because those mitigations may changethe rules that govern network formation. A policy for man-aging systemic risk might operate in a way that invalidatesthe analysis upon which it was predicated. We examine thedynamics of the formation of exposures among financialinstitutions and their commercial customers by modelingthe creation and trading of contractual linkages. Contract-ing entities adjust the terms of contracts based on theirperceptions of market conditions and counterparty relia-bility. Over time the system adapts to engender and with-stand episodic default cascades. We then examine the ef-fect of parameters representing stabilization policies, suchas countercyclical capital requirements and central banklending terms, on the distribution of cascades and on thecapital costs to commercial customers. This analysis cre-ates a solid basis for policy recommendations by endog-enizing feedback between the rules imposed on the finan-cial system and the structure of financial interdependenciesthat emerge in consequence.

Walt E. Beyeler, Robert GlassSandia National [email protected], [email protected]

CP5

A Non-Zero-Sum Game Approach to ConvertibleBonds

Convertible bonds are hybrid securities that embody thecharacteristics of both straight bonds and equities. In thispaper, we investigate how to use a non-zero-sum gameframework to model the interaction between bondholdersand shareholders and to evaluate the bond accordingly.Mathematically, this problem can be reduced to a systemof variational inequalities. We explicitly derive a Pareto-optimal Nash equilibrium to the game.

Nan ChenThe Chinese University of Hong [email protected]

Min DaiDept of Math and Risk Management InstituteNational University of [email protected]

Xiangwei WanThe Chinese University of Hong [email protected]

CP5

Gradient Estimation and Mountain Range Options

This application of gradient estimation drawns from finan-cial engineering and explores several exotic derivatives thatare collectively known Mountain Range options. We em-ploy Monte Carlo simulation to price these options and de-veloping gradient estimates to study the sensitivities to un-derlying parameters, known as “the Greeks’. We find thatIPA and LR/SF methods are efficient methods of gradientestimation for Mountain Range products at a considerablyreduced computation cost compared with the commonlyused finite difference methods.

Andrew HallU.S. Military Academy at West [email protected]

Michael FuRobert H. Smith School of BusinessUniversity of [email protected]

CP5

The Impacts of Risk Aversion and Market Regimeson the Dynamic Hedging and Multiple Exercises ofAmerican Options

We study the problem of dynamically hedging a long po-sition in American options written on a non-traded assetin a regime-switching market. The option holder faces theidiosyncratic risk from the non-tradability of the underlyeras well as the unhedgeable regime-switching risk. Apply-ing the utility indifference pricing methodology, we deter-mine the holder’s optimal hedging and exercising strate-gies, and examine the non-trivial impacts of risk aversionand stochastic regimes on the holder’s policy.

Tim Siu-Tang LeungJohns Hopkins [email protected]

CP5

Static Hedging of Barrier Options in DiffusionModels: An Explicit Exact Solution

We solve the problem of static hedging of (upper) barrieroptions (we concentrate on up-and-out put, but show howother cases follow from this one) in models where the un-derlying is given by a time-homogeneous diffusion processwith, possibly, independent stochastic time-change. Themain result of our paper includes analytic expression for thepayoff of a (single) European-type contingent claim (whichpays a certain function of the underlying value at maturity,without any path-dependence), such that it has the sameprice as the barrier option up until hitting the barrier. Wethen consider some examples, including the Black-Scholes,CEV and zero-correlation SABR models, and investigatean approximation of the exact static hedge with two vanilla

32 FM10 Abstracts

(call and put) options.

Sergey NadtochiyOxford UniversityOxford-Man [email protected]

Peter CarrNYU Courant [email protected]

CP5

Effect of Incorporating Correlation Structure onPricing Mountain Range Options

This paper focuses on the effect of correlation on pricingan Everest option (pays based on the lowest performingstock) and an Atlas option ( call on the mean of a bas-ket from which best/worst performers are removed). Wefirst price using independent Geometric Brownian Motions;we then re-price, modeling correlation based on historicalreturns using various decomposition methods to provideinsight into the effect of including correlation structure inpricing mountain range options.

Scott T. Nestler, Andrew Hall, Alexander SpiegelU.S. Military Academy at West [email protected], [email protected],[email protected]

CP5

Hedging under Arbitrage

It is shown that delta hedging provides the optimal trad-ing strategy in terms of minimal required initial capitalto replicate a given terminal payoff in a continuous-timeMarkovian context. This holds true in market modelswhere no equivalent local martingale measure exists butonly a square-integrable market price of risk. A new prob-ability measure is constructed, which takes the place of anequivalent local martingale measure. In order to ensurethe existence of the delta hedge, sufficient conditions arederived for the necessary differentiability of expectationsindexed over the initial market configuration. The recentlyoften discussed phenomenon of “bubbles’ is a special caseof the setting in this paper. Several examples at the endillustrate the techniques described in this work.

Johannes K. RufColumbia [email protected]

CP5

A Hybrid Asymptotic Expansion Scheme: An Ap-plication to Long-Term Currency Options

This paper develops a hybrid asymptotic expansion schemegiving closed-form approximation for valuation of multi-factor European path-independent derivatives. We ap-ply it specifically to pricing long-term currency optionsunder a market model of interest rates and a stochas-tic volatility model with jumps of spot exchange rates.It also introduces a characteristic-function-based MonteCarlo simulation method with the expansion as a controlvariable. Finally, numerical examples shows effectivenessof our scheme.

Akihiko TakahashiGraduate School of Economics, the University of tokyo

[email protected]

Kohta TakeharaGraduate School of Economics, the University of [email protected]

CP6

The Integrated Correlated Variance As a StatisticalInverse Problem

We consider the inverse problem of option implied inte-grated variance in a Bayesian framework. We presenta method to estimate both the implied integrated vari-ance and the correlation between stock price and volatilityshocks, and discuss the problems and effect of noisy op-tion price data. We suggest possible applications of theimplied integrated variance: volatility derivatives, risk-neutral price densities and related option pricing, andhedging. The Bayesian approach provides not only esti-mates of the unknown of interest, but also information onthe reliability of these estimates.

Ruth KailaHelsinki University of [email protected]

CP6

Equilibrium Wind Hedge Contract StructuresThrough Stochastic Programming

Wind hedge contracts are a new way to help wind projectdevelopers secure financing and manage risks. In such acontract, a strike price of electricity and a quantity arespecified. We use Nash bargaining solutions to capturethe bargaining process between the two contract parties,and model it as a stochastic program, solved through thesample average approximation method. Sensitivity analy-sis is conducted with respect to volatility and parties riskaverseness.

