126 FM12 Abstracts - Society for Industrial and Applied ... · Simulation Schemes for Stopped Lvy...

126 FM12 Abstracts

IC1Optimal Execution in a General One-Sided LimitOrder Book

We construct an optimal execution strategy for the pur-chase of a large number of shares of a financial asset overa fixed interval of time. Purchases of the asset have a non-linear impact on price, and this is moderated over time byresilience in the limit-order book that determines the price.The limit-order book is permitted to have arbitrary shape.The form of the optimal execution strategy is to make aninitial lump purchase and then purchase continuously forsome period of time during which the rate of purchase isset to match the order book resiliency. At the end of thisperiod, another lump purchase is made, and following thatthere is again a period of purchasing continuously at a rateset to match the order book resiliency. At the end of thissecond period, there is a final lump purchase. Any of thelump purchases could be of size zero. A simple condition isprovided that guarantees that the intermediate lump pur-chase is of size zero. This is joint work with GennadyShaikhet and Silviu Predoiu.

Steven E. ShreveCarnegie Mellon UniversityDept of Mathematical [email protected]

IC2Stable Diffusions With Rank-based Interactions,and Models of Large Equity Markets

We introduce and study ergodic diffusion processes inter-acting through their ranks. These interactions give rise toinvariant measures which are in broad agreement with sta-bility properties observed in large equity markets over longtime-periods. The models we develop assign growth ratesand variances that depend on both the name (identity)and the rank (according to capitalization) of each individ-ual asset. Such models are able realistically to capturecritical features of the observed stability of capital distri-bution over the past century, all the while being simpleenough to allow for rather detailed analytical study. Themethodologies used in this study touch upon the questionof triple points for systems of interacting diffusions; in par-ticular, some choices of parameters may permit triple (orhigher-order) collisions to occur. We show, however, thatsuch multiple collisions have no effect on any of the sta-bility properties of the resulting system. This is accom-plished through a detailed analysis of collision local times.The models have connections with the analysis of Queue-ing Networks in heavy traffic, and with competing par-ticle systems in Statistical Mechanics (e.g., Sherrington-Kirkpatrick model for spin-glasses). Their hydrodynamic-limit behavior is governed by generalized porous mediumequations with convection, whereas limits of a differentkind display phase transitions and are governed by Poisson-Dirichlet laws.

Ioannis KaratzasColumbia [email protected]

IC3Simulation Schemes for Stopped Lvy Processes

Jump processes, and Lvy processes in particular, are noto-riously difficult to simulate. The task becomes even harderif the process is stopped when it crosses a certain boundary,

which happens in applications to barrier option pricing orstructural credit risk models. In this talk, I will presentnovel adaptive discretization schemes for the simulation ofstopped Lvy processes, which are several orders of magni-tude faster than the traditional approaches based on uni-form discretization, and provide an explicit control of thebias. The schemes are based on sharp asymptotic estimatesfor the exit probability and work by recursively adding dis-cretization dates in the parts of the trajectory which areclose to the boundary, until a specified error tolerance ismet.

Peter TankovUniversite Paris-Diderot (Paris 7)[email protected]

IC4Talk Title TBA - Avellaneda

Abstract not available at time of publication.

Marco AvellanedaCourant InstituteNew York [email protected]

IC5Optimal Order Placement in Limit Order Books


Xin GuoUniversity of California, [email protected]

IC6Quantitative Absence of Arbitrage and EquivalentChanges of Measure

It is well known that absence of arbitrage is a highly desir-able feature in mathematical models of financial markets.In its pure form (whether as NFLVR or as the existence ofa variant of an equivalent martingale measure R), it is qual-itative and therefore robust towards equivalent changes ofthe underlying reference probability (the ”real-world” mea-sure P). But what happens if we look at more quantitativeversions of absence of arbitrage, where we impose for in-stance some integrability on the density dR/dP? To whichextent is such a property robust towards changes of P? Wediscuss these questions and present some recent results.The talk is based on joint work with Tahir Choulli (Uni-versity of Alberta, Edmonton).

Martin SchweizerETH MathZurich, [email protected]

SP1AWM-SIAM Sonia Kovalevsky Lecture : The Roleof Characteristics in Conservation Laws

Sonya Kovalevsky, in the celebrated Cauchy-Kovalevskytheorem, made clear the significance of characteristics inpartial differential equations. In the field of hyperbolicconservation laws, characteristic curves (in one space di-mension) and surfaces (in higher dimensions) dominate thebehavior of solutions. Some examples of systems exhibit

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interesting, one might even say pathological, characteristicbehavior. This talk will focus on ways that characteristicsin systems of conservation laws give information about thesystems being modeled.

Barbara Lee KeyfitzThe Ohio State UniversityDepartment of [email protected]

SP2The John Von Neumann Lecture: Liquid Crystalsfor Mathematicians

Liquid crystals form an important class of soft matter sys-tems with properties intermediate between solid crystalsand isotropic fluids. They are the working substance of liq-uid crystal displays, which form the basis of a huge multi-national industry. The lecture will describe these fascinat-ing materials, and what different branches of mathematics,such as partial differential equations, the calculus of vari-ations, multiscale analysis, scientific computation, dynam-ical systems, algebra and topology, can say about them.

John BallOxford Centre for Nonlinear PDE Mathematical [email protected]

SP3Past President’s Address: Reflections on SIAM,Publishing, and the Opportunities Before Us

Upon taking up the post of president I had, of course, for-mulated my priorities for SIAM. This talk provides a goodoccasion to revisit some of those. One area turned outto play a vastly larger role than I would have anticipated,namely mathematical publishing and many issues associ-ated with it, ethical, technological, economic, political, andscientific. The future of scholarly publishing is far fromclear, but one thing seems certain: big changes are neededand will be coming. We, as mathematicians, are majorstakeholders. We should also be major agents in guidingthese changes. I will present some of my observations andthoughts as we confront the opportunities before us.

Douglas N. ArnoldSchool of MathematicsUniversity of [email protected]

SP4W. T. and Idalia Reid Prize Lecture: Large Alge-braic Properties of Riccati Equations.

In the eighties there was considerable interest in the alge-braic properties of the following Riccati equation

A∗X +XA−XBB∗X + C∗C = 0, (1)

where A, B, C ∈ A, a Banach algebra with identity, andthe involution operation ∗. Conditions are sought to ensurethat the above equation has a solution in A. The resultswere disappointing and the problem was forgotten untilthis century when engineers studied the class of spatiallydistributed systems. One application was to control forma-tions of vehicles where the algebraic property was essential.This case involves matrices A, B, C with components in a

scalar Banach algebra. Positive results are obtained forboth commutative and noncommutative algebras.

Ruth CurtainUniversity of Groningen, [email protected]

SP5I.E. Block Community Lecture: Creating Reality:the Mathematics Behind Visual Effects

Abstract to follow.

Robert BridsonUniversity of British [email protected]

SP6SIAG/FME Junior Scientist Prize: Market-BasedAapproach to Modeling Derivatives Prices

Most of the existing quantitative methods in Finance relyon the assumptions of the underlying mathematical mod-els. The problem of choosing the appropriate model as-sumptions is one of the cornerstones of modern FinancialEngineering. I am interested in developing modeling frame-works that facilitate the use of historical observations whenmaking the choice of model assumptions. It turns out that,in the markets with a large family of liquid derivative con-tracts, it is rather hard to construct a model that exploitsthe information contained in the historical prices of thesederivatives. In fact, constructing such models requires theuse of the so-called Market-Based Approach. The idea ofthis approach is to treat the liquid derivatives as genericfinancial assets and prescribe the joint evolution of theirprices in such a way that any future arbitrage-free combi-nation of prices is possible. In this presentation, I will out-line the main difficulties associated with the construction ofmarket-based models and will present a general methodol-ogy that bypasses these difficulties. Finally, I will illustratethe theory by describing (both mathematically and numer-ically) a family of market-based models for the Europeancall options of multiple strikes and maturities.

Sergey NadtochiyOxford UniversityOxford-Man [email protected]

JP1Systemic Risk

What is systemic risk, how do we model it, how to we an-alyze it, and what are the implications of the analysis? Iwill address these issues both in a larger historical contextand within current research mathematical finance. The keyproperty of systems subject to systemic risk is their inter-connectivity and the way individual risk can become over-all, systemic risk when it is diversified by inter-connectivity.I will discuss theoretical issues that come up with mean-field and other models and will also show results of numer-ical simulations.

George C. PapanicolaouStanford UniversityDepartment of [email protected]

128 FM12 Abstracts

CP1Pricing Interest Rate Derivatives in a MultifactorHjm Model with Time Dependent Volatility

We investigate the partial differential equation (PDE) forpricing interest rate derivatives in a multi-factor CheyetteModel, that involves time-dependent volatility functionswith a special structure. The high dimensional parabolicPDE that results is solved numerically via a sparse gridapproach, that turns out to be both accurate and efficient.The results are compared to the analytical solution forbonds and caplets and also the Monte Carlo simulationsolution for Bermudan Swaptions.

Ingo BeynaFrankfurt School of Finance & [email protected]

Carl ChiarellaProfessor, School of Finance and Economics, University ofTechnology, Sidney, Broadway NSW 2007, [email protected]

Boda KangUniversity of Technology [email protected]

CP1A Paradigm Shift in Interest-Rate Modeling

This research starts with a solution for modeling non-negative interest rates in an incomplete bond market. Itis the stochastic-splines model, in which instantaneous for-ward rates are almost surely finite and approximately log-normal under both the real-world and the risk-adjustedmeasures. A unique term structure of convenience yieldfor the default-free bond market is introduced for thefirst time to compensate idiosyncratic risk. Addressingon the market completeness issue, the stochastic-volatilitystochastic-splines model is presented whereby bond conve-nience yield vanishes. Under this framework, the marketprice of volatility risk can be computed endogenously. Var-ious applications are given.

Peter LinJohns Hopkins [email protected]

CP1Pricing Swaptions under Multifactor Gaussian HjmModels

Several approximations have been proposed in the liter-ature for the pricing of European-style swaptions undermultifactor term structure models. However, none of themprovides an estimate for the inherent approximation er-ror. Until now, only the Edgeworth expansion techniqueof Collin-Dufresne and Goldstein (2002) is able to char-acterize the order of the approximation error. Under amultifactor HJM Gaussian framework, this paper proposesa new approximation for European-style swaptions, whichis able to bound the magnitude of the approximation er-ror and is based on the conditioning approach initiated byCurran (1994) and Rogers and Shi (1995). All the pro-posed pricing bounds will arise as a simple by-product ofthe Nielsen and Sandmann (2002) setup, and will be shownto provide a better accuracy-efficiency trade-off than all the

approximations already proposed in the literature.

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

Pedro PrazeresSociedade Gestora dos Fundos de Pensoes do Banco [email protected]

CP1Pricing and Hedging the Smile with Sabr: Evi-dence from the Interest Rate Caps Market

This is the first comprehensive study of the SABR(Stochastic Alpha-Beta-Rho) model (Hagan et. al (2002))on the pricing and hedging of interest rate caps. We imple-ment several versions of the SABR interest rate model andanalyze their respective pricing and hedging performanceusing two years of daily data with seven different strikesand ten different tenors on each trading day. In-sampleand out-of-sample tests show that in addition to havingstochastic volatility for the forward rate, it is essential torecalibrate daily either the vol of vol or the correlation be-tween forward rate and its volatility, although recalibrat-ing both further improves pricing performance. The fullystochastic version of the SABR model exhibits excellentpricing accuracy and more importantly, captures the dy-namics of the volatility smile over time very well. Thisis further demonstrated through examining delta hedgingperformance based on the SABR model. Our hedgingresult indicates that the SABR model produces accuratehedge ratios that outperform those implied by the Blackmodel.

Tao L. WuIllinois Institute of Technologytw33 [email protected]

CP2Swing Options in Commodity Markets: A Modelwith Multidimensional Jump Diffusions

The objective of this talk is to study the optimal exercisepolicy of a swing option in the electricity markets. We for-mulate a model in terms of a stochastic control problemin continuous time, subjected to a total volume constraint.The underlying price process is a linear function depend-ing on a multidimensional Levy diffusion. The results areillustrated with examples.

Marcus ErikssonPh.D [email protected]

Jukka LempaCentre of Mathematics for ApplicationsUniversity of [email protected]

Trygve NilssenSchool of ManagementUniversity of [email protected]

CP2Decomposing the Risk from Investing in Foreign

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Commodities

Several papers show that FX rates and commodity pricesare interlinked. When investing in commodities traded ina foreign currency, the investor faces both price risk andFX risk. We investigate how exchange-traded contracts onWTI crude oil and EUR/USD correlate. We propose andestimate a model that accounts for the stochastic correla-tion between the two. This can be used to price and riskmanage foreign commodity positions, e.g., quanto optionsor oil-linked gas contracts.

Nina LangeCopenhagen Business [email protected]

CP2A Real-Time Pricing Model for Electricity Con-sumption

Input your abstract, including TeX commands, here. TheCalifornia electric company, i.e., PGE (Pacific Gas andElectric Co.,), has recently announced its intentions tocharge small businesses in the state with dynamic pricesfor electricity consumption. In this regard, we study areal-time electricity pricing model in the paper and com-pare it with two static pricing models. We show that real-time pricing outplays static pricing when it comes to jointlymaximizing provider and consumer welfare.

Ranjan PalUniversity of Southern [email protected]

CP2A Resampling Particle Filter Parameter Estima-tion For Electricity Prices With Jump Diffusion

In this paper we propose a particle ?lter for parameter es-timation of jump diffusion models employed for modellingelectricity prices 1,2,3,4,5. We consider a jump-diffusionmodel 4. The jumps has the possibility to give a better ex-planation of the behaviour of electricity prices, however es-timation of parameters becomes more complicated 4.Com-plications in parameter estimation will be introduced bythe inclusion of the jump component. The inclusion ofjumps will add several new parameters 4. These parame-ters will describe the jump frequency and distribution. Thejump models are non-Gaussian and this increases the com-plexity of the models 1,2,3,4. A known ?ltering techniquefor these models is particle ?lter 1,2,3. Particle ?lter (PF)is a fully non-linear ?lter with Bayesian conditional prob-ability estimation, compared here with the well-known en-semble Kalman lter (EnKF). A Gaussian resampling (GR)method is proposed to generate the posterior analysis en-semble in an effective and efficient way 3. The performanceof gaussian particle ?lter to model the jump frequency anddistribution parameters will be investigated and bench-marked to other maximum likelihood state estimators.

Bahri UzunogluGotland [email protected]

Dervis BayazitFederal Home Loan Bank of [email protected]

CP3Basket and Spread Options in a Variance GammaModel

Financial asset returns exhibit higher skewness and kurto-sis than those implied by the Normal distribution. Pricepaths can also exhibit jumps, which is particularly true foremerging and commodity markets. In this case, the Vari-ance Gamma (VG) process is more realistic than the geo-metric Brownian motion (GBM) to model the asset pricedynamics. However, valuation of basket and spread options(common derivatives in commodity, FX and other markets)under this model is a very challenging and time-consumingtask. We propose a novel and elegant method for valuationof basket and spread options under VG model, by condi-tioning the VG processes on a realization of the stochasticGamma time change and combining it with the GeneralizedLogNormal (GLN) approximation. We consider a simpler(and easily tractable) case of the identical stochastic timechange for all underlying assets, as well as the more gen-eral case of dierent (but dependent) Gamma time changes.Numerical study shows that the proposed method performsremarkably well in term of option pricing, even for a sim-pler model. Our method is intuitive, computationally veryfast, ecient and exible enough to allow for basket options onarbitrary number of assets and negative portfolio weights.