Andrew L. Liu, Harikrishnan SreekumaranSchool of Industrial EngineeringPurdue [email protected], [email protected]

CP6

Consistent Estimator of Covolatility

We introduce the random lead-lag estimator (RLL) for theintegrated covolatility of a pair of assets traded nonsyn-chronously and observed with microstructure noise. Weobtain expressions for bias and variance of RLL under gen-eral assumptions and demonstrate that RLL is n1/3 con-sistent in the absence of noise. The rate is same if there isnoise and we use a subsampled version of RLL with properchoice of sampling frequencies. Method is applied to NAS-DAQ data.

Qiuyan XuAcademia Sinica, [email protected]

Rituparna SenUniversity of California at [email protected]

Changjie MaUniversity of California - Davis

FM10 Abstracts 33

[email protected]

CP6

Determining Clearing Prices for Coupled Day-Ahead Electricity Markets

The European power grid is divided into several marketareas connected by power lines with restricted transmissioncapacity. Hence supply and demand of adjacent areas cannot always be balanced. The goal of a day-ahead auction isto determine prices and cross border flow maximizing theeconomic surplus of all participants. In general electricitywill be transmitted from a low price to an high price area.A MIQP is used to model this challenge.

Johannes C. MullerUniversity of [email protected]

Sebastian PokuttaTechnische Universitat [email protected]

Alexander MartinUniversity of [email protected]

CP6

Time Series Analysis of Functional Data for TermStructure Modeling

We develop time series analysis of functional data, treat-ing the whole yield curve as a random realization from adistribution on functions. The method consists of Prin-cipal Components Analysis of Functional data and subse-quently modeling the principal component scores as vectorARMA. This provides a unified framework for studying thetime and maturity components of interest rates under oneset-up with few parametric assumptions. We compare ourforecasts to Diebold and Li (2006).

Rituparna SenUniversity of California at [email protected]

Claudia KlueppelbergTechnische Universitat [email protected]

CP6

Hedge Funds Regulation and Systemic Risk Con-trol

Contrast to regulated Mutual Funds, Hedge Funds are pri-vate and lightly regulated entities who are not obliged todisclose their activities to the general public. However,hedge funds risk taking activity using ways such as shortselling and excessive leverage and their increasingly cor-related strategies pose substantial threats to the fnancialstability of the great economy. We propose a simple frame-work which adopts the theory of acceptible risks and capi-tal requirements using the limited available data on hedgefunds, to control for risks at the fund level as well as ona systemic level. We model the risky cash ow assets lessthe liability (or Net Asset Value) directly using either aGaussian process or a Variance Gamma process and applythe method to demeaned NAV data on 3622 hedge funds

from Jan 2005 to April 2009. Funds are analysed for theirrequired capital and the value of the option to put lossesback to the taxpayer. A systemic approach with corre-lated largest market participants is also proposed. The 30largest funds of April 2009 with total Asset Under Man-agement over $620 Bn are studied with proposed systemiccapital charges to be held by the broad economy and cap-ital charges at the fund level accounting for the residualidiosyncratic risk component.

Yue Xiao, Dilip MadanUniv. of [email protected], [email protected]

CP6

A Unifying Approach to the Nonparametric Esti-mation of Risk Measures

This talk is concerned with the nonparametric estimationof risk measures. Fairly general results on the strong rateof convergence as well as on the asymptotic distribution ofplug-in estimates will be given. The results are very flexiblew.r.t. to both the underlying data and the estimator ofthe unknown distribution function. The statements on theasymptotic distribution rely on a version of the FunctionalDelta Method (FDM) which, in contrast to the classicalFDM, is suitable also for weighted empirical processes.

Henryk ZahleSaarland UniversityDepartment of [email protected]

CP6

Challenges of Trading Illiquid Natural Gas Options

With the boom of natural gas market, more financial re-quests are imposed on various locations, which are off mainhubs (e.g. Henry hub) and not tradable in exchange. Trad-ing derivatives, especially high-risk options, brings us prof-itable opportunities bearing new challenges. After exam-ining existing techniques to deal with non-liquid options,we will propose novel and practical solution for construct-ing the volatility surface and hedging options under thenatural gas context.

Wentao ZhaoConocoPhillips [email protected]

Kevin Kindallconocophillips companykevin.g.kindall@conocophillips

CP7

Pricing Cross-Currency Interest Rate Derivativeswith Target Redemption Features on GraphicsProcessing Units via a PDE approach

We present a GPU-based parallel pricing via a PDE ap-proach of exotic cross-currency interest rate derivatives,with strong emphasis on Power Reverse Dual Currency(PRDC) swaps with Foreign Exchange Target Redemption(FX-TARN) feature. The FX-TARN provision provides acap on the FX-linked PRDC coupon amounts, and once theaccumulated coupon amount reaches this cap, the under-lying PRDC swap terminates. By introducing an auxiliarystate variable to keep track of the total accumulated PRDC

34 FM10 Abstracts

coupon amount, over each period of the tenor structure,the valuation of a FX-TARN PRDC swap requires to solvea set of independent PDEs. Highly efficient GPU-basedparallel ADI finite difference methods are used for the so-lutions of these PDEs. Numerical examples illustrating theconvergence properties and the efficiency of the numericalmethods are provided.

Duy Minh DangDepartment of Computer ScienceUniversity of [email protected]

Christina ChristaraUniversity of [email protected]

Ken JacksonDept. of Computer ScienceUniversity of [email protected]

Asif LakhanyAlgorithmics [email protected]

CP7

Optimizing Market Value-at-Risk Computationson GPUs

The latest financial crisis has highlighted the need for moreresponsive market risk management systems and more per-vasive stress testing. While the microprocessor industryhas recently introduced transformative computing capa-bilities in the form of general-purpose graphics processingunits (GPUs), its potential for quantitative risk estimationis currently under-realized. This presentation explains howMonte-Carlo simulation based estimation approaches suchas Value-at-Risk (VaR) and Economic Capital (EC) can beoptimized to take advantage of the widely available GPUs.We describe a three-phase optimization approach to lever-age high performance numerical linear algebra routines, re-duce standard error and maximize the utilization of theunderlying resources of the GPU. We apply this approachto demonstrate (i) on-demand VaR estimation, scalable tothe group-wise portfolios of even the largest financial insti-tutions, and (ii) more pervasive stress testing by concurrentexecution of batches of EC estimates under different mod-eling assumptions. A reoccurring theme throughout thetalk will be the implications of the very latest advances inGPU technology on quantitative financial modeling.

Matthew F. DixonDepartment of Mathematics, UC [email protected]

Jike ChongUniversity of California, [email protected]

Kurt KeutzerEECS DepartmentUniversity of California, [email protected]

CP7

Price Sensitivity Estimation in the Hull-White

Short-Rate Model

This paper extends the likelihood ratio and the weakderivative techniques for price sensitivity estimation tothe short-rate model of Hull and White. Three problemsarise: (1) non-differentiable payoff functions depend onmodel-parameters. (2) Exotic options break down payoff-independency of both methods. (3) In contrast to eq-uity derivatives, the Delta and Gamma of an interest-ratederivative depend on the whole path. We propose solutionsto all the items.

Carlos Sanz Chacon, Eduard DubinGoethe University [email protected],[email protected]

CP7

A Robust Regression Monte Carlo Method forPricing High-Dimensional American-Style Options

We present a new regression-based Monte Carlo methodfor pricing multi-asset American-style options. The keyidea is to fit the model function for the continuation valueby robust regression. Moreover, we suggest a new tech-nique for calculating the coefficients of the model functionto decrease the number of basis functions and to enable theparallelization of our approach. In addition, we extend ear-lier results for variance reduction via importance sampling.We can improve convergence significantly.

Christian JonenUniversity of [email protected]

CP7

Order Book Dynamics and Price Impact

We study the price impact of order book events using theTAQ database for a large set of stocks. Our study re-veals a linear relation between order imbalance and pricechanges with a slope inversely proportional to the mar-ket depth. We argue that our linear price impact model,together with a scaling argument, implies the empiricallyobserved ”square-root” relation between price changes andaggregate traded volume measured in number of shares.

Arseniy Kukanov, Rama ContColumbia [email protected], [email protected]

Sasha StoikovCornell [email protected]

CP7

Discontinuous Galerkin Methods for Elliptic Par-tial Differential Equations with Random Coeffi-cients

This talk proposes two numerical methods for solving ellip-tic partial differential equations with random coefficients.The first approach transforms a stochastic problem into aparametrized one that is then discretized by the discon-tinuous Galerkin (DG) method. A priori error estimatesin the energy norm and L2 norm are derived. The secondapproach utilizes the Monte Carlo Discontinuous Galerkin(MCDG) method. The error bound in the stochastic andspace domain are both derived. Numerical simulations of

FM10 Abstracts 35

the MCDG method are tested on various meshes. Resultsshow that the nonsymmetric MCDG method is stable in-dependently of meshes and the value of the penalty pa-rameter. Symmetric and incomplete MCDG methods arestable only when the penalty parameter is large enough.Comparisons with the Monte Carlo finite element methodare presented for several test problems. As an application,the pricing of American options is discussed.

Kun LiuRice [email protected]

CP7

Regularized Robust Optimization Approach for thePortfolio Execution Cost Problem

Execution cost problem minimizes total cost and risk ofthe execution of a portfolio of risky assets over a fixednumber of periods. Execution cost is defined by (erro-neously estimated) price impact functions. One practiceto account for this uncertainty is to apply the robust op-timization methodology. Under this worst-case approach,the investor accepts a suboptimal trading strategy for thenominal problem to ensure that the solution performs rea-sonably well, when the data varies in an uncertainty set.There are two main concerns with such an approach: (1)it might be very sensitive to the specification of the un-certainty set, (2) it might be too conservative. We pro-pose a regularized robust optimization approach which hasbetter stability properties, and attempts to rectify thesetwo shortcomings; that is, given any uncertainty set forthe parameters, we construct a regularized uncertainty setby including a regularization constraint. The regulariza-tion constraint is a matrix inequality of the Hessian of theobjective function and a regularization parameter. An at-tractive aspect of our method is that the obtained solutionis not only robust to the potential estimation errors in theparameters of the price impact functions, but also is ro-bust to the possible changes in the specification of the un-certainty set. Regularization parameter controls diversityof the portfolio, degree of conservatism and the obtainedobjective value.

Somayeh MoazeniSchool of Computer ScienceUniversity of [email protected]

CP7

Numerical Methods for Highly Non-Linear Finan-cial Models

We are interested in strong convergence and almost surestability of numerical approximations to the solution ofstochastic differential equations (SDEs) with highly nonlin-ear coefficients. Our goal is to justify efficient Multi-levelMonte Carlo simulations for many of stochastic volatilityand interests rate models that do not satisfy standard as-sumptions required for strong convergence. In additionwe examine global almost sure asymptotic stability in thisnon-linear setting for considered schemes.

Lukas Szpruch

University of Strathclyde/ University of [email protected]

CP8

No-Arbitrage Pricing under Cross-Ownership

We generalize Merton’s asset valuation approach to sys-tems of multiple financial firms where cross-ownership ofequities and liabilities is present. The liabilities, which mayinclude debts and derivatives, can be of differing seniority.We derive equations for the prices of equities and recov-ery claims under no-arbitrage. An existence result and auniqueness result are proven. Examples and an algorithmfor the simultaneous calculation of all no-arbitrage pricesare provided.

Tom FischerInstitute of MathematicsUniversity of [email protected]

CP8

Stylized properties and risk management of creditdefault swaps

We study the stylized facts of 5-year CDS spreads in 2005-09 and find that CDS spread returns exhibit positive au-tocorrelations, heteroscedasticity and heavy tails. We alsofind evidence of common jumps across obligors while thosejumps do not necessarily relate to any credit events. Ob-serving that the commonly used affine models are not capa-ble to explain the stylized features, we propose an ARMA-GARCH type model which appears to have better riskmanagement performance.

Yu Hang KanIndustrial Engineering and Operations ResearchDepartmentColumbia University - New York [email protected]

Rama ContColumbia [email protected]

CP8

American Options and Callable Bonds un-der Stochastic Interest Rates and EndogenousBankruptcy

A new characterization of the American-style option is pro-posed under a very general multifactor Markovian and dif-fusion framework. The efficiency of the proposed pricingsolutions is shown to depend only on the use of a viablevaluation method for the corresponding European-style op-tion and for the transition density of the model’s statevariables. Under a Gauss-Markov stochastic interest ratessetup, these new American option pricing solutions areshown to be significantly more accurate than the approx-imations already available in the literature. This resultis also used to price callable corporate bonds under an en-dogenous bankruptcy structural approach, by decomposingthe option to call or default into a European put on thefirm value plus two early exercise premium components.

Joao Pedro V. NunesISCTE-IUL Business [email protected]

CP8

Pricing and Hedging in Affine Models with Jump

36 FM10 Abstracts

to Default

In this paper we analyze a general class of pricing mod-els for European equity derivatives where the risk-neutralstock prices, interest rates and default of stock are jointlydriven by an affine process. We extend the notion of a dis-counted moment generation function of the log stock priceto the case when the underlying can default and show thatit can be used for call option pricing using Carr-Madansmethod as well as for derivation of prices of power pay-offs. Other European payoffs can be approximated using amix of power payoffs and vanilla options. As we show theresults are superior compared to using only power payoffsor only vanilla options. Moreover, within the class of suchpricing models we determine those that are complete anddiscuss hedging by continuous trading in stock, corporateand government bonds as well as liquid vanilla options.The results are applied to the hedging of a variance swap.As a special case we consider Heston model with jump todefault and stochastic interest rates.