Svetlana BorovkovaVrije Universiteit [email protected]

CP3High-order Short-time Expansions for ATM Op-tion Prices Under the CGMY Model

In this presentation, we derive a novel second-order ap-proximation for ATM option prices under the CGMY Lvymodel, and then extend to a model with an addition Brow-nian motion. The third-order asymptotic behavior of theoption prices as well as the asymptotic behavior of the cor-responding Black-Scholes implied volatilities are also ad-dressed. Our numerical results show that in most casesthe second-order term significantly outperform the first or-der approximation.

Ruoting GongSchool of MathematicsGeorgia Institute of [email protected]

CP3Efficiently Simulating the Double-Barrier First-Passage Time in Jump-Diffusion Models

We present a fast and accurate Monte-Carlo simulationto obtain double-barrier first-passage time probabilities ina jump-diffusion model with arbitrary jump size distri-bution; extending single-barrier results by Metwally andAtiya [2002]. The presented algorithm is unbiased and sig-nificantly faster than a brute-force Monte-Carlo simulationon a grid. As an application, we discuss corridor bonus cer-tificates, floor certificates, and digital first-touch options.

Peter HieberUniversity of [email protected]

130 FM12 Abstracts

Lexuri FernandezUniversidad Autonoma de [email protected]

Matthias SchererTechnische Universitat MunchenChair of Mathematical [email protected]

CP3Numerical Solution of Jump-Diffusion SDEs

Jump-diffusions are ubiquitous in finance and economics.This paper develops, analyzes and tests a discretizationscheme for multi-dimensional jump-diffusion SDEs withgeneral state-dependent drift, volatility, and jump inten-sity function. Unlike conventional schemes, our schemeallows for an unbounded jump intensity–a feature of manystandard jump-diffusion models in credit, equity, FX andcommodity markets. The convergence of the discretizationerror is proved to be of weak order one. Numerical experi-ments illustrate our results.

Gerald TengStanford [email protected]

Kay GieseckeStanford UniversityDept. of Management Science and [email protected]

CP4Model Risk Based on the Distribution of the HedgeError

When pricing and hedging a derivative, we face model risk,that is, the risk of choosing the wrong dynamics for the fi-nancial market. We propose a measure of model risk basedon the hedge error that can be interpreted as a capitalcharge. This has several positive implications beyond esti-mating the riskiness of a claim in terms of model risk. Wecalculate these model risk measures for several examplesand derive its general properties.

Nils DeteringFrankfurt School of Finance and [email protected]

CP4Why Is It So Hard to Estimate Expected Returns?

A key part of experiment design is determining how muchdata to collect. When the data comes in the form of atimeseries, the sample size is expressed both by the countN of the observations and the duration T of the historicalperiod over which observations were made. For an assetwhose price has continuous sample paths, we demonstratethat the standard error of any unbiased estimator of theprice of risk is bounded below by 1/

√T .

John A. DodsonUniversity of MinnesotaCenter for Financial and Actuarial [email protected]

CP4A New Perspective on Dependence Within Finan-cial Markets

Many financial instruments are inherently multivariatein their origination. A rigorous empirical valuation re-quires simultaneous analysis of many components. Nonlin-ear and inter-temporal dependencies, extreme events, andlarge datasets introduce additional challenges. Indepen-dent component analysis is an indispensable tool for find-ing suitable representations of the complex multivariate in-formation within financial markets. We introduce a novelstatistical framework for independent component analysisof financial data and illustrate its use on several importantfinancial applications.

David S. MattesonCornell UniversityDepartment of Statistical [email protected]

CP4The Herd Behavior Index: a New Measure for theImplied Degree of Co-Movement in Stock Markets

We introduce a new measure for the implied degree ofherd behavior, one of the driving factors of systemic risk.This forward looking Herd Behavior Index (HIX) is model-independent and based on observed option data. As anillustration, we determine historical values of the 30-daysHIX for the Dow Jones Industrial Average.

David VynckeGhent UniversityDepartment of Applied Mathematics and [email protected]

Jan Dhaene, Daniel Linders, Wim SchoutensUniversity of [email protected],[email protected],[email protected]

CP5Incorporating Parameter Risk into DerivativesPrices - An Approach to Bid-Ask Spreads

We present a new method based on convex risk measures toincorporate parameter risk (e.g. estimation and calibrationrisk) into derivative prices. As an application we calculateparameter risk-implied bid-ask spreads of exotics, enablingus to compare the parameter risk of different models anddifferent exotics. Furthermore, we introduce a nonpara-metric calibration procedure to real bid-ask prices usingdistortion risk measures, compare our results to given para-metric distortion calibrations and present a new parametricfamily.

Karl F. Bannor, Matthias SchererTechnische Universitat MunchenChair of Mathematical [email protected], [email protected]

CP5Analytical Calculation of Risk Measures for Vari-

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able Annuity Guaranteed Benefits

With the increasing complexity of investment options in lifeinsurance, more and more insurers have adopted stochasticmodeling methods for the assessment and management ofinsurance and financial risks, with the most prevalent beingMonte Carlo simulation. In this paper we propose an al-ternative analytical method for the calculation of risk mea-sures for variable annuity guaranteed benefits. The tech-niques for analytical calculations are based on the study ofan integral of geometric Brownian motion as well as asymp-totic analysis of special functions. As we demonstrate bynumerous examples on quantile risk measure and condi-tional tail expectation, the numerical algorithms developedin this paper appear to be accurate and computationallyefficient.

Runhuan Feng, Hans W VolkmerUniversity of Wisconsin-MilwaukeeDepartment of Mathematical [email protected], [email protected]

CP5Fair Valuation of Drawdown Insurance

Drawdowns are path-dependent measures of risk and havebeen used extensively in the description of market crashes.We evaluate the market price of a market crash as mea-sured through drawdowns by considering an investor whowishes to insure herself against the risk of a market crashand does so by purchasing insurance claims against draw-downs. We further examine the fair valuation of drawdowninsurance in the possibility of early cancellation and iden-tify optimal cancellation strategies.

Olympia HadjiliadisGraduate Center of CUNY, New YorkBrooklyn College, [email protected]

Tim LeungDepartment of Operations Research and IndustrialEngineeringColumbia [email protected]

Hongzhong ZhangDepartment of StatisticsColumbia [email protected]

CP5Diversification and Crash-Protection Using Vari-ance Swap Calendar Spreads

Volatility can be also considered an asset class. Varianceswaps, one of the main investment vehicles, provide expo-sure to realized volatility. Implied volatility is often higherthan the realized volatility will turn out to be. We ex-plain how a variance swap calendar spread benefits fromboth negative risk premium and negative correlation withthe underlying stock index. Via backtesting we show howthe strategy added to a stock/bond portfolio significantlydiversifies crash risk.

Qixiang ZhouMathFinance [email protected]

Nils DeteringFrankfurt School of Finance and [email protected]

Uwe WystupMathFinance [email protected]

CP6Optimal Cash Holdings in a Firm

The precautionary principle of cash-holdings is empiricallywell analysed. However, the quantitative modelling of suchcash holdings is exceptionally sparse. This is due to thepath dependent nature of the problem and the fact thatcash holdings may both increase and decrease in time. Assuch, novel numerical solutions to the problem are required.We show how to model endogenous cash holdings within aFirms valuation and extract numerical solutions. In doingso we provide a solid basis by which Real Options analy-sis, dividend payments, debt issuance, cash holdings, andcorporate finance decisions (investments) can finally all beviewed in a consistent, non-contradictory and more realis-tic fashion. This analysis and need for consistency has beencalled for within many papers, and we hope our (economi-cally robust) approach shows how mathematics can providea more unifying approach to the theory of the Firm.

Paul V. Johnson, Geoff Evatt, Mingliang ChengUniversity of ManchesterSchool of [email protected],[email protected],[email protected]

CP6Risk Aversion and Managerial Cash-Flow Esti-mates in Real Options

While there are a number of academic papers discussingthe importance of accounting for risk aversion in real optionvaluation, none of them are applicable to discrete cash-flowestimates supplied by managers. Here, we develop an ap-proach which explicitly incorporates managerial cash-flowestimates and accounts for risk-aversion through indiffer-ence valuation. Interestingly, we find that the real optionvalue not only deteriorates as risk-aversion increases, itdrops to zero above a critical risk-aversion level.

Yuri LawryshynUniversity of [email protected]

CP6Irreversible Investment with Regime Switching :Revisit with Linear Algebra

We consider irrevesible investment problems with regimeswitching feature under a monopoly setting. Several pa-rameters describing the economic environment varies ac-cording to a regime switching with general number ofstates. We present the derivation of the value functionvia solving a system of simultaneous ordinary differentialequations with knowledge of linear algebra. It is found thatthe functional form of the value function depends on thedecomposition of a coefficient matrix.

Keiichi Tanaka

132 FM12 Abstracts

Tokyo Metropolitan [email protected]

CP6Embedded Currency Exchange Options in Roll-over Loans

In ship and aircraft financing long term roll-over loans areoften equipped with the right to change the currency everyquarter at spot. The loan taker then pays LIBOR of therespective currency plus a pre-determined constant salesmargin. If the capital outstanding exceeds 105% calcu-lated in the original currency, the amortization is requiredto the level of 105% of the original currency. By clever cur-rency management the loan taker can amortize the loanfaster and terminate the loan early. Essentially the loantaker owns a series of options on the cross currency ba-sis spread with unknown notional amounts. We determinethe key drivers of risk, an approach to valuation and hedg-ing, taking into consideration the regulatory constraintsof a required long term funding. We present a closed-formapproximation to the pricing problem and illustrate its sta-bility.

Uwe WystupFrankfurt School of Finance & ManagementMathFinance [email protected]

CP7Dynamic Quadratic Hedging in the Presence ofPartially Hedgeable Assets and Liabilities

We consider an incomplete market where an investor whoowns a partially hedgeable asset faces a liability at time T.The investor’s aim is to minimize the terminal replicationerror based on a quadratic loss criterion in this setting.We investigate the solution to the quadratic hedging prob-lem using the stochastic linear-quadratic optimal controlapproach through the corresponding (stochastic Riccati)BSDEs and provide some examples.

Coskun CetinCalifornia State University, [email protected]

CP7BSDEs with BMO Market Price of Risk

We study quadratic semimartingale BSDEs arising inpower utility maximization when the market price of risk isof BMO type. In a Brownian setting we provide a necessaryand sufficient condition for the existence of a solution butshow that uniqueness fails to hold in the sense that thereexists a continuum of distinct square-integrable solutions.This feature occurs since, contrary to the classical Ito rep-resentation theorem, a representation of random variablesin terms of stochastic exponentials is not unique. We studywhen the BSDE has a bounded solution and derive a newdynamic exponential moments condition which is shown tobe the minimal sufficient condition in a general filtration.The main results are complemented by several interestingexamples which illustrate their sharpness as well as impor-tant properties of the utility maximization BSDE.

Christoph FreiUniversity of [email protected]

Markus MochaHumboldt-Universitat zu [email protected]

Nicholas WestrayImperial College [email protected]

CP7A Continuous Time Bank Run Model for Insol-vency, Recovery and Rollover Risks

We propose a continuous time bank run model for incor-porating insolvency, recovery and rollover risks. The firmfinances by issuing both long and short term debt, and theshort term debt holders need to decide whether to roll overor to withdraw their debt (i.e. to run the bank) when theircontracts expire. We show there exists a threshold strat-egy (i.e. the bank run barrier) for the short-term creditorsto decide when to run. We decompose the total credit riskinto an insolvency component and an illiquidity componentbased on such an endogenous bank run barrier togetherwith an exogenous insolvency barrier. The short term debtin our model can have either a discrete tenor structure, ora more realistic staggered tenor structure. The problemis reduced to an optimal stopping time problem with con-straint, which is solved by the BSDE method.

Gechun LiangUniversity of [email protected]

CP7Quadratic Reflected Bsdes with Bounded Condi-tions. Application to American Options.

In this talk, I present an elementary and totally pertur-bative method for dealing with the well-posedness of somereflected BSDEs : existence, uniqueness and stability. Itworks for a smooth coefficient f which has a growth atmost quadratic in z, when the terminal condition as wellas the lower obstacle are bounded. I then connect theseequations with the problem of pricing american options inan incomplete market.

Arnaud LionnetOxford-Man Institute for Quantitative Finance,University of [email protected]

CP7A Simple Proof of BichtelerDellacherieMokobodzkiTheorem

We give a simple and quite elementary proof of the cel-ebrated BichtelerDellacherieMokobodzki Theorem, whichstates that a process is a good integrator if and only if it isa semi-martingale. Moreover we reformulate its statementin a way that -we believe- is more natural.

Pietro SiorpaesUniversity of Vienna (Universitat Wien)math [email protected]

Mathias BeiglbockUniversity of Vienna (Universitat Wien) math [email protected]

FM12 Abstracts 133

CP8Inference for the Fractional Heston Model Usingthe Auxiliary Particle Filter

The fractional Heston Model is a generalization of the Hes-ton Model obtained by replacing Brownian motion by frac-tional Brownian motion in the two equations that definethe Heston model. After defining the fractional Hestonmodel and showing its representation as a Dynamic statespace model, we will use that auxiliary particle filter bothto sample the volatility process and to update the posteriordistribution of the parameters sequentially as data arriveover time. We apply our approach to simulated and realdata with success. Keywords:- Fractional Heston Model,maximum likelihood estimation, particle filter, auxiliaryparticle filter, sequential Bayesian inference.

Muhannad Al-SaadonyUniversity of PlymouthUnited [email protected]

CP8Non-Parametric Calibration of the Local VolatilitySurface for European Options

Assuming the volatility surface is smooth, a second or-der Tikhonov regularization is applied to the calibrationproblem. Additionally a new approach for choosing theTikhonov regularization parameter is proposed. Using theTAPENADE automatic differentiation tool in order to ob-tain adjoint code of the direct model is employed as anefficient way to obtain the gradient of cost function withrespect to the local volatility surface. Finally we performfour numerical tests aimed at assessing and verifying theaforementioned techniques.

Jian GengDepartment of Mathematics Florida State [email protected]

Michael NavonFlorida State [email protected]

Xiao ChenLawrence Livermore National LaboratoryCenter for Applied Scientific [email protected]

CP8Small-time Asymptotics For Some StochasticVolatility Models

In the paper SMALL-TIME ASYMPTOTICS FORFAST MEAN-REVERTING STOCHASTIC VOLATIL-ITY MODELS they investigate two rates for the mean-reversion time δ in terms of the maturity ε, namely δ = εγ

for γ = 2, 4. Looking at this model and a few others wecharacterize the behaviors for γ > 2 and for 1 < γ < 2 andshow how this relates to Moderate Deviations and Super-large Deviations, respectively. This argument also showswhy γ = 2 is special.