Alexander Wugalter, Patrick CheriditoPrinceton [email protected], [email protected]

MS1

Credit Valuation Adjustment (cva) and DynamicHedging: Experience Through the Crisis


Eduardo CanabarroMorgan [email protected]

MS1

Resilience to Contagion in Financial Networks


Rama [email protected]

MS1

Credit Default Swaps and Systemic Risk


Andreea MincaUniversite Pierre & Marie [email protected]

MS1

Counterparty Risk Management for Central Clear-ing Counterparties


Leandro [email protected]

MS2

The Electricity Bid Stack: Linking Coal, Gas,Power and Emissions Prices

The observed bidding behavior of power generators illus-

trates the clear link between the dynamics of underlyingfuel and emissions costs and resulting power prices. Thisrelationship allows us to build a bid stack based structuralmodel for both CO2 and electricity prices, which intuitivelycaptures important effects such as merit order changes andfuel switching. We analyze the resulting dependence struc-ture between the various energy prices, and the implica-tions for derivative pricing in these markets.

Michael CoulonPrinceton [email protected]

MS2

The Effect of Model Error on the Valuation andHedging of Natural Gas Storage

We study the effect of model error on the valuation andhedging of the natural gas storage real option. The modelerror that we consider is due to the assumed number offactors in a multifactor futures price model differing fromthe true number of factors. We find that model error hasa differential impact on the valuation and hedging of thereal option to store natural gas.

Nicola SecomandiCarnegie MellonTepper School of [email protected]

Guoming LaiMcCombs School of BusinessUniversity of Texas at [email protected]

Francois Margot, Alan Scheller-Wolf, Duane SeppiTepper School of BusinessCarnegie Mellon [email protected], [email protected],[email protected]

MS2

Inventory and Forward Dynamics

What can one expect from risk-neutral price processes inwhich inventory is explicitly included as a state variable?Inventory impact on commodity price dynamics has been atopic of discussion for many decades, and a set of stylizedfacts have emerged from empirical observation. A varietyof modeling efforts have also been attempted to explainsome of these stylized facts with varying degrees of suc-cess. Valuation and hedging of many structured commodi-ties transactions, often in the near total absence of tradedcorrelation products, requires that particular attention bepaid to effects of inventory on volatility structure. Herewe show how a simple inventory based forward model canyield a surprisingly wide variety of returns distributions,and contrast the implications of this model to both empir-ical observations and commonly used pricing models.

Glen SwindleManaging [email protected]

MS2

Semi-Lagrangian Timestepping for Gas Storage

FM10 Abstracts 37

Problems

Stochastic dynamic programming approaches for the val-uation of natural gas storage, and the determination ofthe optimal continuous-time injection/withdrawal strategy,give rise to HJB P(I)DEs which are typically solved us-ing finite differences [Thompson et. al., 2009 and Chenand Forsyth, 2007] achieving first-order convergence tothe viscosity solution. This talk will show how to for-mulate a semi-Lagrangian approach that can generate asecond-order accurate discretisation, providing efficiencygains over existing approaches.

Antony WareUniversity of [email protected]

MS3

Modeling Trade Duration and Price Innovations forHigh Frequency and Algorithmic Trading

Using a hidden Markov model to capture the dynamicsof duration and price revisions, we argue that high fre-quency traders (HFT) profit from liquidity incentives (re-bates) in certain regimes and from trading algorithms inothers. Regimes are characterized by the duration betweentrades and the statistical properties of price revisions whichare then used to drive a Marked Point Process for assetprices. Model parameters are estimated before and afterHFTs came into the market.

Alvaro CarteaUniversidad Carlos [email protected]


MS3

High Frequency Traders and Asset Prices

We derive the distribution of transaction prices in limitorder markets populated by low frequency traders (LFT)before and after the entrance of a high frequency trader(HFT). In the presence of the HFT that distribution hasmore mass around the center and thinner far tails. Weshow that the HFT makes positive expected profits by“sniping’ out LFT orders , and that the faster LFT’s sub-mit and vary their orders, the more profits the HFT makes.The model predicts that in the time of crisis the HFT pro-vides less liquidity

Jaksa CvitanicUniversity of Southern [email protected]

MS3

The Dynamic Mixed Hitting-Time Model for Mul-tiple Transaction Prices and Times

We propose a structural model for durations betweenevents and associated marks. We model the durations asthe successive passage times of an underlying Brownianmotion relative to in itself random boundaries. Multivari-ate Brownian motions allow us to incorporate a vector ofasset returns (the marks) combined with a single durationgenerating process. Our model, applied to high-frequencyfinancial data, embeds the standard autoregressive condi-

tional duration models in a multivariate structural settingwith GARCH effects.

Eric RenaultUniversity of North Carolina, Chapel [email protected]

Thijs van der Heijden, Bas J.M. WerkerTilburg [email protected], [email protected]

MS3

Estimation of Jump Tails

We propose non-parametric framework for estimating jumptails of discretely-observed Ito semimartingales. The ap-proach is based on a set of estimating equations associ-ated with the compensator for the jump measure that onlyutilizes assumption of regular variation in the jump tails,along with in-fill asymptotics for identifying the jumps.The estimation allows for general dynamic dependenciesin the jump tails, and does not restrict the continuous partof the process.

Viktor TodorovKellogg School of ManagementNorthwestern [email protected]

Tim BollerslevDuke [email protected]

MS4

Investment Strategies Under Atlas Models

We study Atlas-type models of equity markets with localcharacteristics that depend on both name and rank, and inways that induce a stability of the capital distribution. Er-godic properties are examined with reference to the theoryof reflected Brownian motions in polyhedral domains andalso of the corresponding adjoint differential operators. Inthe context of such models, we discuss various investmentstrategies, including the so-called growth-optimal and uni-versal portfolios.

Tomoyuki IchibaUniversity of California, Santa BarbaraDepartment of [email protected]

Vassilios Papathanakos, Adrian Banner, IoannisKaratzas, Robert [email protected], [email protected],[email protected], [email protected]

MS4

Inferring Preferences from Agents’ Choices

We pursue an inverse approach to utility theory: instead ofspecifying agent’s utility function and deriving her actions,we assume we observe her actions (i.e. her consumptionand investment strategies) and derive utility function forwhich the observed behaviour is optimal. This is done ina one-period model and in continuous time both in a de-terministic and stochastic setting. We typically find thatthe consumption and investment strategies have to satisfy

38 FM10 Abstracts

a consistency condition (e.g. a PDE) if they come from aclassical utility maximisation problem. We further showthat agent’s important characteristics such as attitude to-wards risk (e.g. DARA) can be directly deduced from herconsumption/investment choices.