Jerome Grand’maisonUniversity of Southern [email protected]

CP8Stochastic Calibration to Implied Volatility Sur-faces

This paper provides a two-step method to fully calibratethe implied volatility surface in the environment of ran-dom volatility. The first step consists of the Fourier trans-form method (Malliavin and Mancino (2009)) for estimat-ing model parameters of stochastic volatility models, andthe second step solves an optimization problem by meansof Monte Carlo simulation with variance reduction tech-niques. We compare fitting accuracies with the fast Fouriertransform method (Carr and Madan (1999)) and perturba-tion method (Fouque et al. (2003, 2011)). In addition, itis natural to generalize our calibration procedure to theimplied volatility surface of American options.

Chuan-Hsiang HanNational Tsing-Hua [email protected]

CP8Understanding Jumps in the High-Frequency VIX

This article provides a comprehensive nonparametric high-frequency analysis of jumps in the VIX (S&P500 volatilityindex). A comparison of the VIX and the S&P500 futurestime series (1992-2010) shows that 97% of jumps in the VIXare spurious. This finding not only leads to a new interpre-tation of the broadly used VIX dataset but also extends theliterature on volatility jumps and on the return-volatilityrelationship.

Inna KhagleevaUniversity of Illinois at [email protected]

CP8Implied Volatiltiy from Black-Scholes and OtherFormulas

We show that if the parameters of an arbitrary stock pricemodel are used in the Black-Scholes formula for calculatingoption prices for finitely many strikes, the implied volatility(a function of time t) will be bounded by a value whichdepends only on strikes. Our model-free results, which canbe used in calibration, provide sets of constraints limitingthe acceptable values of the implied volatility parameters.We use the Heston model for illustration.

Olivia MahMonash [email protected]

Kais Hamza, Fima KlebanerSchool of Mathematical SciencesMonash University, Clayton Campus Victoria [email protected], [email protected]

CP9Extensions of the Lt Method for Option Pricing

Monte Carlo (MC) and quasi-Monte Carlo (QMC) meth-ods are often used in pricing complex derivatives. Themerit of QMC is that, theoretically at least, higher conver-gence rates can be obtained than regular MC. The payofffunction is usually high-dimensional and non-smooth, elim-

134 FM12 Abstracts

inating the advantage of using QMC. Imai & Tan (2006)introduced the LT method which minimizes the effectivedimension of the problem by transforming the normal vari-ates using an orthogonal transformation, thereby improv-ing the QMC method. We extended their method for valu-ing options that have a barrier feature on an underlyingasset, incorporating and extending an idea from Staum &Glasserman (2001). These options have a payoff that de-pends on whether the asset does or does not cross a certainlevel during the life of the option. If the probability of (not)hitting is large enough, then much more paths have to besampled for reliable results. Our method greatly reducesthe required number of paths and our aim is to extend thismethod to Levy market models.

Nico [email protected]

Ronald Cools, Dirk NuyensDept. of Computer [email protected], [email protected]

CP9Variance Reduction for Monte Carlo Simulationof European Call Options Under the CoupledAdditive-Multiplicative Noise Model

We propose a variance reduction method for Monte Carlocomputation of option prices in the context of the Cou-pled Additive-Multiplicative Noise model. Four differentschemes are applied for the simulation. The methods selectcontrol variates which are martingales in order to reducethe variance of unbiased option price estimators. Numer-ical results for European call options are presented to il-lustrate the effectiveness and robustness of this martingalecontrol variate method.

Wanwan HuangFlorida State [email protected]

Brian EwaldDepartment of MathematicsFlorida State [email protected]

CP9Central Limit Theorem for the Multi-Level MonteCarlo Algorithm and Applications to Option Pric-ing

This paper deals with the problem of the multi-level MonteCarlo method, introduced by Giles (Multilevel Monte Carlopath simulation Operations Research, 2008; 56:607-617) asan extended method of the statistical Romberg one intro-duced by Kebaier (Romberg Extrapolation: A New Vari-ance Reduction Method and Applications to Option Pric-ing. Ann. Appl. Probab. 15 (2005), no. 4, 2681-2705).When approximating the expected value of a function ofa stochastic differential equation solution, these methodsimprove efficiently the computational complexity of stan-dard Monte Carlo. In this work, we analyze the asymp-totic error of this algorithm and establish a central limittheorem based on a new stable functionalcentral limit the-orem on the error in the Euler scheme for a given level.This allows us to obtain the optimal choice of the param-eters method.Then, weinvestigate the application of this

method to the pricing of Asian options. In this setting, theapproximation relies on the discretization of the integralof the price process over a time interval. We also analyzethe error process and prove a stable functional central limittheorem. Finally, We use our result in order to optimizethe choice of the parameters, which are different from theones in the Euler scheme. Numerical simulations were pro-cessed.

Ahmed Kebaier, Ben Alaya MohamedUniversity Paris [email protected], [email protected]

CP9A Hybrid Pricing Method for Options with MultiAssets

A numerical method is studied for options with multi-underlying assets. Instead of imposing artificial boundarycondition for the multi-dimensional Black-Scholes equa-tion, we calculate certain one-dimensional model equationat each time-step using pre-simulated Monte-Carlo timeseries. With standard finite difference method using ninepoint stencil, our method reduce the computational do-main of the governing equation (the two dimensional Black-Scholes equation) exceedingly. As benchmark tests, weconsider the call on the maximum option which has ananalytic solution, and a complicated structured note fromthe derivative market.

Yongsik KimDepartment of MathematicsYonsei [email protected]

Hyeong-Ohk BaeDepartment of Financial EngineeringAjou [email protected]

Tae-Chang JoInha [email protected]

CP9Control Variate Methods and Applications in Asianand Basket Options Pricing and Hedging underJump-Diffusion Models

We discuss control variate methods with applications toAsian and basket option pricing under exponential jumpdiffusion models for the underlying asset prices. We firstrevisit the single control variate method and then discussthe multivariate control variate method in detail. Con-ditions which ensure the variance of an m−variate con-trol variates is smaller than that of a k−variate controlvariates (1 ≤ k < m) are given and proved. Based onthese conditions, more efficient control variates can be con-structed. For arithmetic Asian and basket options, controlvariates conditional on geometric means of asset prices areconstructed. Numerical results show that the constructedcontrol variate is much more efficient than the classicalcontrol variate when pricing Asian options even in highdimensional cases.

Yongzeng LaiDepartment of MathematicsWilfrid Laurier [email protected]

FM12 Abstracts 135

Zhongfei LiLingnan (University) collegeSun Yat-Sen [email protected]

Yan ZengLingnan (University) CollegeSun Yat-Seng [email protected]

CP9Taylor-Like Anova Expansion for High DimensionalPdes Arising in Finance

The solution of high dimensional problems in short timeas well as with high precision is of great importance in fi-nance. For this purpose we propose an approximation toan ANOVA decomposition of the problem, which is only oflinear order in the dimension of the full problem and supe-rior in precision. We will call this approximation Taylor-like ANOVA. We develop this approximation up to higherorders and show its efficiency by numerical experiments.

Philipp SchroederGoethe Center for Scientific ComputingGoethe University [email protected]

Thomas GerstnerGoethe University [email protected]

Gabriel WittumGoethe Center for Scientific ComputingGoethe University [email protected]

CP10Optimal Order Routing in Limit Order Markets

When executing a trade, traders in electronic equity mar-kets can choose to submit a limit order or a market order,as well as the venue to submit this order, if the stock istraded in several exchanges. This decision is influenced bythe order flow characteristics and queue sizes in each limitorder book, as well as the structure of transaction fees andrebates across exchanges. We show that this optimal orderrouting problem may be formulated as a convex optimiza-tion problem and propose a stochastic algorithm for solvingit. We study this problem under various statistical assump-tions on the order flow and show the interplay between thefee structure, the order flow and the risk preferences of thetrader in determining the optimal routing decision.

Arseniy KukanovColumbia [email protected]

Rama ContCNRS (France) & Columbia [email protected]

CP10Optimal Trade Execution with Dynamic Risk Mea-sures

We propose a model for optimal trade execution in an illiq-uid market that minimizes a coherent dynamic risk of the

sequential transaction costs. The prices of the assets aremodeled as a discrete random walk perturbed by both tem-poral and permanent impacts induced by the trading vol-ume. We show that the optimal strategy is time-consistentand deterministic if the dynamic risk measure satisfies aMarkovian property. We also show that our optimal ex-ecution problem can be formulated as a convex program,and propose an accelerated first-order method that com-putes its optimal solution. The efficiency and scalability ofour approaches are illustrated via numerical experiments.

Qihang LinCarnegie Mellon UniversityTepper School of [email protected]

Javier PenaCarnegie Mellon [email protected]

CP10An Optimal Trading Rule under Switchable MeanReversion Market

This work provides an optimal trading rule that allowsbuying or selling of an asset whose price is governed bymean-reversion model. In the model, the equilibrium levelis controlled by an 2-state Markov chain. With the slippagecost imposed, the goal is to maximize the overall return.The value functions are characterized by considering theassociated HJB equations. This paper also shows that thesolution of the original optimal problem can be obtained bysolving four quasi-algebraic equations. Finally, numericalexamples are given for demonstration.

Duy NguyenUniversity of [email protected]

CP10Price Impact and Market Indifference Prices withPower Utilities

We investigate the price impact of large transactions in anequilibrium pricing model with HARA utility functions.A market maker trades with a large investor at a pricethat allows him to preserve his expected utility, the so-called market indifference price. In this setting we look atmarginal prices and illiquidity premia in comparison to theBlack-Scholes model as well as hedging and replication ofnon-traded (OTC) claims.

Nadim SahTU [email protected]

CP10A Self-exciting Point Process Model for Limit Or-der Books

The statistical properties of events affecting a limit or-der book -market orders, limit orders and cancellations-reveal strong evidence of clustering in time, significantcross-correlation across event types and significant depen-dence of the order flow on the bid-ask spread. We showthat these dependencies may be adequately represented bya multi-dimensional self-exciting point process, for whicha tractable parameterization is proposed. Using high-

136 FM12 Abstracts

frequency data from the Trades and Quotes database, weperform a Maximum Likelihood Estimation of the modeland assess its predictive performance for a variety of stocks.

Ekaterina VinkovskayaColumbia UniversityDept of [email protected]

Allan AndersenCopenhagen Business [email protected]

Rama ContCNRS, France, and Columbia [email protected]

CP10Evolutionary Game Dynamics Using a Non-Equilibrium Price Formation Rule for Trading withMarket Orders

Markets have dynamics that may result in excess volatilityand other phenomena that are a challenge to explain us-ing rational expectation models. Following Farmer (2002)and identifying trading strategies with species and capitalinvested in a strategy with a population, we use the repli-cator equation to identify the evolutionary game dynamicsbetween the relevant agents. We then extend the dynamicsspatially in order to examine the progression toward mar-ket efficiency caused by the evolution of capital. We ob-serve interesting dynamics including the phenomenon thatthe market becomes efficient as new strategies find themand cause them to disappear.

Gareth Q. WittenUniversity of Cape TownPontificia Universidad Catolica del Per, [email protected]

CP11On the Existence of Shadow Prices.

For utility maximization problems under proportionaltransaction costs, it is known that the original market withtransaction costs can sometimes be replaced by a friction-less shadow market that yields the same optimal strategyand utility. In this paper we present a counterexamplewhich shows that shadow prices may fail to exist. We thenprove that short selling constraints are a sufficient condi-tion for their existence, even in very general multicurrencymarket models with discontinuous bid-ask-spreads.

Giuseppe [email protected]

Luciano CampiParis 13 [email protected]

Johannes Muhle-KarbeDepartement MathematikETH [email protected]

Jan Kallsen

Kiel [email protected]

CP11Indifference Pricing with Uncertainty Averse Pref-erences

We consider the indifference valuation of an uncertain mon-etary payoff from the perspective of an uncertainty aversedecision-maker. We study how the indifference valuationdepends on the decision-maker’s attitudes toward uncer-tainty. We obtain a characterization of comparative uncer-tainty aversion and various characterizations of increasing,decreasing, and constant uncertainty aversion.

Flavia Giammarino, Pauline BarrieuLondon School of [email protected], [email protected]

CP11Portfolio Optimization Based on Independent Setsof Market Cliques

We consider the problem of selecting an optimal mar-ket portfolio that maximizes expected return and includeshighly correlated disjoint market cliques (i.e., memberswithin a clique are pairwise highly correlated) which arepairwise anticorrelated based on a correlation function de-fined on the set of cliques. We present integer program-ming models that can be effectively used to construct suchan optimal portfolio that satisfies given clique correlationthresholds.

Athula D. GunawardenaUniversity of [email protected]

Robert MeyerComputer Science DepartmentUniversity of [email protected]

Thisath KularatnaOptSolv [email protected]

Michael MonaghanBlackthorne Capital Management, [email protected]

Joseph HaskeUniversity of [email protected]

CP11Portfolio Optimization under Convex IncentiveSchemes

We consider the utility maximization problem of terminalwealth from the point of view of a portfolio manager paidby an incentive scheme given as a convex function g of theterminal wealth. The manager’s own utility function Uis assumed to be smooth and strictly concave, however theresulting utility function U ◦g fails to be concave. As a con-sequence, this problem does not fit into the classical port-folio optimization theory. Using duality theory, we provewealth-independent existence and uniqueness of the opti-mal wealth in general (incomplete) semimartingale markets

FM12 Abstracts 137

as long as the unique optimizer of the dual problem has acontinuous law. In many cases, this fact is independent ofthe incentive scheme and depends only on the structure ofthe set of equivalent local martingale measures. We pro-vide explicit examples for complete and incomplete marketmodels.

Stephan SturmORFE DepartmentPrinceton [email protected]

Maxim BichuchDepartment of Operations Research and FinancialEngineeringPrinceton [email protected]

CP11Optimal Portfolios for Hedge Funds and TheirManagers

Hedge fund managers receive fees proportional to profits,and may reinvest them. We find the fund and personalportfolio that maximize managers’ expected utility frompersonal wealth, when relative risk aversion is constant,and investment opportunities constant and separate, butcorrelated. Managers do not reinvest fees, allocating ex-cess personal wealth in Merton portfolio. But they man-age funds like Merton investors with risk aversion shrunktowards one. Managers do not hedge fund exposure withpersonal positions.

Gu WangBoston University, Department of Mathematics [email protected]

Paolo GuasoniBoston UniversityDublin City [email protected]

CP11An Equilibrium Approach to Utility-Based and In-difference Pricing

The utility-based and utility indifference pricing are frame-works for pricing contingent claims. Since these principlesare based on utility maximization principle, prices are op-timal for each investor with utility function. Our purposeis to expand these frameworks for deducing the equilib-rium price. Another purpose is to clarify the relationshipbetween utility-based and utility indifference framework.This discussion will be also done in the setting of the mar-ket with transaction costs.

Daisuke YoshikawaMizuho-DL Financial Technology co., [email protected]

Mark DavisImpreial College [email protected]

CP12Optimal Decumulation: An

Investment-Consumption Models for Retirees

We consider the optimal investment-consumption problemfor retirees with uncertain lifespan. We assume that theirinitial wealth can spread between both risky and riskless(liquid) investments and an income-producing (irrevoca-ble) life annuity with default risk. We examine whetherdefault risk (or the perception of default risk) rationallyaffects a retirees decision to purchase an annuity upon re-tirement. We formulate our problem as a Hamilton-Jacobi-Bellman equation and do a thorough numerical study forCRRA investors.

Jeffrey HumpherysBrigham Young [email protected]

David BabbelUniversity of PennsylvaniaWharton School of [email protected]

Craig MerrillBrigham Young UniversityMarriott School of Businesscraig [email protected]

CP12Voluntary Retirement and Annuity Contract

We consider an optimal financial planning problem of aneconomic agent who has an option to retire from laborvoluntarily. The economic agent with labor income deter-mines his/her investment strategy, consumption, and re-tirement strategy along with annuity. We investigate therelation between the annuity contract and the condition forthe voluntary retirement. We also analyze how the pres-ence of voluntary retirement option affects the purchase ofan annuity and the annuity market.

Minsuk KwakKorea Advanced Institute of Science and [email protected]

Yong Hyun ShinSookmyung Women’s [email protected]

CP12Bang-Bang Controls on Some Optimal InsuranceProblems

In this talk, we are interested in finding an optimal solutionfor a large class of optimal insurance problems. This classof problems includes those whose risks are measured byValue at Risk, Average Value at Risk, Conditional TailExpectation and law-invariant convex risk measures. Wehave found that Bang-Bang controls are optimal to all ofthem. This result also holds for multi-dimensional optimalinsurance problems such as those in adverse selections.

Siu Pang YungMath. Dept., University of Hong [email protected]

CP12Optimal Consumption and Portfolio Choice withLife Insurance under Uncertainty and Borrowing

138 FM12 Abstracts

Constraints

We develop a duality approach to study a family’s optimalconsumption, portfolio choice and life insurance purchasewhen the family receives deterministic labor income whichmay be terminated due to premature death or retirementof the family’s wage earner. The family faces a borrowingconstraint and the wage earner has an uncertain lifetime.We establish the existence of an optimal solution to theoptimization problem and solve the problem explicitly forseveral cases.

Xudong ZengShanghai University of Finance and [email protected]

CP12Optimal Dividend Payments for the Piecewise-Deterministic Compound Poisson Risk Model

This work deals with optimal dividend payment problemfor a piecewise-deterministic compound Poisson insurancerisk model. The objective is to maximize the expecteddiscounted dividend payout up to ruin time. When thedividend payment rate is restricted, the value function isshown to be a solution of the corresponding HJB equa-tion. For the case of unrestricted payment rate, the valuefunction and an optimal barrier strategy are determinedexplicitly with exponential claim size distributions.

Runhuan FengUniversity of Wisconsin-MilwaukeeDepartment of Mathematical [email protected]

Shuaiqi ZhangCentral South UniversitySchool of Mathematical Science and [email protected]

Chao ZhuUniversity of [email protected]

CP13On the Credit Risk of Secured Loans

We use stochastic control techniques to analyze the creditrisk of secured revolving loans, whose collateral cannot beliquidated immediately. The objective function is a trade-off between the expected loss due to a liquidation event andthe shortfall due to the borrower drawing on the credit lineless than the full amount available. We exhibit the lender’soptimal strategies and compare them with the standardLTV-based lending policy favored by practitioners.

Agnes TourinPolytechnic Institute of [email protected]

Fabian AsticMoody’s Investors serviceCredit policy/[email protected]

CP13Conditional Expected Default Rate Calculations

for Credit Risk Applications

Calculation of portfolio loss distributions for large numbersof correlated losses (e.g. credit risk applications) typicallyuse brute force Monte Carlo simulation. We use an asymp-totic probabilistic model based on the Central Limit The-orem for solving the portfolio risk aggregation problem forcredit risky portfolios. We then prove a theorem that en-ables efficient computation of the conditional expectationof the default rate for any subportfolio, conditioned on thetotal portfolio loss. This theorem enables us to solve thecapital allocation problem (using expected shortfall as therisk measure) without resorting to Monte Carlo simulation.The approach is very efficient, even for portfolios with sev-eral million positions.

Andrew BarnesGeneral ElectricGlobal Research [email protected]

CP13Measure Changes for Reduced-Form Affine CreditRisk Models

We consider a reduced-form credit risk model, with defaultintensity driven by an affine process. We fully character-ize the family of all locally equivalent probability measureswhich preserve the structure of the model, providing nec-essary and sufficient conditions on their density process.In particular, this allows for a rigorous treatment of dif-fusive and jump-type risk premia. As an application, wecharacterize the family of all risk-neutral measures for ajump-to-default Heston model.

Claudio FontanaUniversity of [email protected]

CP13Killed Brownian Motion with a Prescribed LifetimeDistribution and Models of Default

The inverse first passage time problem asks for some dis-tribution whether there is a barrier such that the first timea Brownian motion crosses the barrier has the given dis-tribution. We consider a ‘smoothed’ version of this prob-lem in which the first passage time is replaced by the firstinstant that the time spent below the barrier exceeds anindependent exponential random variable. We show thatany distribution results from some unique barrier.

Alexandru Hening, Steven Evans, Boris EttingerUC [email protected], [email protected], [email protected]

CP13Analysis of Recovery Rate of Non-Performing Con-sumer Credit

There have been more studies on recovery rate modeling ofbonds than on recovery rate modeling of personal loans andretail credit. Little to no research have been conducted onrecovery rates in non-performing retail credit with empha-sis on third-party buyers. From an empirical point of view,in order to analyze the recovery rate distributions acrossthe different industries, over nine million defaulted or non-performing consumer credit data provided by a German

FM12 Abstracts 139

debt collection company are used. A variety of statisticaland data mining methods will be examined with respect toprediction and classification. A two-stage model which firstclassifies debts as extreme or non-extreme with respect torecovery rate is applied; then, the extreme debts are clas-sified into full payment and non-payment. Moreover, thenon-extreme recovery rates are predicted in the entire unitinterval [0,1].

Markus HoechstoetterChair of Statistics, Econometrics and MathematicalFinanceKarlsruhe Institute of Technology (KIT), [email protected]

Abdolreza NazemiKarlsruhe Institute of Technology (KIT), [email protected]

Svetlozar T. RachevDepartment of Applied Mathematics at Stony BrookUniversityNew York, [email protected]

CASLAV BozicInformatics Institute, Faculty of Business Engineering,Karlsruhe Institute of Technology, [email protected]

CP13Maximum Likelihood Estimation for Large Inter-acting Stochastic Systems

Parameter estimation for a large system is facilitated byuse of the asymptotic SPDE to which the system weaklyconverges. Standard particle filtering methods are oftennot applicable for parameter estimation of the SPDE. Amethod of moments reduces the SPDE into an SDE sys-tem. We then develop a particle filtering method for theSDE system. Theoretical convergence of the finite sys-tem’s likelihood to the asymptotic likelihood is discussed.Important credit risk and mortgage applications motivatethe method.

Justin SirignanoStanford [email protected]

Gustavo SchwenklerStanford UniversityDep. of Management Science and [email protected]


MS1Price Dynamics in Limit Order Markets: LimitTheorems and Diffusion Approximations

We propose a queueing model for the dynamics of a limitorder book in a liquid market where buy and sell ordersare submitted at high frequency. We derive a functionalcentral limit theorem for the joint dynamics of the bid andask queues and show that, when the frequency of order

arrivals is large, the intraday dynamics of the limit orderbook may be approximated by a Markovian jump-diffusionprocess in the positive outhunt, whose characteristics areexplicitly described in terms of the statistical properties ofthe underlying order flow [Cont Larrard 2011]. This resultallows to obtain analytical expressions for the probability ofa price increase or the distribution of the duration until thenext price move, conditional on the state of the order bookand characterize various other quantities as solutions of el-liptic PDEs in the positive orthant [Cont Larrard 2012].Our results allow for a wide range of distributional and de-pendence assumptions in the orders and apply to a wideclass of stochastic models proposed for order book dynam-ics, including Poisson point processes, self-exciting pointprocesses [Cont, Andersen Vinkovskaya 2011] and modelsof the ACD-GARCH family.


Adrien DE LARRARDLaboratoire de Probabilites & Modeles AleatoiresUniversite Pierre & Marie Curie (Paris VI)[email protected]

MS1Information and the Value of Guaranteed TradeExecution

In many markets, uncertainty about whether a trade is ex-ecuted can be removed by paying a price premium. Weuse financial markets as a particular setting in which tostudy this trade-off. In particular, we assess the role ofinformation in the choice between certain trade at a pricepremium in an intermediated market such as a dealer mar-ket or a limit order book and contingent trade in a darkpool. Our setting consists of intrinsic traders and specula-tors, each endowed with heterogeneous fine-grained privateinformation as to an assets value, that endogenously decidebetween these two venues. We solve for an equilibrium inthis setting, and address three main questions: First, weillustrate how the choice between certain and contingenttrade depends on information available to an individualagent, as well as the overall distribution of informationacross all agents. Second, we analyze how the premium forcertain trade over contingent trade affects the strategic be-havior of traders. Finally, we demonstrate how the optionfor contingent trade affects the ability of intermediatingmarket makers to set transaction costs to maximize profit.

Krishnamurthy Iyer, Ramesh JohariStanford [email protected], [email protected]

Ciamac C. MoallemiColumbia [email protected]

MS1Mean-variance Optimal Adaptive Order Executionand Dawson-Watanabe Superprocesses

It is well-known that the mean-variance optimization ofadaptive order execution strategies is not dynamically con-sistent. By localizing the mean-variance criterion, one isled to the optimization of the mean versus quadratic vari-ation, which is a dynamically consistent stochastic controlproblem with fuel constraint. We show how this latter

140 FM12 Abstracts

problem can be solved by means of Dawson-Watanabe su-perprocesses.

Alexander SchiedUniversity of [email protected]

MS1Optimal Liquidation in a Limit Order Book

We consider an asset liquidation problem at the market mi-crostructure level, conditional on observing the limit orderbook. The optimization problem is formulated in terms ofa sequence of stopping times, at which we submit marketsell orders. We describe the shape of the trade and notrade regions for various assumptions on the price processand the latency of the trader. In the empirical section,we show that our optimal policy significantly outperformsa benchmark TWAP algorithm on US treasury bonds. Inaddition we can efficiently calculate the cost of latency inthe trade execution.

Sasha F. Stoikov, Rolf WaeberCornell [email protected], [email protected]

MS2Pricing a Contingent Claim Liability with Transac-tion Costs Using Asymptotic Analysis for OptimalInvestment

We price a contingent claim liability using the utility in-difference argument. We consider an agent, who investsin a stock and a money market account with the goal ofmaximizing the utility of his investment at the final timeT in the presence of a proportional transaction cost in twocases with and without the liability. In both cases, we pro-vide a rigorous derivation of the asymptotic expansion ofthe value function and obtain a “nearly optimal” strategy.Additionally, we derive the asymptotic price of the contin-gent claim liability.

Maxim BichuchDepartment of Operations Research and FinancialEngineeringPrinceton [email protected]

MS2Shadow Prices and Well Posedness in the OptimalInvestment and Consumption Problem with Trans-action Costs

We revisit the optimal investment and consumption modelof Davis and Norman (1990) and Shreve and Soner (1994),following a shadow-price approach similar to that ofKallsen and Muhle-Karbe (2010). Making use of the com-pleteness of the model without transaction costs, we re-formulate and reduce the HJB equation for this singularstochastic control problem to a free-boundary problem for afirst-order ODE with an integral constraint. Having shownthat the free boundary problem has a twicely differenciablesolution, we use it to construct the solution of the origi-nal optimal investment/consumption problem without anyrecourse to the dynamic programming principle. Further-more, we provide an explicit characterization of model pa-rameters for which the value function is finite.

Jin Hyuk Choi

Department of MathematicsUniversity of Texas at [email protected]

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

Mihai SirbuUniversity of Texas at [email protected]

MS2Optimal Investment with Small Transaction Costsand General Stochastic Opportunity Sets

For an investor with constant absolute risk aversion, we in-formally derive the first-order asymptotics of the optimalinvestment strategy as the bid-ask spread becomes small.For general Ito processes, the first order correction term isexpressed in terms of the quadratic variation of the friction-less optimizer. This result allows to quantify the impactof, e.g., predictability and stochastic volatility on portfo-lio choice in the presence of transaction costs. Appliedto an investor holding a random endowment, it also leadsto a generalization of the asymptotic utility-based hedgingstrategies determined by Whalley and Wilmott (1997) fora constant opportunity set. This is joint work with JanKallsen.


Jan KallsenKiel [email protected]

MS2The Optimal Use of Options to Reduce the Effectof Transaction Costs in a Portfolio

Options are redundant in a portfolio of cash and stock ifwe assume the market of Black and Scholes, which includesno transaction costs. When we include transaction costs,however, options, when used correctly, can become quiteuseful in reducing the ill-effects these costs create. Specif-ically, let ε represent the scale of a small proportional lossfrom any trade. Given an investor’s utility preference, theloss in expected utility due to transaction costs in a cash

and stock portfolio is, at best, O(

ε23

). However, by in-

cluding options in the portfolio, we can improve this to

O(

ε67

), which is much closer to the O (ε) loss guaranteed

by even one trade. We detail the specific optimal strategythat accomplishes this.

Dan OstrovSanta Clara [email protected]

Jonathan GoodmanCourant [email protected]

FM12 Abstracts 141

MS3Modeling and Simulation of Systemic Risk inInsurance-Reinsurance Networks

We propose a dynamic insurance network model that al-lows to deal with reinsurance counter-party default riskswith a particular aim of capturing cascading effects at thetime of defaults.An equilibrium allocation of settlements isfound as the unique optimal solution of a linear program-ming problem. This equilibrium allocation recognizes 1)the correlation among the risk factors, which are assumedto be heavy-tailed, 2) the contractual obligations, whichare assumed to follow popular contracts in the insuranceindustry (such as stop-loss and retro-cesion), and 3) theinterconnections of the insurance-reinsurance network. Weare able to obtain an asymptotic description of the mostlikely ways in which the default of a specific group of in-surers can occur, by means of solving a multidimensionalKnapsack integer programming problem. Finally, we pro-pose a class of provably strongly efficient estimators forcomputing the expected loss of the network conditioningthe failure of a specific set of companies.

Jose BlanchetColumbia [email protected]

Yixi SHIIEOR Dept, Columbia [email protected]

MS3Pricing of Path-Dependent Vulnerable Claims inRegime Switching Markets

We study pricing of path-dependent vulnerable claims inregime-switching markets. The key theoretical tool under-lying our results is a Poisson series representation of vulner-able claims, which we develop using a change of probabil-ity measure technique. We employ such a representation,along with a short-time asymptotic expansion of the claim’sprice in terms of the Laplace transforms of the symmetricDirichlet distribution, to develop an efficient method forpricing claims which may depend on the full path of the un-derlying Markov chain. The proposed approach is appliedto price not only simple European claims such as default-able bonds, but also a new type of path-dependent claimsthat we term self-decomposable, as well as the importantclass of vulnerable call and put options on a stock. Weprovide a detailed error analysis and illustrate the accuracyand computational complexity of our algorithms on mar-ket traded instruments, such as defaultable bond prices,barrier options, and vulnerable European options.