Alexander CoxUniversity of [email protected]

David HobsonUniversity of [email protected]

Jan K. OblojUniversity of OxfordMathematical Institute and the Oxford-Man [email protected]

MS4

Optimal Investment with High-watermark Perfor-mance Fee

We consider the problem of optimal investment and con-sumption when the investment opportunity is representedby a hedge-fund charging proportional fees on profit. Thevalue of the fund evolves as a geometric Brownian motionand the performance of the investment and consumptionstrategy is measured using discounted power utility fromconsumption on infinite horizon. The resulting stochas-tic control problem is solved using dynamic programmingarguments. We show by analytical methods that the as-sociated Hamilton-Jacobi-Bellman equation has a smoothsolution, and then obtain the existence and representationof the optimal control in feedback form using verificationarguments. The presentation is based on joint work withKarel Janecek.

Mihai SirbuUniversity of Texas at [email protected]

MS4

Examples of Incomplete-market Equilibria in Con-tinuous Time


Gordan ZitkovicThe University of Texas at AustinDepartment of [email protected]

MS5



Jean Pierre FouqueUniversity of California Santa [email protected]

MS5

The Brazilian Financial System: Network Struc-ture and Systemic Risk Analysis

Using a unique data set of interbank exposures and capi-tal levels of Brazilian financial institutions, we show that

such banking networks may be modeled as directed scale-free networks with regularly-varying degree and exposuredistributions. We define two indicators of the systemic riskgenerated by the failure of an institution - the Default Im-pact and the Contagion Index - and investigate the natureand magnitude of default contagion and systemic risk inthe Brazilian financial system.


Amal MoussaDepartment of Statistics, Columbia [email protected]

Edson Bastos e SantosBanco Central do [email protected]

MS5

The Most Likely Path to Systemic Failure


Richard SowersUniversity of Illinois at [email protected]

Kay GieseckeStanford Universitygiesecke @ stanford.edu

Konstantinos SpiliopoulosBrown Universitykonstantinos [email protected]

MS5

Entangled Financial Systems

This paper analyzes counterparty risk in systems wherebanks hedge risks using a network of bilateral over-the-counter contracts. If banks have large exposures to a fewcounterparties, they do not buy insurance against a lowprobability counterparty default even though it is sociallydesirable. This is because they do not take into accountthat their own failure also drags down other banks: anetwork externality. Mandatory counterparty insurance iswelfare improving.

Adam ZawadowskiBoston University School of [email protected]

MS6

A New Perspective on Commodity Market Models



MS6

Dynamic Bertrand Oligopoly

We study continuous time Bertrand oligopolies in which

FM10 Abstracts 39

a small number of firms producing similar goods competewith one another by setting prices. We analyze a static ver-sion of this game, then setup the nonzero-sum stochasticdifferential game and its associated system of HJB partialdifferential equations in the case of linear demand func-tions. We characterize certain qualitative features of thegame using an asymptotic approximation in the limit ofsmall competition. The equilibrium of the game is furtherstudied using numerical solutions.

Andrew LedvinaPrinceton [email protected]

Ronnie SircarORFEPrinceton [email protected]

MS6

Optimal Dynamic Hedging for a Large Investor inan Illiquid Market

The solution to Δdelta-hedging a European option in acomplete, Black- Scholes market is well known. We presentthe solution in the incomplete case when the agent faces aliquidity cost that is proportional to the size of his trad-ing. This is the situation faced by many large hedge fundswhose trades adversely affect market prices (‘slippage’).The trader’s objectivebalances his mean expected cost ofhedging against the variance of his mark-to-market port-folio at the end of a fixed trading horizon. This naturally-falls within the mean-variance framework of a QuadraticHamilton-Jacobi-Bellman Equation. In contrast to thecomplete case where the trader is ableto maintain a per-fect Black-Scholes Hedge, an agent facing a proportionalliquidity cost is generally mishedged and trades towardsbeing hedged. We derive a simple analytic solution for theagent’s trading intensity, which we and is proportional tothe degree of mishedge, inversely proportional to the liq-uidity cost, and increases towards the end of the tradinghorizon. We describe the effectiveness of our strategy us-ing numerical simulations with TAQ data and comment onits relation to a result of Garleanu and Pedersen on theMerton Problem in an illiquid market.

Tianhui LiPrinceton [email protected]

MS6

Exploration and Exhaustibility in DynamicCournot Games

Motivated by oligopolies in oil markets, we study the ef-fect of resource exploration in dynamic Cournot models.A producer may undertake costly exploration to replenishhis exhaustible reserves. We assume that new discoveriesoccur according to a Poisson process with intensity givenby the exploration effort. We treat both the case of a mo-nopolist and a duopoly game between the producer and aninexhaustible competitor. This leads to a study of systemsof nonlinear first order delay ODE’s. We derive asymp-totic expansions for the case of a small exploration rateand present numerical investigations.

Michael LudkovskiUC Santa [email protected]

Ronnie SircarORFEPrinceton [email protected]

MS7

Conditional Certainty Equivalent


Marco MaggisMilano [email protected]

MS7

External Risk Measures and Basel II Accord

We propose new data-based risk measures called naturalrisk statistics that are characterized by a new set of ax-ioms based on comonotonicity from decision theory. Nat-ural risk statistics include VaR with scenario analysis, inparticular Basel II risk measures, and other risk measuresproposed to address the procyclicality issue in Basel II, asspecial cases; therefore, we provide a theoretical frameworkto understand and to extend Basel II, if needed.

Xianhua PengHong Kong University of Science and [email protected]

Steven Kou, Chris C. HeydeColumbia [email protected], [email protected]

MS7

Risk Assessment for Cash Flows under Model andDiscounting Ambiguity

We study the risk assessment of uncertain cash flows interms of dynamic convex risk measures for processes as in-troduced in Cheridito, Delbaen, and Kupper (2006). Theserisk measures take into account not only the amounts butalso the timing of a cash flow. We discuss their robustrepresentation in terms of suitably penalized probabilitymeasures on the optional σ-field. This yields an explicitanalysis both of model and discounting ambiguity. We fo-cus on supermartingale criteria for time consistency. Inparticular we show how “bubbles” may appear in the dy-namic penalization, and how they cause a breakdown ofasymptotic safety of the risk assessment procedure.

Irina PennerHumboldt [email protected]

Beatrice AcciaioUniversity of [email protected]

Hans FollmerHumboldt-Universit”{a}t zu [email protected]

MS7

Dual Characterizations and Constructions for

40 FM10 Abstracts

Weakly Time Consistent Convex Risk Measures

We present characterizations of weak time consistency forconvex risk measures in terms of their dual representations.Then we derive several guidelines for the construction ofsuch risk measures. Forward in time, this involves a uniqueupdating rule for obtaining φt from a given φs with s <t. Backward in time, we analyse the rules that the dualrepresentation θs of φs must satisfy to guarantee weak timeconsistency, given a dual representation θt for φt.