Agostino CapponiSchool of Industrial EngineeringPurdue [email protected]

Jose E. Figueroa-LopezPurdue [email protected]

Jeff NisenPurdue UniversityStatistics [email protected]

MS3Default and Systemic Risk in Equilibrium

In a finite horizon continuous time market model, we con-sider risk averse utility maximizers who invest dynamicallyin a risk-free money market account, a stock written ona default-free dividend process, and a defaultable bond.Prices are determined via equilibrium. We analyze conta-gion arising endogenously between the stock and the de-faultable bond via the interplay between equilibrium be-havior of investors, risk preferences, and cyclicality prop-erties of the default intensity. The equilibrium price ofthe stock experiences a jump at default, despite that thedefault event has no causal impact on the dividend pro-cess. We characterize the direction of the jump in termsof a relation between investor preferences and the cyclical-ity properties of the default intensity. A similar analysis isperformed for the market price of risk and investor wealthprocesses. The impact of heterogeneity of preferences onthe default exposure carried by different investors is alsoinvestigated.

Martin LarssonCornell [email protected]


MS3Filtered Likelihood for Point Processes

We develop likelihood estimators of the parameters of amarked point process and of incompletely observed ex-planatory factors that influence the arrival intensity alongwith the point process itself. The factors follow jump-diffusions whose drift, diffusion, and jump coefficients areallowed to depend on the point process. We provide condi-tions guaranteeing consistency and asymptotic normalityas the sample period grows. We also establish an approxi-mation to the likelihood and analyze the convergence andasymptotic properties of the associated estimators. Nu-merical results illustrate our approach.

Gustavo SchwenklerStanford UniversityDep. of Management Science and [email protected]


MS4Excursions in Atlas Models of Equity Market

Let us consider an equity market of finite number of stockswhere behavior of their capitalization is a multidimensionaldiffusion characterized with their rankings. Such model cancapture flows of market capitalizations as it was observedby Fernholz et al. In this talk we consider some questionson excursion measure and time-reversibility for these flowsof market capitalization with application to portfolio man-agement under such abstract equity market.

Tomoyuki Ichiba

142 FM12 Abstracts

University of California, Santa BarbaraDepartment of [email protected]

MS4Optimal Investment for All Time Horizons andMartin Boundary of Space-time Diffusion

I review the definition and basic properties of the forwardperformance processes, including their relation to the morestandard investment criteria, and the associated SPDEcharacterization. I, then, concentrate on the problem ofconstructing the forward investment performance processesin a Markovian setting. In this case, the problem reducesto the so-called ”forward Hamilton-Jacobi-Bellman equa-tion”, which, in some cases, can be transformed into a time-reversed linear parabolic equation. I characterize the so-lutions of this (ill-posed) problem explicitly, extending theclassical Widders theorem on positive solutions to the time-reversed heat equation. Finally, I consider closed-form ex-amples of the Markovian forward performance processesin some specific stochastic volatility models, including themean-reverting log-price (Schwartz) model.

Sergey NadtochiyOxford UniversityOxford-Man [email protected]

MS4Volatility-Stabilized Markets

We consider models which generalize the Volatility-stabilized markets introduced in Fernholz and Karatzas(2005). We show how to construct a weak solution of theunderlying system of stochastic differential equations, ex-press the solution in terms of time changed squared-Besselprocesses, and argue that this solution is unique in distri-bution. Moreover, we discuss sufficient conditions for theexistence of a strong solution and show that strong relativearbitrage opportunities exist in these markets.

Radka PickovaColumbia [email protected]

MS4Generalizations of Functionally Generated Portfo-lios

I will present generalizations on functionally generatedportfolios (FGPs) of stochastic portfolio theory. The as-sets and the benchmark may be any strictly positive wealthprocesses, as opposed to merely the stocks and the marketportfolio, respectively. Another generalization is that thegenerating function may be stochastic, so that the gen-erated portfolio can be adjusted to changing market con-ditions. These FGPs can be applied to arbitrary cointe-grated market modes exploiting their mean-reversion in arisk-controlled manner.

Winslow C. StrongUniversity of California Santa [email protected]

MS5Optimal Investment in the Presence of High-water

Mark Fees

In this talk, we consider the Merton problem for an agentwho may invest in a money market fund, a stock, and ahedge fund that is subject to a performance fee. This feeis assessed each time the cumulative profit-to-date derivedfrom the investment in the hedge fund reaches a new run-ning maximum. We will study the associated HJB equa-tion and examine some qualitative properties of the opti-mal strategy.

Gerard BrunickUniversity of CaliforniaSanta [email protected]

Karel JanecekRSJ algorithmic [email protected]

Mihai SirbuUniversity of Texas at [email protected]

MS5A Uniqueness Theorem for a Degenerate QVI Ap-pearing in An Option Pricing Problem

We prove the missing uniqueness theorem for the viscositysolution of a degenerate quasi-variational inequality, whichmakes the probability-free theory of option pricing in theinterval market model, essentially complete.

Naıma El FarouqUniversity Blaise Pascal, Clermont-Ferrand, [email protected]

Pierre bernhardINRIA-Sophia [email protected]

MS5Existence, Uniqueness, and Global Regularity forDegenerate Obstacle Problems in Mathematical Fi-nance

The Heston stochastic volatility process, which is widelyused as an asset price model in mathematical finance, is aparadigm for a degenerate diffusion process where the de-generacy in the diffusion coefficient is proportional to thesquare root of the distance to the boundary of the half-plane. The generator of this process with killing, calledthe elliptic Heston operator, is a second-order degenerateelliptic partial differential operator whose coefficients havelinear growth in the spatial variables and where the degen-eracy in the operator symbol is proportional to the distanceto the boundary of the half-plane. With the aid of weightedSobolev spaces, we prove existence, uniqueness, and globalregularity of solutions to stationary variational inequalitiesand obstacle problems for the elliptic Heston operator onunbounded subdomains of the half-plane. In mathematicalfinance, solutions to obstacle problems for the elliptic He-ston operator correspond to value functions for perpetualAmerican-style options on the underlying asset.

Paul FeehanRutgers [email protected]

FM12 Abstracts 143

Panagiota DaskalopoulosColumbia [email protected]

MS5Approximate Solutions to Second Order ParabolicEquations with Time-dependent Coefficients

We consider second order parabolic equations with co-efficients that vary both in space and in time (non-autonomous). We derive closed-form approximations tothe associated fundamental solution by extending theDyson-Taylor commutator method that we recently es-tablished for autonomous equations. We establish errorbounds in Sobolev spaces and show that by includingenough terms, our approximation can be proven to be ac-curate to arbitrary high order in the short-time limit. Weshow how our method extends to give an approximation ofthe solution for any fixed time and within any given toler-ance. Some applications to option pricing are presented. Inparticular, we perform several numerical tests, and specif-ically include results on Stochastic Volatility models.

Victor NistorPennsylvania State [email protected]

Anna MazzucatoDepartment of Mathematics, Penn State [email protected]

Wen ChengPenn State [email protected]

MS6Mixed Deterministic Monte-Carlo Simulations forFinance

Mixing Monte-Carlo and PDE methods can substantiallyspeed-up computations because it allows use of closedform solutions for some of the components. It can alsosolve problems like unknown boundary conditions for com-plex stochastic volatility models. Applying the methodcombined with Longstaff-Schwartz projection can lead toefficient computations of early exercise contracts. Theconvergence of the methods will be established with er-ror estimates and we shall report performance on multi-dimensional problems.

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

Gregoire [email protected]

MS6Two-dimensional Fourier Cosine Series ExpansionMethod for Pricing Financial Options

The COS method for pricing European and Bermudan op-tions with one underlying asset was developed by Fang andOosterlee (2008, 2009). We extend the method to higherdimensions, with a multi-dimensional asset price process.The algorithm can be applied to, for example, pricing two-color rainbow options, but also to pricing under the Heston

stochastic volatility model. For smooth density functions,the method converges exponentially in the number of termsin the Fourier cosine series summations.

Marjon Ruijter, Kees OosterleeCWI - Center for Mathematics and Computer [email protected], [email protected]

MS6Risk-Neutral Valuation of Real Estate Options

We propose a novel and intuitive risk-neutral valuationmodel for real estate derivatives. The resulting index be-havior can easily be analyzed and closed-form pricing so-lutions are derived for forwards, swaps and European putand call options. We demonstrate the application of themodel by valuing a put option on a house price index. Au-tocorrelation in the index returns appears to have a largeimpact on the option value. We also study the effect ofan over- or undervalued real estate market. The observedeffects are significant and as expected.

Stefan [email protected]

David van [email protected]

Marc FranckeOrtec [email protected]

Antoon PelsserUniversity of [email protected]

MS6Efficient Option Pricing of Asian Options based onFourier Cosine Expansions

In this talk we present an efficient pricing method for Asianoptions under Levy processes, based on Fourier–cosine ex-pansions and Clenshaw–Curtis quadrature. The pricingmethod has been developed for both European–style andAmerican–style Asian options, written on different typesof average (arithmetic, geometric and harmonic), and fordiscretely and continuously monitored versions. Fast con-vergence of Fourier cosine expansions and Clenshaw–Curtisquadrature ensures exponential convergence in the Asianoption prices in most cases, which reduces the computingtime of the method to milliseconds for geometric Asian op-tions and a few seconds for arithmetic Asian options. Themethod’s convergence behavior is explained by an erroranalysis. Its performance is further demonstrated by vari-ous numerical examples, where we also show the power ofan implementation on the Graphics Processing Unit (GPU)where hundreds of speedup is achieved for pricing early–exercise Asian options, in particular.

Bowen ZhangDelft University of [email protected]

Cornelis W. OosterleeDelft University of TechnologyCentrum Wiskunde en Informatica (CWI)[email protected]

144 FM12 Abstracts

MS7Sampling Error of the Supremum of a Levy Process

Lvy processes are often used in finance to model the dy-namics of asset prices. The supremum of a Lvy processis of interest when one is pricing financial contracts whosepayoffs depend on the supremum of the underlying assetprice process. While the maximum of a discretely sampledLvy process can often be handled very efficiently using nu-merical methods, not much is known about the continuoussupremum of a general Lvy process. We present results onthe discrepancy between the discrete maximum and contin-uous supremum of a Lvy process. Using Spitzers identityand results from analytic number theory, we derive explicitexpressions for the sampling errors for various commonlyused Lvy processes. The results help us better understandthe error of approximating the continuous supremum of aLvy process by a discrete maximum.

Liming FengDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at [email protected]

MS7Positive Subordinate CIR Processes with Two-Sided Mean-Reverting Jumps

We present the SubCIR jump-diffusion process. TheSubCIRsdiffusion dynamics are those of a CIR pro-cess. The SubCIRs jump componentincludes two-sidedmean-reverting (state-dependent) jumps. The process re-mainsstrictly positive if the CIR process satisfies Fellerscondition. Theanalytical tractability of the SubCIR pro-cess makes it a richer extension tothe CIR process (com-pared to previous models) and it is also a naturalalternativefor interest rates and credit models.

Rafael Mendoza-ArriagaUniversity of Texas at [email protected]

MS7Default Swap Games

We consider the valuation of game-type credit defaultswaps that allow the protection buyer and seller to raise orreduce the respective position once prior to default. Undera structural credit risk model based on spectrally negativeLevy processes, we analyze the existence of the Nash equi-librium and derive the associated saddle point. Using theprinciples of smooth and continuous fit, we determine thebuyer’s and seller’s equilibrium exercise strategies, whichare of threshold type.

Kazutoshi YamazakiOsaka [email protected]

Tim LeungJohns Hopkins [email protected]

MS7Multifactor Term Structure of Interest Rates under

Regime Shifts and Levy Jumps

We develop a tractable dynamic term structure models un-der jump-diffusion with Levy Jumps and regime shifts withtime varying transition probabilities. The model allows forregime-dependent jumps while both jump risk and regime-switching risk are priced. Two types solutions, including(log-linear) approximate solutions and exact solutions forthe term structure are obtained for affine-type models un-der different conditions. For the approximate solutions, wederive the error bound, which is in the first order only. Forthe exact solutions, we further obtain closed-form expres-sions for special cases. Joint work with Xiangdong Liu,Lawrence C. Evans, and Shu Wu.

Yong ZengUniversity of Missouri at Kansas CityDepartment of Mathematics and [email protected]

Xiangdong LiuJinan [email protected]

Lawrence EvansUniversity of [email protected]

Shu WuUniversity of [email protected]

MS8Risk Measures and Fine Tuning of High FrequencyTrading Strategies

Alvaro CarteaUniversidad Carlos [email protected]

Sebastian JaimungalUniversity of Toronto, [email protected]

MS8New Models for Optimal Execution and High-frequency Market Making

Two related papers will be presented that rely on the samemathematical finding. The first one ”Dealing with the in-ventory risk” solves the Avellaneda-Stoikov problem. Itcorresponds to the case of a market maker who has tocontinuously set a bid and a ask quote and we derive theoptimal quotes with closed-form approximations based onspectral ideas. The second one deals with the classicalsubject of optimal liquidation and is one of the first at-tempts to solve the problem with limit orders instead ofliquidity-consuming market orders. This second paper willbe presented for very general intensity functions.

Olivier GueantUniversite Paris-DiderotUFR de [email protected]

FM12 Abstracts 145

MS8Optimal HF Trading in a Prorata Microstructure

We propose a framework to study optimal trading poli-cies in a one-tick pro-rata limit order book, as typicallyarises in short-term interest rate futures contracts. Thehigh-frequency trader has the choice to trade via marketorders or limit orders, which are represented respectively byimpulse controls and continuous controls. We model anddiscuss the consequences of the two main features of thisparticular microstructure: first, the limit orders sent bythe high frequency trader are only partially executed, andtherefore she has no control on the executed quantity. Forthis purpose, cumulative executed volumes are modelled bycompound Poisson processes. Second, the high frequencytrader faces the overtrading risk, which is the risk of bru-tal variations in her inventory. The consequences of thisrisk are investigated in the context of optimal liquidation.The optimal trading problem is studied by stochastic con-trol and dynamic programming methods, which lead to acharacterization of the value function in terms of an inte-gro quasi-variational inequality. We then provide the as-sociated numerical resolution procedure, and convergenceof this computational scheme is proved. Next, we exam-ine several situations where we can one one hand simplifythe numerical procedure by reducing the number of statevariables, and on the other hand focus on specific casesof practical interest. We examine both a market makingproblem and a best execution problem in the case wherethe mid-price process is a martingale. We also detail a highfrequency trading strategy in the case where a (predictive)directional information on the mid-price is available. Eachof the resulting strategies are illustrated by numerical tests.

Huyen PhamUniversity Paris Diderothuyn pham ¡[email protected]¿

Fabien GuilbaudUniversity Paris [email protected]

MS9Stochastic Perron’s Method and Verification with-out Smoothness using Viscosity Comparison: Ob-stacle Problems and Dynkin Games

We adapt the Stochastic Perron’s method in Bayraktar andSirbu (to appear in the Proceedings of the American Math-ematical Society) to the case of double obstacle problemsassociated to Dynkin games. We construct, symmetrically,a viscosity sub-solution which dominates the upper valueof the game and a viscosity super-solution lying below thelower value of the game. If the double obstacle problemsatisfies the viscosity comparison property, then the gamehas a value which is equal to the unique and continuous vis-cosity solution. In addition, the optimal strategies of thetwo players are equal to the first hitting times of the twostopping regions, as expected. The (single) obstacle prob-lem associated to optimal stopping can be viewed as a veryparticular case. This is the first instance of a non-linearproblem where the Stochastic Perron’s method can be ap-plied successfully. (Joint work with Mihai Sirbu. Availableon ArXiv.)

Erhan BayraktarUniversity of MichiganDepartment of [email protected]

MS9Optimal Consumption and Investment in Incom-plete Markets with General Constraints

We study an optimal consumption and investment problemin a possibly incomplete market with general, not neces-sarily convex, stochastic constraints. We give explicit solu-tions for investors with exponential, logarithmic and powerutility. Our approach is based on martingale methodswhich rely on recent results on the existence and uniquenessof solutions to BSDEs with drivers of quadratic growth.

Patrick CheriditoPrinceton [email protected]

MS9Dynamic Portfolio Choice with Multiple Decentral-ized Agents


Andrew LimIndustrian Engineering and Operations ResearchUniversity of California, [email protected]

MS9Constructing Sublinear Expectations on PathSpace

We provide a general construction of time-consistent sub-linear expectations on the space of continuous paths. Ityields the existence of the conditional G-expectation of aBorel-measurable (rather than quasi-continuous) randomvariable, a generalization of the random G-expectation,and an optional sampling theorem that holds without ex-ceptional set.

Marcel NutzDepartment of MathematicsColumbia [email protected]

Ramon Van HandelPrinceton [email protected]

MS10Resilience to Contagion in Financial Networks

Propagation of balance-sheet or cash-flow insolvency acrossfinancial institutions may be modeled as a cascade processon a network representing their mutual exposures. We de-rive rigorous asymptotic results for the magnitude of conta-gion in a large financial network and give an analytical ex-pression for the asymptotic fraction of defaults, in terms ofnetwork characteristics. Our results extend previous stud-ies on contagion in random graphs to inhomogeneous di-rected graphs with a given degree sequence and arbitrarydistribution of weights. We introduce a criterion for theresilience of a large financial network to the insolvency of asmall group of financial institutions and quantify how con-tagion amplifies small shocks to the network. Our resultsemphasize the role played by ”contagious links’ and showthat institutions which contribute most to network insta-bility in case of default have both large connectivity and alarge fraction of contagious links. The asymptotic results

146 FM12 Abstracts

show good agreement with simulations for networks withrealistic sizes.

Hamed AminiSwiss Finance Institute, Ecole polytechnique federale [email protected]


Andreea MincaCornell [email protected]

MS10Coupled Diffusions, Swarming and Systemic Risk


Jean Pierre FouqueUniversity of California Santa [email protected]

MS10Failure and Rescue in an Interbank Network

This paper is concerned with systemic risk in the inter-bank market. We model this market as a directed graphin which the banks represent the nodes and the liabilitiesbetween the banks represent the edges. Our work buildson the modelling paradigm of Eisenberg and Noe (2001),extending it by introducing default costs in the system.We provide a rigorous analysis of those situations in whichbanks have incentives to bailout distressed banks. Suchincentives exist under very mild conditions. We illustrateour results with some simple examples, and go on to dis-cuss possible measures of soundness of a financial system,together with possible policy implications for resolution ofdistress.

Luitgard VeraartDepartment of MathematicsLondon School of [email protected]

Chris RogersChair of Statistical ScienceCambridge [email protected]

MS10Feedback Effects and Endogenous Risk in FinancialMarkets

We present a mathematical model which allows to quan-tify the impact of fire sales of assets of a fund undergoinglosses on the volatilities and correlations of assets held bythe fund. Our model shows that the liquidation of largepositions by funds may result in spikes in volatilities andcorrelations, even in absence of liquidity dry-up, and givesplausible explanations for the large hedge fund losses ofAugust 2007. We show that our model can be used forforensic analysis of financial data, to recover characteris-tics of the portfolio undergoing fire sales from public data,by solving an inverse problem. We show the consistencyof the estimator obtained and apply it to simulated and

empirical data.

Lakshithe WagalathUniversite Pierre & Marie [email protected]


MS11Dynamic Modeling of Systemic Risk

We generalize the Eisenberg-Noe model to allow for multi-ple clearing dates, as well as uncertainty in future liabilitiesand cash inflows. The clearing payment vectors are sequen-tially recovered as the solutions of robust linear program-ming problems solved over the planned horizon. We showexistence and uniqueness of the clearing payment vectorsover time. We perform a sensitivity analysis of the lossand payment vector with respect to borrowing and equityconstraints. We employ the Shapley value methodologyto dynamically attribute the systemic risk to the individ-ual nodes in the network. We conclude with a numericalassessment of the proposed methodology on a systemic net-work consisting of a large number of highly interconnectedfinancial institutions.

PengChu ChenPurdue [email protected]


MS11Estimating Hedge Fund Risk Factors

The estimation of hedge fund returns and the risk factorsthat impact them is a critical step in the construction ofportfolios. In particular, so called fund-of-funds have thearduous task of building portfolios of hedge fund strategiesbased on limited and low frequency observations. This isquite daunting in the hedge fund space due to the gen-erally small sample sizes and opaque nature of that in-dustry’s data. To overcome these difficulties, it is desiredto estimate risk factors based on market observables andreverse engineer a hedge fund exposure to those factors.The model that we propose will be used to analyze anddecompose the risk of various hedge fund indices on com-mon factors at a high frequency (e.g., daily, or intra-day)based on their habitual low frequency observations (typi-cally monthly). Specifically, we will jointly model the risk-factors (e.g., stock returns) and the asset returns (e.g.,a hedge fund strategy) in a fat-tailed, stochastic volatil-ity environment implemented with a Bayesian approachvia a Rao-Blackwellised (R-B) particle filter. We utilize avector Stochastic-Volatility model with smoothed observ-able returns to extract the potentially time-varying ex-posure of low frequency hedge fund performance on highfrequency data. By making use of a particle filter withRao-Blackwellization, we reduce the parameter space sig-nificantly resulting in a more accurate estimate of the dis-tibution of the parameter state. This approach can beused for analyzing hedge fund performance and their ad-vertized strategies as well as in forensic risk-management.The latter of which is a critical need given the generally

FM12 Abstracts 147

low transparency of the hedge fund industry.

Douglas JohnstonQuantalysis, [email protected]

Petar DjuricStony Brook [email protected]

MS11Smooth and Monotone Covariance Estimation forElliptical and Generalized Hyperbolic Distribu-tions

We consider the problem of high-dimensional covarianceestimation from severely limited observations. Strong as-sumptions on the structure of the underlying random vec-tor have to be made for the problem to be well-defined.Some examples developed in the literature include: covari-ance selection models with sparse inverse covariances, low-rank structures (PCA models and factor analysis), sparseplus low-rank structures, multi-scale structures. We con-sider another assumption which is important for a varietyof applications including term-rate risk-modeling in com-putational finance: smoothness and monotonicity. We re-view our previous formulation for multivariate Gaussianrandom vectors based on semi-definite programming, andextend the method for elliptical and generalized hyperbolicdistributions. We use efficient convex optimization algo-rithms and compare the methods using various penalizedBregman divergences as objective functions with examplesfrom interest rate modeling.

Dmitry MalioutovDRW [email protected]

Xiaoping ZhouStony Brook [email protected]

MS11Nonparametric Prediction in a Limit Order Book

We propose a novel non-parametric approach to short-termforecasting of the mid-price in a limit order book. We in-troduce a state vector describing the state of the orderbook at each time. The predictor is based on two features,computed for each value of the state vector. Implicit as-sumptions of our method are very mild and are supportedby our preliminary real-data experiments on NYSEs Open-Book which yield promising empirical results.

Ilya Pollak, Deepan PalgunaPurdue [email protected], [email protected]

MS12Dynamic Assessment Indices

Measuring performance and risk of cash flows is a crucialissue in finance. A Dynamic Assessment Index (DAI) is aquasiconcave, monotone function, mapping cash flows intoprocesses which represent their risk or performance evalu-ations in time. Using L0-separation theorems, we providean upper semicontinuous robust representation and studythe impact of different time consistency conditions; in par-

ticular, how past performances may impact the present as-sessment of risk. Illustrative examples will be discussed.

Martin KarliczekDepartment of Mathematics, Humboldt University [email protected]

MS12Minimal Supersolutions of BSDEs and RobustHedging

We study minimal supersolutions of BSDEs - related toPeng’s g-expectation - which can be seen as superhedg-ing functionals. We prove existence, uniqueness, mono-tone convergence, Fatou’s Lemma and lower semicontinuityof our functional. Unlike usual BSDE methods, based onfixed point theorems, the existence relies on compactnessmethods. We then study some robust extensions whichcorrespond to the problem of superhedging under volatilityuncertainty. The talk is based on joint works with SamuelDrapeau and Gregor Heyne.

Michael KupperHumboldt University [email protected]

MS12Set-valued Dynamic Risk Measures in Marketswith Transaction Costs

Set-valued risk measures appear naturally when marketswith transaction costs are considered and capital require-ments can be made in a basket of currencies or assets.In this talk we study dual representation and time con-sistency properties of dynamic set-valued risk measures.It turns out that only a stronger time consistency calledmulti-portfolio time consistency is equivalent to a recur-sive form of the risk measure as well as to an additiveproperty for the acceptance sets, which is a central resultin the scalar case.

Birgit RudloffPrinceton [email protected]

MS12Portfolio Choice with Time-consistent DynamicRisk Measures

We study portfolio selection based on time-consistent dy-namic risk measures in a general continuous-time setting.The setting features discontinuities in the asset price pro-cesses, with a general and possibly infinite activity jumppart besides a continuous diffusion part, and general andpossibly non-convex trading constraints. We character-ize the minimal risk processes as solutions to BackwardStochastic Differential Equations (BSDEs). We prove ex-istence and uniqueness of the solution in the general classof jump BSDEs having a driver function that grows at mostquadratically. We further compute these solutions in a fewexamples by numerically solving the corresponding BSDEsusing regression techniques.

Mijda StadjeDepartment of Econometrics and Operations ResearchTilburg School of Economics and Management,[email protected]

148 FM12 Abstracts

Roger LaevenDepartment of Quantitative EconomicsUniversity of [email protected]

MS13The Valuation of Double Barrier Options underMultifactor Pricing Models

The (vast) literature on the pricing of barrier options ismainly focused on the valuation of European-style con-tracts under single-factor option pricing models (such asthe geometric Brownian motion and the CEV processes).This paper extends the literature in two directions. First,European-style (double) barrier options are priced undera multifactor and Markovian financial model that is ableto accommodate stochastic volatility, stochastic interestrates, endogenous bankruptcy, and time-dependent barri-ers. Second and more importantly, quasi-analytical pric-ing solutions are also proposed for American-style (double)barrier option contracts under the same general financialmodel. The proposed pricing solutions are shown to beaccurate, easy to implement, and efficient.

Jose C. DiasISCTE-IUL Business [email protected]

Joo NunesBRU-UNIDE and ISCTE Business [email protected]

MS13Exponential Time Differencing Methods for Pric-ing and Hedging American Options

Exponential time differencing (ETD) methods based on theCox and Matthews approach are developed to solve a non-linear BlackScholes model for pricing and hedging Ameri-can options with transaction cost. Each of these methodsavoids solving nonlinear systems, whilst, well known stan-dard methods would require solving nonlinear systems ateach time step. Numerical experiments are performed onexotic path-dependent American options with transactioncost to demonstrate the computational efficiency, accuracyand reliability of the methods.

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

Mohammad YousufKing Fahd University of Petroleum and MineralsSaudi [email protected]

Britta KleefeldBrandenburgische Technische Universitat [email protected]

MS13Efficient and Robust Time Stepping Under Jump-diffusion Models

Partial-integro differential (PIDE) formulations are oftenused to solve option pricing problems where the underlying

asset follows a jump-diffusion process. The main challengelies in the efficient treatment of the jump term resulting afull matrix. We discuss some efficient, robust, and accuratetime discretization methods including schemes treating thejump term explicitly.

Santtu SalmiUniversity of [email protected]

Jari ToivanenStanford [email protected]

MS13Pricing American Options Under Jump-diffusionModels

Under jump-diffusion models, a linear complementarityproblem (LCP) with a partial-integro differential opera-tor can formulated for the price of an American option. Asthe discretization of the jump term leads to a full matrix,it preferable to use special techniques to solve the result-ing LCPs. We discuss various efficient methods for theseLCPs.

Jari ToivanenStanford [email protected]

Santtu SalmiUniversity of [email protected]

MS14Efficient Laplace Inversion, Wiener-Hopf Factor-ization and Pricing Lookbacks

We construct very fast and accurate methods of approx-imate Laplace inversion, calculation of the Wiener-Hopffactors for wide classes of Levy processes with exponen-tially decaying Levy densities, and pricing lookback op-tions. In all cases, we use appropriate conformal changesof variables, which allow us to apply the simplified trape-zoid rule with small number of terms. The same techniqueis applicable for calculation of pdf’s of the supremum andinfimum processes, and prices and sensitivities of optionswith lookback and barrier features.

Svetlana Boyarchenko, Department of Economics, University of Texas atAustin,1 University Station C3100, Austin,TX 78712–0301, [email protected]

MS14Quadratic Hedging of Barrier Options under Lep-tokurtic Returns Driven by an Exponential LvyModel

We examine quadratic hedging of barrier options in a modelrealistically calibrated to reflect the leptokurtic nature ofequity returns. We compute the hedging error of the opti-mal hedging strategy andevaluate prices that yield reason-able risk-adjusted performance for the hedger. Our mainfinding is that the impact of hedging errors on prices is sev-eral times higher than the impact of other pricing biasesstudied in the literature, in particular the effect of barrier

FM12 Abstracts 149

misalignment and of discrete monitoring.

Ale CernCass Business School, [email protected]

MS14Exact Simulation of the Heston Jump-Diffusion

In this talk, we extend the Heston stochastic volatilitymodel to include state-dependent jumps in the price andthe volatility, and develop a method for the exact simu-lation of this model. The jumps arrive with a stochasticintensity that may depend on time, price, volatility andjump counts. They may have an impact on the price or thevolatility, or both. The random jump size may depend onthe price and volatility. Numerical experiments illustratethe features of the exact method. This is a joint work withProf. Erhan Bayraktar at the University of Michigan andProf. Kay Giesecke at Stanford University.

Xueying Hu, Erhan BayraktarUniversity of MichiganDepartment of [email protected], [email protected]


MS14Efficient Pricing and Reliable Calibration in theHeston Model and its Generalizations

We suggest a general scheme for improvement of FT-pricing formulas for European option and give efficient rec-ommendations for the choice of the parameters of the nu-merical scheme, which allow for very accurate and fast cal-culations. We demonstrate that an indiscriminate choiceof parameters of a numerical scheme leads to an inaccu-rate pricing and calibration. As applications, we considerthe Heston model and its generalization, and several otheraffine models. For many parameter sets documented in em-pirical studies of financial markets, relative accuracy bet-ter than 0.01 % can be achieved by summation of less than10-20 terms even in the situations in which the standardapproach requires more than 200. In some cases, the one-term formula produces an error of several percent, and thesummation of two terms — less than 0.5 %. Typically, 10terms and fewer suffice to achieve the error tolerance ofseveral percent and smaller.high-level commands.