Berend RoordaTwente [email protected]

MS8

Strict Local Martingale Deflators and PricingAmerican Call-Type Options

We solve the problem of pricing and optimal exercise ofAmerican call-type options in markets which do not nec-essarily admit an equivalent local martingale measure.This resolves an open question proposed by Fernholz andKaratzas [Stochastic Portfolio Theory: A Survey, Hand-book of Numerical Analysis, 15:89-168, 2009].


Kostas KardarasBoston UniversityDepartment of Mathematics and [email protected]

Hao XingBoston [email protected]

MS8

Optimal Stopping with Irregular Reward Functionsand Jumps

In this talk, we will examine optimal stopping problemswith bounded Borel-measurable reward functions for one-dimensional diffusions with compound Poisson jumps. Byidentifying the value function as a limit of a sequence ofvalue functions of optimal stopping problems for generaldiffusions, we extend recent results obtained for irregularreward functions on one-dimensional diffusions. Specifi-cally, we show the value function is continuous and canbe characterized as the unique solution of a variational in-equality in the sense of distributions.

Thomas J. EmmerlingUniversity of [email protected]


MS8

On Valuation Equations for Stochastic Volatility

Models

We study the valuation partial differential equation for Eu-ropean contingent claims in a general framework of stochas-tic volatility models, where the standard Feynman-KacTheorem cannot be applied because the diffusion coeffi-cients may degenerate on the boundaries of the state spaceand grow faster than linearly. We allow for various typesof model behavior; for example, the volatility process inour model can potentially reach zero and either stay thereor instantaneously reflect, and asset-price processes may bestrict local martingales under a given risk-neutral measure.Our main result is an extension of the standard Feynman-Kac Theorem in the context of stochastic volatility models.Sharp results on the existence and uniqueness of classi-cal solutions to the valuation equation are obtained usinga combination of probabilistic and analytical techniques.The role of boundary conditions is also discussed.

Hao XingBoston [email protected]


Constantinos KardarasBoston [email protected]

MS8

Optimal Stopping for Dynamic Convex Risk Mea-sures

We use martingale and stochastic analysis techniques tostudy a continuous-time optimal stopping problem, inwhich the decision maker uses a dynamic convex risk mea-sure to evaluate future rewards. We also find a saddle pointfor an equivalent zero-sum game of control and stopping,between an agent (the stopper) who chooses the termina-tion time of the game, and an agent (the controller, ornature) who selects the probability measure.

Song YaoUniversity of [email protected]


Ioannis KaratzasColumbia [email protected]

MS9

Riding on Smiles

This paper investigates the calibration performance of sev-eral multifactor stochastic volatility models. There is anempirical evidence that the dynamics of the implied volatil-ity surface is driven by several factors. This leads to theextensions of the seminal Heston stochastic volatility modelproposed by several authors. Using a data set of derivativeson the major indices we study the calibration properties ofthese models using the FFT as the pricing methodology.

FM10 Abstracts 41

We also study if adding jumps improves significantly thecalibration accuracy of the models. We compare the cal-ibration performance of those models over a large sampleperiod. We also focus on basket option pricing modelsand more precisely on the WASC model (Wishart AffineStochastic Correlation). We explain how to calibrate itand explain how it is related to the previous problem. Fi-nally, we provide some price approximations for vanilla op-tions that enlighten the properties of smile generated bythe Wishart stochastic volatility and the WASC models.What is more, it provides a simple way to relate differentmodels.

Jose Da FonsecaAuckland University of TechnologyDepartment of [email protected]

Martino GrasselliUniversity of [email protected]

MS9

Fast Calibration of Time Dependent Heston Modelwith Malliavin Calculus

Using a small volatility of volatility expansion and Malli-avin calculus techniques, we derive an accurate analyticalformula for the price of vanilla options for any time depen-dent Heston model (the accuracy is less than a few bps forvarious strikes and maturities). In addition, we establishtight error estimates. The advantage of this approach overFourier-based methods is its rapidity (gain by a factor 100or more) while maintaining a competitive accuracy. Fromthe approximative formula, we also derive some corollariesrelated first to equivalent Heston models and second, tothe calibration procedure in terms of ill-posed problems.

Eric BenhamouPricing [email protected]

Emmanuel GobetEcole [email protected]

Mohammed MiriPricing [email protected]

MS9

Discretization of Levy-Driven Stochastic Differen-tial Equations with Applications to the Levy LiborModel

We present new algorithms for weak approximation ofstochastic differential equations driven by pure jump Levyprocesses. The method is built upon adaptive discretiza-tion based on the times of large jumps of the driving pro-cess. Our technique avoids the simulation of the incrementsof the Levy process, and in many cases achieves better con-vergence rates than the traditional Euler scheme. To illus-trate the method, we discuss option pricing in the Libormarket model with jumps.

Peter Tankov

Ecole [email protected]

Arturo Kohatsu-HigaOsaka Universitykohatsu at [email protected]

MS9

High Order Numerical Schemes for Affine Pro-cesses with Applications

We present several high order weak numerical schemes foraffine processes (generalizing for instance the Ninomiya-Victoir scheme) which are derived by carefully consideringapproximations of the Riccati equations appearing in theFourier transform. Several examples, in particular fromthe theory of covariance matrix valued affine processes, areconsidered.

Josef TeichmannDepartment of MathematicsETH Z”[email protected]

MS10

Stochastic Volatility and Path-dependent Options:the Asian Case

In this talk we review recent result on extending the notionof local volatility to handle path-dependent claims. Wethen specialize to the case of Asian options. In this context,we present new results on weak uniqueness for degeneratediffusions with coefficients which are merely continuous.These results combine tools from the theory of singularintegrals on Lie groups with the localization machinery ofStroock and Varadhan.

Gerard BrunickUniversity of TexasDepartment of [email protected]

MS10

Recent Developments in Variance Contracts


Peter CarrNYU Courant [email protected]

MS10

Large and Small Strike Asymptotics of the ImpliedVolatility


Archil GulisashviliOhio [email protected]

MS10

Stochastic Volatility Modelling under Fast Mean

42 FM10 Abstracts

Reversion Regimes


Jorge P. [email protected]

MS11

An Efficient Unbiased SABR Model SimulationScheme

The Stochastic Alpha Beta Rho (SABR) stochastic volatil-ity model is widely used for the pricing of fixed incomeinstruments. In this presentation we deal with the dif-ficulties of the basic Euler scheme when simulating theSABR model, i.e. the possible negative rates, the martin-gale property and the discretization bias. We propose anunbiased time-discretization scheme for the SABR modelbased on careful analysis of its analytic properties. Ex-periments with realistic model parameters show that thisscheme is robust.

Bin ChenCWI [email protected]

MS11

Reduced Basis for Solutions of Black-Scholes Equa-tions with Jump Processes

We introduce a one dimensional Galerkin basis to numeri-cally solve parabolic partial (integro-)differential equationswhich arise in option pricing theory. Basis functions are de-signed on Black-Scholes solutions and this choice is drivenby the two main constraints: the numerical efficiency in thecomputation of the basis and of the Galerkin matrices andthe suitable global shape and correct asymptotic behaviourfor boundary condition. A convergence proof is given andnumerical tests are performed. The basis is tried also forcalibration of local volatilities.