Sergei LevendorskiiUniversity of [email protected]

MS15Central Clearing Mechanisms for Credit DefaultSwaps

Central clearing of Credit default swaps through CentralCounterparties (CCPs) has been proposed as a tool formitigating systemic risk and counterpart risk in CDS mar-kets. The design of CCPs for CDS involves the implemen-tation of margin requirements and a clearing fund (or de-fault fund), for which various designs have been proposed.We study the impact of the design of these requirements

on the risk of the CCP and the incentives for CDS clearing.

JinBeom KIMIEOR Dept, Columbia [email protected]


MS15Central Clearing of OTC Derivatives : Bilateral vsMultilateral Netting

We study the impact of a central counterparty (CCP) forOTC derivatives on expected interdealer exposures. Theresults are sensitive to assumptions on heterogeneity ofrisk across asset classes as well as correlation of exposuresacross asset classes; empirically plausible specifications ofthese parameters lead to the conclusion that the gain frommultilateral netting in a CCP largely overweighs the loss ofnetting across asset classes in bilateral netting agreements.

Thomas KOKHOLMAarhus [email protected]


MS15Measuring Contagion in Financial Networks

Liabilities between financial entities form a network. Theclearing of liabilities and thereby contagion of risk anddefault depend on this network structure. We provide amathematical model to understand clearing and propaga-tion of default in such financial networks. This yields aprecise measure for the systemic risk induced by individ-ual financial entities. The model allows to compute opti-mal bailout strategies that either minimize the cost of theintervention or maximize the stabilizing effect for a givenbailout budget. Finally, the computational efficiency of themodel allows to analyze large scale networks quickly.

Sebastian StillerTechnische Universitat [email protected]

MS15Are CDS Auctions Biased?

We study settlement auctions for credit default swaps(CDS). We find that the one-sided design of CDS auctionsused in practice gives CDS buyers and sellers strong incen-tives to distort the final auction price, in order to maximizepayoffs from existing CDS positions. Consequently, theseauctions tend to overprice defaulted bonds conditional onan excess supply and underprice defaulted bonds condi-tional on an excess demand. We propose a double auctionto mitigate this price bias. We find the predictions of ourmodel on bidding behavior to be consistent with data onCDS auctions.

Haoxiang ZHUStanford University

150 FM12 Abstracts

[email protected]

SongZi DUGraduate School of BusinessStanford [email protected]

MS16Endogenous Equilibria in Liquid Markets with Fric-tions and Boundedly Rational Agents

We propose a simple binary mean field game, where Nboundedly rational agents may decide to trade or not ashare of a risky asset in a liquid market. Agents’ utilitydepends on returns, which are endogenously determinedtaking into account observed and forecasted demand andan exogenous transaction cost. The explicit dependence onpast demand generates endogenous dynamics of the sys-tem. It is shown that pure strategy Nash equilibria exist.We study under a rather general setting (risk attitudes,pricing rules and noises) the aggregate demand for the as-set, the emerging returns and the structure of the equilibriaof the asymptotic game. We prove that boom and crash cy-cles may arise and that transaction costs have a stabilizingeffect on the market.

Paolo Dai Prauniversity of [email protected]

Fulvio FontiniDepartment of Economics and ManagementUniversity of [email protected]

Elena Sartori, Marco TolottiDepartment of ManagementCa’ Foscari University of [email protected], [email protected]

MS16Large Portfolio Asymptotics for Loss From Default

We prove a law of large numbers for the loss from defaultand use it for approximating the distribution of the lossfrom default in large, potentially heterogenous portfolios.The density of the limiting measure is shown to solve anon-linear SPDE, and the moments of the limiting mea-sure are shown to satisfy an infinite system of SDEs. Thesolution to this system leads to the distribution of the limit-ing portfolio loss, which we propose as an approximation tothe loss distribution for a large portfolio. Numerical testsillustrate the accuracy of the approximation, and highlightits computational advantages over a direct Monte Carlosimulation of the original stochastic system.


Konstantinos SpiliopoulosBrown [email protected]

Richard SowersUniversity of Illinois at [email protected]

Justin SirignanoStanford [email protected]

MS16Branching and Interacting Particle Models of Sys-temic Risk

We propose an interacting particle system description ofthe banking system. While net bank assets evolve in-dependently under normal conditions, defaults trigger amean-field type interaction that creates systemic risk. Wework with a stochastic size of the economy, with new banksadded spontaneously according to a mean-field birth pro-cess. We present some preliminary results about systemstability and the properties of the corresponding mean-fieldlimit.

Michael LudkovskiUC Santa [email protected]

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

MS16Most Likely Path to Systemic Failure

In this talk, I will present recent results on modeling thedynamics of correlated default events in the financial mar-ket. An empirically motivated system of interacting pointprocesses is introduced and we study how different types ofrisk, like contagion and exposure to systematic risk, com-pete and interact in large-scale systems. Large deviationarguments are used to approximate the tail of the defaultloss in large portfolios and to identify the way that atyp-ically large (i.e. “rare’) default clusters are most likely tooccur. The results give insights into how different sourcesof default correlation interact to generate atypically largeportfolio losses.

Konstantinos SpiliopoulosBrown [email protected]


Richard SowersDepartment of MathematicsUniversity of [email protected]

MS17Quasi-convex Dynamic Programming for StorageEvaluation

The value of a storage facility can often be representedas a quasi-convex function of the market price and cur-rent capacity utilization. This talk will describe a dynamicprogramming procedure to take advantage of this struc-ture. The method relies on progressive refinement of outerapproximations of the sub-level sets of the value function

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in each stage.

John BirgeUniversity of ChicagoBooth School of [email protected]

MS17A Kernel Based Approach to Gas Storage andSwing Contracts Valuations in High Dimensions

We are expanding upon our previous work [Boogert andMazieres, “A Radial Basis Function Approach to Gas Stor-age Valuation”, 2011], by introducing multi-factor priceand volume dimensions encountered in both gas storageand swing contracts. This is achieved by introducing newmultivariate methods (Kernel based: Radial Basis Func-tions and the Tensor of Radial Basis Functions) to themulti-dimensional Least-Squares Monte Carlo method usedto value these contracts with the spot approach.

Denis MazieresLondon [email protected]

Alexander BoogertEnergyQuants [email protected]

MS17Approximate Linear Programming Relaxations forCommodity Storage Real Option Management

The real option management of commodity conversion as-sets based on high dimensional forward curve evolutionmodels commonly used in practice gives rise to intractableMarkov decision processes. Focusing on commodity stor-age, we derive approximate dynamic programs from re-laxations of approximate linear programs formulated usinglow dimensional value function approximations. We evalu-ate the performance of our approximate dynamic programson natural gas and oil instances.

Selvaprabu Nadarajah, Francois MargotCarnegie Mellon UniversityTepper School of [email protected], [email protected]

Nicola SecomandiCarnegie MellonTepper School of [email protected]

MS17Natural Gas Storage Valuation, Optimization,Market and Credit Risk Management

We present a model for the valuation, optimization, andpricing of the credit risk of gas storage contracts. A re-duced form term structure model of the curve dynam-ics is derived that facilitates dimension reduction with-out sacrificing realism. A system of PDEs is derived andsolved using RBF collocation. When the number of injec-tion/withdrawal opportunities is large, RBF-PDE methodcan solve problems where heuristic approaches would beimpractical. The RBF expansions facilitate pricing of

credit risk.

Matt ThompsonQueen’s UniversityQueen’s School of [email protected]

MS18Small-time Expansions for Stochastic VolatilityModels with Levy Jumps

We analyze the short-time (equivalently, near expiration)behavior of the tail distributions and option prices of aclass of stochastic volatility (SV) models obtained by su-perposing a classical continuous SV process (say, the Hes-ton process) with an independent pure-jump Levy process.Polynomial expansions in time of arbitrary order are ob-tained for the tail distributions and out-of-the money op-tion prices, assuming certain smoothness conditions on theLevy density of the jump component and a small-time largedeviation principle for the continuous component. As a re-sult, we are able to disentangle the effects of the variousmodel parameters in the short-time behavior of the optionprices and rank their contribution according to the firstpower at which they appear in the polynomial expansion.This talk is based on a joint work with C. Houdre and R.Gong.

Jose E. Figueroa-LopezPurdue [email protected]

MS18Large Deviations and Stochastic Volatility withJumps: Asymptotic Implied Volatility for AffineModels

We consider the implied volatility of European options inan affine stochastic volatility model with jumps, as timetends to infinity. We show that under a simultaneousrescaling of the option strike a non-degenerate limitingvolatility smile exists and describe it by a formula whichcan be expressed in terms of the parameters of the under-lying model. The result is based on a large-deviation prin-ciple for affine stochastic volatility models, that is derivedvia the Gartner-Ellis theorem. We exhibit some specific ex-amples including a Heston model with and without jumps,Bates’ model with state-dependent jump intensity and theBarndorff-Nielsen-Shephard model.

Martin Keller-ResselTU [email protected]

Antoine Jacquier, Aleksandar MijatovicImperial College [email protected], [email protected]

MS18A New Look at Short-term Implied Volatility inModels with Jumps

This talk analyses the behaviour of the implied volatil-ity smile for short-dated options in semimartingale modelswith jumps. We introduce a new renormalization of thestrike variable such that the implied volatility for short-maturity options converges to a nonconstant finite limit,characterised by the diffusion and jump components of the

152 FM12 Abstracts

model. This limit yields calibration algorithms for short-dated options and sheds new light on the difference betweenfinite and infinite variation jumps in pricing models.

Aleksandar MijatovicImperial College [email protected]

Peter TankovParis [email protected]

MS18Parametric Inference and Dynamic State Recoveryfrom Option Panels

We develop parametric estimation procedure for optionpanels observed with error. We provide semiparametrictests for the option price dynamics based on the distancebetween the spot volatility extracted from the options andthe one obtained nonparametrically from high-frequencydata on the underlying asset. We further construct newformal tests of the model fit for specific regions of thevolatility surface and for the stability of the risk-neutraldynamics over a given period of time.

Viktor TodorovKellogg School of ManagementNorthwestern [email protected]

Torben G. Andersen, Nicola FusariNorthwestern [email protected], [email protected]

MS19A Decomposition Formula for Option Prices in theHeston Model and Applications to Option PricingApproximation

By means of classical Its calculus we decompose optionprices in the Heston volatility framework as the sum ofthe classical Black-Scholes formula with volatility param-eter equal to the root-mean-square future average volatil-ity plus a term due to correlation and a term due to thevolatility of the volatility. This decomposition formula al-lows us to construct first and second order option pricingapproximation formulas that are extremely easy to com-pute, as well as to study their accuracy for short maturi-ties. Moreover we see the corresponding approximationsfor the implied volatility are linear (first-order approxima-tion) and quadratic (second-order approximation) in thelog-stock price variable.

Elisa AlosUniversitat Pompeu [email protected]

MS19Small-noise Expansion for Projected Diffusions andImplied Volatility Asymptotics

Given a diffusion in Rn, we prove a small-noise expan-sion for the density of its projection on a subspace of di-mension p ≤ n. Our proof relies on the Laplace methodon Wiener space and stochastic Taylor expansions in thespirit of Azencott-Benarous-Bismut. Our result (assumingHormander’s condition on the vector fields) applies to (i)

small-time asymptotics, (ii) tails of the distribution and(iii) small-noise expansions. In the context of stochasticvolatility models, we recover the Busca-Berestycki-Florentformula (applying (i)) and Gulisashvili-Stein expansion(from (ii)). This is a joint work with J.D. Deuschel (TUBerlin), P. Friz (TU Berlin) and S. Violante (Imperial Col-lege London).

Antoine JacquierImperial College [email protected]

Peter FrizTU BerlinWeierstrass Institute

Jean-Dominique DeuschelTU Berlin

Sean ViolanteImperial College London

MS19Asymptotics of Implied Volatility to Arbitrary Or-der

In a unified model-free framework that includes long-expiry, short-expiry, extreme-strike, and jointly-varyingstrike-expiry regimes, we find asymptotic implied volatilityand implied variance formulas in terms of L, with rigorouserror estimates of order 1/L to any given power, where Ldenotes the absolute log of an option price that approacheszero. Our results therefore sharpen, to arbitrarily highorder of accuracy, the model-free asymptotics of impliedvolatility in extreme regimes. We then apply these generalformulas to particular examples: Levy and Heston. Jointwork with Kun Gao.

Roger Lee, Kun GaoUniversity of [email protected], [email protected]

MS19Multi-Factor Stochastic Volatility Models for Op-tions and Options on Variance

Through perturbation methods we reconcile skews of im-plied volatilities for options and options on variance in thecontext of multi-scale stochastic volatility models.

Jean Pierre FouqueUniversity of California Santa [email protected]

Yuri SaporitoUC Santa [email protected]

Jorge P. [email protected]

MS20On the Multi-Dimensional Controller and StopperGames

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled

FM12 Abstracts 153

diffusion evolving in a multi-dimensional Euclidean space.In this game, the controller affects both the drift and thevolatility terms of the state process. Under appropriateconditions, we show that the game has a value and thevalue function is the unique viscosity solution to an obsta-cle problem for a Hamilton-Jacobi-Bellman equation.

Yu-Jui HuangUniversity of Michigan, Department of [email protected]

Erhan BayraktarUniversity of MichiganDepartment of [email protected]

MS20Numerical Solutions of Optimal Risk Control andDividend Optimization Policies

This work develops numerical methods for finding optimaldividend pay-out and reinsurance policies. The surplusis modeled by a regime-switching process subject to bothregular and singular controls. Markov chain approximationtechniques are used to approximate the value function andoptimal controls. The proofs of the convergence of the ap-proximation sequence to the surplus process and the valuefunction are given. Examples are presented to illustratethe applicability of the numerical methods.

Zhuo JinUniversity of Melbourne, [email protected]

George YinWayne State UniversityDepartment of [email protected]

Chao ZhuUniversity of [email protected]

MS20Outperformance Portfolio Optimization via theEquivalence of Pure and and Randomized Hypoth-esis Testing

We study the portfolio problem of maximizing the outper-formance probability over a random benchmark throughdynamic trading with a fixed initial capital. Under a gen-eral incomplete market framework, this stochastic controlproblem can be formulated as a composite pure hypothesistesting problem. We analyze the connection between thispure testing problem and its randomized counterpart, andfrom latter we derive a dual representation for the maxi-mal outperformance probability. Moreover, in a completemarket setting, we provide a closed-form solution to theproblem of beating a leveraged exchange traded fund. Fora general benchmark under an incomplete stochastic fac-tor model, we provide the Hamilton-Jacobi-Bellman PDEcharacterization for the maximal outperformance probabil-ity.