Nicolas LantosNatixis CS BankUniversity of Paris [email protected]

Olivier PironneauUniversity of Paris VI (Pierre et Marie Curie)[email protected]

MS11

Pricing Inflation Products with Stochastic Volatil-ity and Stochastic Interest Rates

In this presentation we consider a Heston type inflationmodel, where we model the nominal and real interest ratesby a two-factor Hull-White model. We consider the casewith all the correlations being non-zero. For pension fundssuch an inflation model is for example important to deter-mine the value of conditional (future) indexations. Due tothe presence of the Heston dynamics our derived inflationmodel is able to capture the implied volatility skew/smilewhich is present in inflation option market data. In par-

ticular, we derive an efficient pricing formula of inflationdependent plain vanilla options. Using these pricing for-mulas we perform a calibration of the inflation model andcompare implied volatility surfaces.

Stefan [email protected]

Lech Aleksander GrzelakDelft University of [email protected]

David von [email protected]


MS11

Quantization Methods for Multiple Exercise Op-tions on GPGPU

The Quantization Tree algorithm has proven to be quitean efficient tool for the evaluation of financial derivativeswith non-vanilla exercise rights as Bermudan- or Swingoptions. Since this approach involves compute-intensiveMonte-Carlo simulations to estimate the transition proba-bilities for the underlying Markov process in the Quantiza-tion Tree, we present an efficient GPGPU implementationfor this problem, which reduces the computational timedramatically.

Gilles PagesUniversity of Paris [email protected]

Benedikt WilbertzUniversite Paris [email protected]

MS12

Liquidity and Risk Management: Crossing Net-works Impact

It is generally acknowledged that a spiraling feedback be-tween risk management and liquidity can arise: tighter riskmanagement leads to more restricted portfolios, resultingin illiquidity because of the need to engage in increasinglylarger transactions. In turn, the price impact of the latterinduces changes in values at risk. As an alternative tradingplatform with lesser price impact risk, crossing networks(a.k.a. dark pools) have experienced rapid growth overthe past few years. Though one of their disadvantages islonger time to execution, there is empirical evidence to sug-gest that they are particularly used when bid-ask spreadsare very large. In this paper I present a stochastic controlmodel that helps determine critical levels for bid and askprices beyond which value-at-risk related transactions arerouted through crossing networks that use the mid-pointsof national best bid and offer prices (NBBO).

Farid AitSahliaUniversity of [email protected]

FM10 Abstracts 43

MS12

Optimal Liquidation in Limit Order Books withStochastic Liquidity

We consider the problem of optimally placing market or-ders so as to minimize the expected liquidity costs frombuying a given amount of shares over a fixed period of time.The limit order book approach suggested by Obizhaevaand Wang (2006) is used to model the liquidity price im-pact. We add the following feature: The liquidity supplyand likewise the price impact coefficient are assumed to bedescribed by a stochastic differential equation instead ofbeing constant over time.

Antje FruthQuantitative Products LaboratoryTechnische Universitat [email protected]

Torsten SchonebornAHL ResearchMan Investments Ltd., [email protected]

Mikhail UrusovUniversity of [email protected]

MS12

Cetin-Jarrow-Protter Model of Liquidity in a Bi-nomial Market

The binomial version of CJP model of liquidity is investi-gated. The discrete- time super replicating cost convergesto the solution of a partial differential equation derived byCetin et al. in continuous-time. Hence, we show that theliquid- ity premium does not vanish in the limit. Moreover,efficient numerical methods are developed to compute thesuperreplicating cost and hedge. In particular, an up-and-out call option is studied.

Selim GokayETH [email protected]

Halil Mete SonerETH [email protected]

MS12

Continuous Equilibria with Heterogeneous Prefer-ences and Unspanned Endowments

We present a class of Brownian based models which pro-duce tractable incomplete equilibria. The models are basedon finitely many investors with heterogeneous exponentialutilities over intermediate consumption who receive par-tially unspanned income. The investors can trade continu-ously on a finite time interval in a money market account aswell as a risky security. Besides establishing the existenceof an equilibrium, our main result shows that if aggregateincome is not continuous over time the resulting equilib-rium can display a lower interest rate and a higher riskpremium relative to the usual Pareto efficient equilibrium.

Kasper LarsenDept. of Mathematical SciencesCarnegie Mellon [email protected]

MS13

Modeling the Forward Surface of Mortality

Longevity risk constitutes an important risk factor for in-surance companies and pension plans. For its analysis, butalso for evaluating mortality-contingent structured finan-cial products, modeling approaches allowing for uncertain-ties in mortality projections are needed. One model classthat has attracted interest in applied research as well asamong practitioners are forward mortality models, whichare defined based on forecasts of survival probabilities ascan be found in generation life tables and infer dynamicson the entire age/term-structure – or forward surface – ofmortality. However, thus far, there has been little guidanceon identifying suitable specifications and their properties.The current paper provides a detailed analysis of forwardmortality models driven by a finite-dimensional Brownianmotion. In particular, after discussing basic properties, wepresent an infinite-dimensional formulation, and we exam-ine the existence of finite-dimensional realizations for time-homogenous Gaussian forward models, which are shown topossess important advantages for practical applications.

Daniel BauerGeorgia State UniversityDepartment of Risk Management and [email protected]

Fred Espen BenthUniversity of [email protected]

Ruediger KieselUniversity of [email protected]

MS13



Carole BernardUniversity of [email protected]

MS13



Yi LuSimon Fraser University, [email protected]

MS13



Weidong TianUniversity of North Carolina at [email protected]

MS14

On the Least-Squares Monte Carlo Approach toBackward SDEs

Many option pricing and portfolio selection problems in

44 FM10 Abstracts

mathematical finance can be reformulated in terms of back-ward stochastic differential equations (BSDEs). As the cor-responding BSDE can rarely be solved in closed form, nu-merical algorithms for BSDEs are of prime importance. Inthis talk we will review some results on the least-squaresMonte Carlo approach for simulating BSDEs and discusssome practical matters such as choice of the basis func-tions, variance reduction, and how to check the ‘quality’ ofthe simulated solution.

Christian Bender, Jessica SteinerUniversitat des SaarlandesSaarbrucken, [email protected], [email protected]

MS14

Adjoint Techniques in Financial Models


Michael B. GilesMathematical InstituteOxford [email protected]

MS14

Numerical Speed-up Factors for Model Calibrationin SDEs


Christoph KabeHSH Nordbank Securities, [email protected]

MS14

Optimal Dynamic Hedging: A Double-HedgedMonte Carlo Method

The dynamic hedging of options with a bond and with theunderlying asset has been extensively studied in the past.In practice, however, options are often dynamically hedgedas well with some other financial instruments. We proposea least squares Monte Carlo method which allows to simu-late this. The method provides very low variance by locallyminimizing risk. Numerical results will be given. We hedgewith vanilla puts respectively with variance swaps.

Tobias LippLaboratoire Jacques-Louis LionsPierre and Marie Curie [email protected]

Gregoire LoeperBNP [email protected]

MS15

Optimal Order Execution

In this talk, we review various models of market impact.We use variational calculus to derive optimal executionstrategies, and show that in many conventional models,static strategies are dynamically optimal. We then presenta model in which the optimal strategy does depend on thestock price and derive an explicit closed-form solution forthis strategy by solving the HJB equation. We conclude byexploring the sensitivity of expected cost in this model to

the execution strategy. This is joint work with AlexanderSchied.

Jim GatheralBaruch [email protected]

MS15

On Credit Risk, First Passage Time Problems andHeat Polynomials

Motivated by a direct and inverse problem in credit risk, werelate the first hitting probabilities of diffusions to the so-called heat polynomials [Rosenbloom and Widder (1959)]and generalized Airy functions. We will present numericalexamples.

Gerardo Hernandez-del-ValleDepartment of StatisticsColumbia [email protected]

MS15

Optimal Liquidation in Dark Pools

We consider a finite time horizon, multi-asset optimal liq-uidation problem in discrete time for an investor havingaccess to both a traditional trading venue and a dark pool.Our model captures the price impact of trading in transpar-ent traditional venues as well as the execution uncertaintyof trading in a dark pool. We prove existence and unique-ness of optimal trading strategies for risk averse mean-variance-like traders and find that dark pools change opti-mal trading strategies and can significantly reduce tradingcosts. Their effect can be reduced by adverse selection andtrading restrictions.

Torsten SchonebornAHL ResearchMan Investments Ltd., [email protected]

Peter KratzHumboldt University [email protected]

MS15

Price Volatility as a Limit of Queuing Systems

We present a stochastic model for the bid and ask quotesof a traded asset. We describe methods for computing theprobability p(x, y) that the next price move is up, condi-tional on the bid (x) and ask sizes (y). We then define theefficient price to be a weighted average of the bid and theask prices, where p(x, y) is the weight applied on the askprice. The instantaneous volatility of this efficient pricemay be interpreted as as a microstructure-adjusted volatil-ity.

Sasha StoikovORIECornell [email protected]

Marco AvellanedaCourant InstituteNew York University

FM10 Abstracts 45

[email protected]

MS16

A Fourier-Based Valuation Method of Bermudanand Barrier Options under Heston’s Model

We present an efficient Fourier-based numerical methodfor pricing Bermudan and discretely monitored barrier op-tions under the Heston stochastic volatility model. Thetwo-dimensional pricing problem is dealt with by a combi-nation of a Fourier cosine series expansion, and high-orderquadrature rules in the other dimension. By a transfor-mation from the variance to the log-variance domain, wedeal with parameter sets that do not satisfy Feller’s condi-tion. Error analysis and experiments confirm a fast errorconvergence


Fang FangRabobank Internationalwellstone [email protected]

MS16

An Iterative Method for Pricing American OptionsUnder Jump-diffusion Models

An implicit finite difference method for the linear com-plementarity problem (LCP) formulation of American op-tions under jump-diffusion models leads to the solution ofLCPs with full matrices at each time step. We propose aniteration which solves a sequence of LCPs with the corre-sponding model without jumps at each time step. As theseLCPs are easier to solve and the iteration converges quicklythis gives an efficient way to price American options underjump-diffusion models.

Santtu SalmiUniversity of [email protected]

Jari ToivanenStanford [email protected]

MS16

A Front-fixing Finite Element Analysis of Ameri-can Options

In this talk, I will present our recent work in front-fixingfinite element methods for the valuation of American op-tions. The free boundary problems on unbounded domainswill be truncated to variable domain problems and thenconverted into nonlinear boundary value problems on rect-angular domains. Finite element methods and Newton’smethod will be employed to solve the nonlinear problemsnumerically. Stability and solution nonnegativity are es-tablished under some appropriate assumptions. Numericalresults are given to examine our methods and to comparethem with the other methods.

Hongtao YangUniversity of Nevada, Las [email protected]

MS16

Finite Element Methods for Option Pricing

We are concerned with finite element approximations tothe evaluation of American options. Following W. Alle-gretto etc, SIAM J. Numer. Anal. 39 (2001), 834–857, weintroduce a novel practical approach to the discussed prob-lem, on the basis of which the sharp error estimates andthe superconvergence are presented. Moreover, the globalsuperconvergence result can be used to generate an efficienta posteriori error estimator. Some numerical examples areprovided to demonstrate our theoretical results.

Shuhua ZhangTianjin University of Finance and EconomicsTianjin, [email protected]

MS17

Calibration Problems in Option Pricing

We consider the problem of identifying volatility functionsin Black-Scholes type equations from market data. Start-ing from an overview on different approaches, we focus onan optimal control approach in a Lagrangian framework.A regularized cost functional is minimized over a suitableset of admissible volatilities. We present analytical resultson first- and second-order optimality as well as numericalresults.

Bertram DuringUniversity of [email protected]

MS17

Adjoint Based Calibration of Local Volatility Mod-els

In the past the use of adjoints has been quite successfulin the computation of Greeks. But adjoints are also veryuseful in the context of the calibration of various financialmodels using SDEs. However, in this talk we investigatethe pros and cons of the adjoint approach in the PDE basedcalibration of financial models. As an example we considerthe calibration of local volatility models applying Dupiresequation in a least squares setting.

Andre LoerxUniversitaet [email protected]

MS17

On-the-fly Bid/Ask-Vol Fitting with Applicationsin Model Calibration

The fitting of market bid/ask-quotes is a prerequisite forany type of model calibration. Since the quotes differin quality as well as quantity over timeslices and strikes,and are furthermore coupled by hundreds of arbitrage-constraints, the bid/ask-fitting is a nontrivial task. Inthis talk we will show that it is nevertheless possible tosolve the associated optimization problem on-the-fly, anddemonstrate the efficiency of the method in the calibrationof local stochastic volatility models.

Jan H. [email protected]

46 FM10 Abstracts

MS17

Calibration with Model Reduction through POD

Option pricing models driven by Levy processes often leadto partial differential equations including an additional in-tegral term. Usually the solution of the resulting systemsof equation is quite expensive. In a calibration processmany of these similar problems have to be solved. Here,proper orthogonal decomposition - embedded in a well-defined trust region algorithm - can be used as a methodof model reduction with significant decrease of computingtime.

Matthias SchuUniversitat [email protected]

fm10 abstracts · in this talk, we present a recent methodology based on stochastic analysis to...

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