Jie YangUniversity of Illinois at [email protected]

Tim Leung

Johns Hopkins [email protected]

Qingshuo SongCity University of Hong [email protected]

MS20Optimal Trend-following Trading Rules under aThree-state Regime-switching Mode

Assume the market follows a regime switching model withthree states, a set of sufficient conditions are developed toguarantee the optimality of trend-following trading strate-gies. A dynamic programming approach is used to verifythese optimality conditions. The value functions are char-acterized by the associated HJB equations. The results inthis paper will help an investor to identify market condi-tions and to avoid trades which might be unprofitable evenunder the best market information.

Jie YuRoosevelt [email protected]

Qing ZhangUniversity of GeorgiaDepartment of [email protected]

MS21Evaluating Callable and Putable Bonds: An Eigen-function Expansion Approach


Dongjae [email protected]

MS21Building Financial Models with Time Changes


Vadim LinetskyNorthwestern [email protected]

MS21Pricing Derivatives on Multiscale Diffusions: AnEigenfunction Expansion Approach

Using tools from spectral analysis, singular and regu-lar perturbation theory, we develop a systematic methodfor analytically computing the approximate price of aderivative-asset. The payoff of the derivative-asset maybe path-dependent. Additionally, the process underlyingthe derivative may exhibit killing (i.e. jump to default) aswell as combined local/nonlocal stochastic volatility. Thenonlocal component of volatility is multiscale, in the sensethat it is driven by one fast-varying and one slow-varyingfactor. The flexibility of our modeling framework is con-trasted by the simplicity of our method. We reduce thederivative pricing problem to that of solving a single eigen-value equation. Once the eigenvalue equation is solved,the approximate price of a derivative can be calculated

154 FM12 Abstracts

formulaically. To illustrate our method, we calculate theapproximate price of three derivative-assets: a vanilla op-tion on a defaultable stock, a path-dependent option on anon-defaultable stock, and a bond in a short-rate model.

Matthew LorigPrinceton UniversityORFE [email protected]

MS21Closed-form Expansions of Option Prices underTime-changed Dynamics

We consider a broad class of option pricing models andderive a simple closed-form expansion of option prices inthese models in terms of Black-Scholes prices and higher-order Greeks. The expansion provides a transparent andinformative decomposition of option prices. Moreover, itcan be used for a large class of flexible models which allowfor both stochastic volatility and jumps. Finally, it allowsfor fast model calibration.

David PedersenAarhus [email protected]

Elisa NicolatoUniversity of [email protected]

MS22Optimal Portfolios under Worst Case Scenarios

Standard portfolio theories such as Expected Utility The-ory, Yaari’s Dual Theory, Cumulative Prospect Theory andMean-Variance optimization all assume that investors onlylook at the distributional properties of strategies and donot care about the states of the world in which the cash-flows are received. In a very interesting paper, Dybvig(1988a, 1988b) essentially showed that in these instancesoptimal portfolios are decreasing in the state-price density,also pointing indirectly to the important role of diversifiedportfolios. In this paper we first observe that the worst out-comes for optimal strategies exactly occur when the marketdeclines (i.e. during a financial crisis), but this is at oddswith the aspirations and requirements of many investors.Hence we depart from the traditional behavioral settingand study optimal strategies for investors who do not onlycare about the distribution of wealth but, additionally, alsoimpose constraints on its interaction with the (stressed) fi-nancial market. Preferences become state-dependent andwe are able to assess the impact of these on trading deci-sions. We construct optimal strategies explicitly and showhow they outperform traditional diversification strategiesunder worst-case scenarios.

Carole Bernard, Jit-Seng ChenUniversity of [email protected], [email protected]

Steven VanduffelVrije Universiteit Brussel, [email protected]

MS22Myopic Loss Aversion, Reference Point, and

Money Illusion

We use the portfolio selection model presented in He andZhou (2011, Management Science, Volume 57, Issue 2,pages 315–331) and the NYSE equity and U.S. treasurybond returns for the period 1926-1990 to provide a rigor-ous treatment of Benartzi and Thaler’s myopic loss aver-sion theory. We find that in addition to the agent’s lossaversion and evaluation period, his reference point also hasa significant effect on optimal asset allocation. We demon-strate that the agent’s optimal allocation to equities is con-sistent with the market observation when he has reasonablevalues of degree of loss aversion, evaluation period, and ref-erence point. We also find that the optimal allocation toequities is sensitive to these parameters. We then examinethe implications of money illusion for asset allocation andpricing. Finally, we extend the model to a dynamic setting.

Xuedong HeColumbia UniversityDepartment of Industrial Engineering and [email protected]

Xunyu ZhouUniversity of Oxford andThe Chinese University of Hong [email protected]

MS22Consumption-based Behavioral Portfolio Selectionin Continuous Time

We study the optimal consumption-investment problem ina continuous-time financial market with behavioural cri-teria featured by S-shaped utility function and probabilitydistortions. Different formulations of the problem are stud-ied. When optimal solutions exist, we get explicit formsbased on some algebraic equations.

Hanqing JinOxford [email protected]

MS22Utility Maximization with Addictive ConsumptionHabit Formation in Incomplete Markets

We study the utility maximization problem of consumptionwith addictive habit formation in the general incompletesemimartingale market. By introducing the auxiliary stateand dual processes and defining the value function both oninitial wealth and initial habit, we embed our original pathdependent problem into an abstract time separable opti-mization problem with the shadow random endowment.We establish existence and uniqueness of the optimal solu-tion using convex duality approach on L0

+ spaces.

Xiang YuDepartment of Mathematics,The University of Texas at [email protected]

MS23The Log Optimal Portfolio under TransactionCosts and the Shadow Price: The GeometricOrnstein-Uhlenbeck Process and a Counterexam-

FM12 Abstracts 155

ple

As in (Gerhold/Muhle-Karbe/Schachermayer 2011) wefind the growth optimal portfolio for the geometricOrnstein-Uhlenbeck process under proportional transac-tion costs by constructing a shadow price. This is a priceprocess, such that the optimization problem without fric-tions for that price has the same solution as the one undertransaction costs. This technique allows us to explicitlycompute fractional Taylor expansions of arbitrary order forall quantities of interest. Similar results have (to the best ofour knowledge) so far only been obtained for the Black Sc-holes model. Moreover, we present a counterexample thatshadow prices may not exist in general even in discrete timeand for “well-behaved’ markets.

Christoph Czichowsky, Philipp DeutschU of [email protected],[email protected]


Walter SchachermayerU of [email protected]

MS23Market Depth and Trading Volume Dynamics

We derive the process followed by trading volume, in amarket with finite depth and constant investment oppor-tunities. A representative investor, with a long horizon andconstant relative risk aversion, trades a safe and a risky as-set with a liquidity cost proportional to trading speed. Anordinary differential equation identifies the trading policyand welfare. In the high-liquidity limit, trading volumefollows approximately an Ornstein-Uhlenbeck process, andincreases with liquidity, volatility, and risk aversion.

Paolo GuasoniBoston UniversityDublin City [email protected]

Marko WeberDublin City UniversityScuola Normale [email protected]

MS23Long-run Investment under Drawdown Con-straints: optimal portfolios and numeraire prop-erty

We consider long-run investment problems under draw-down constraints: the current wealth can not fall belowa given function of its past maximum. We work in a gen-eral semimartingale setting. First, we show that this prob-lem is equivalent to an unconstrained problem but with amodified utility function: both the value and the optimalportfolio are given explicitly in terms of their unconstrainedcounterparts (joint work with Vladimir Cherny). Second,we analyse in more detail the growth optimal portoflio un-der linear drawdowns. We show it enjoys the numeraireproperty along specific sequences of stopping times and

asymptotically but not for all times. A turnpike theoremshows it is a limit of numeraire strategies on finite hori-zons (joint work with Constantinos Kardaras and EckhardPlaten).

Jan OblojMathematical Institute, University of Oxfordand the Oxford-Man Institute of Quantitative [email protected]

MS23Wealth vs Risk in a Continuous Time Model

We discuss a continuous time optimization problem whichcombines two conflicting objectives of maximizing the port-folio wealth up to a level and minimizing the conditionalvalue-at-risk of the portfolio wealth loss. The associatedutility function is not differentiable nor strictly concaveand does not satisfy Inada’s condition. We use the dualcontrol method to show that there is a classical solution tothe HJB equation and that the optimal value function issmooth if the optimal control satisfies an exponential mo-ment condition. We find the closed-form optimal feedbackcontrol and optimal value function for a wealth maximiza-tion problem.

Harry ZhengImperial College [email protected]

MS24Stress Tests: From Arts to Science (Overview)

Expectations on stress tests are high in the financial in-dustry: they should measure the resilience of individualfinancial institutions and of the whole banking system aspart of an economy. Additionally, they should act as acalmative for nervous markets. It is time to assess theexpectations about what information can realistically beobtained from stress tests. How should we choose scenar-ios which are at the same time plausible and informativeof potential weaknesses? How can we assess the validityof our models and the potential consequences where ourmodels break down? How can we adequately discriminateadverse external shocks and dangerous endogenous effects?

Thomas BreuerResearch Centre PPE, Fachhochschule [email protected]

MS24Finding Stress Scenarios That Get the Job Done,with Credit Risk Applications

We introduce new methods to generate finite representa-tive collections of plausible yet severe scenarios. We applythese methods to generate credit risk scenarios and demon-strate, via numerical experiments, that with respect to cer-tain performance measures, our method is better able todiscover (ex ante) scenarios close to those that occurred(as determined ex post), than previously described meth-ods. Moreover, our methods discover these scenarios atsubstantially lower computational cost.

Craig A. FriedmanStandard & [email protected]

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MS24Stress Testing Model Risk


Paul [email protected]

MS24Must Stress Tests be Credible?


Til SchuermannOliver [email protected]

MS25Utility Indifference Pricing in Energy Markets


Luciano CampiParis 13 [email protected]

MS25Probabilistic Approach to Mean Field Games andthe Control of McKean Vlasov Dynamics


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

MS25Levy Semistationary Processes with Applicationsto Electricity Markets

So called Levy semistationary processes (LSS processes)constitute a rather general class of continuous time mov-ing average processes. Our motivation is employing theseprocesses to model electricity and commodity forwardsand spots. We discuss and analyze numerical simulationprocedures for LSS processes and energy forward randomfields, by means of stochastic partial differential equations,Fourier methods and finite dimensional approximations.

Heidar I. Eyjolfsson, Fred Espen BenthUniversity of [email protected], [email protected]

MS25Forward-Backward SDE Games and StochasticControl under Model with Uncertainty


Agnes [email protected]

MS26Forward Equations and Mimicking Theorems for

Discontinuous Semimartingales

We derive a forward partial integro-differential equation forprices of call options in a model where the dynamics of theunderlying asset under the pricing measure is described bya -possibly discontinuous- semimartingale. A uniquenesstheorem is given for the solutions of this equation. Werelate this result to the construction of a Markovian pro-jection - a Markov process which mimics the marginalsdistributions of the semimartingale. This result gener-alizes Dupire’s forward equation to a large class of non-Markovian models with jumps.

Amel BentataUniversite Pierre & Marie Curie, [email protected]


MS26Functional Ito Calculus and the Pricing and Hedg-ing of Path-dependent Derivatives

We provide a brief overview of the Functional Ito Calcu-lus [Dupire 2009; Cont & Fournie 2010], which providesa convenient mathematical framework for analyzing path-dependent functionals of Ito processes, and show that itmay be used to derive a ’universal’ pricing equation whichholds for a wide class of path-dependent options on an un-derlying asset whose price follows an Ito process. This uni-versal pricing equation is a functional analog of the back-ward Kolmogorov equation: we present a uniqueness re-sult for solutions of this equation and show that it verifiesa comparison principle. Finally, we provide a unified ap-proach to the computation of hedging strategies for path-dependent options.


David FournieMorgan [email protected]

MS26Local Vs Non-Local Forward Equations for OptionPricing

When the underlying asset is a continuous martingale,call option prices solve the Dupire equation, a forwardparabolic PDE in the maturity and strike variables. Bycontrast, when the underlying asset is described by adiscontinuous semimartingale, call price solve a partialintegro-differential equation (PIDE), containing a non-local integral term. We show that the two classes of equa-tions share no common solution: a given set of option pricesis either generated from a continuous martingale (”diffu-sion”) model or from a model with jumps, but not both.In particular, our result shows that Dupires inversion for-mula for reconstructing local volatility from option pricesdoes not apply to option prices generated from models withjumps.

Yu GuColumbia [email protected]

FM12 Abstracts 157


MS26Degenerate Parabolic PDEs, Martingale Problemsand a Mimicking Theorem for Ito Processes

We prove existence, uniqueness and regularity of solutionsin weighted Holder spaces for a certain class of degener-ate parabolic partial differential equations with unboundedcoefficients on the half space. We show that the mar-tingale problem associate with the differential operator iswell-posed, which implies existence and uniqueness of weaksolutions to the corresponding stochastic differential equa-tions. The weak solutions match the one-dimensional prob-ability distributions of a certain class of Ito processes.

Camelia A. Pop, Paul FEEHANRutgers [email protected], [email protected]

MS27Credit Risk Concentration under Stress

We present a general approach to implementing stress sce-narios in multi-factor credit portfolio models, which isbased on the truncation of risk factors. We derive ana-lytic formulae for credit correlations under stress and ana-lyze their asymptotic behavior in normal variance mixture(NVM) models. It turns out that correlations in heavy-tailed NVM models are less sensitive to stress than inmedium- or light-tailed models.

Michael KalkbrenerDeutsche BankFrankfurtmichael kalkbrener ¡[email protected]

MS27Risk Assessment Modelling of Systemic Institu-tions

The Bank of England has developed a top-down stress test-ing and systemic risk model (RAMSI). The model containsa network of banks, with each bank modelled in consider-able detail. RAMSI allows the banks to be shocked by(deterministic or stochastic ) macroeconomic scenarios todetermine the resilience of the system under stress. Thebanks can themselves propagate stress around the systemthrough second round effects. We present the model andan illustration of its use.

Jack McKeownBank of [email protected]

MS27A Systematic Approach to Multi-period StressTesting of Portfolio Credit Risk

We propose a new method for analysing multiperiod stressscenarios for portfolio credit risk more systematically thanin current macro stress tests. The plausibility of a scenariois quantified by its distance from an average scenario. Fora given level of plausibility, we search systematically forthe most adverse scenario. We show how this method canbe applied to some models already in use by practitioners.

Martin SummerOeNB, Austrian Central [email protected]

Thomas Breuer, Martin JandackaResearch Centre PPE, Fachhochschule [email protected], [email protected]

Javier MenciaFinancial Stability DepartmentBanco de [email protected]

MS27Lessons and Limits of Stress Tests as a Macropru-dential Supervisory Tool


Konstantinos TsatsaronisBank for International [email protected]

MS28Derivatives on Non-Storable Renewable Resources:Fish Futures and Options, Not So Fishy after All.

We study forward prices and prices of European call op-tions, which are written on a non-storable renewable re-source. An example for such derivatives is provided by fu-tures and options on fresh salmon traded in large volumesat Fish Pool (Norway) since 2008. The introduction of sim-ilar exchanges in the United States and other countries iscurrently discussed. The pricing formulas are derived fromfirst principles, starting of by modeling the dynamics of theresource reserves, and assuming that resource extractionis managed as open access. We derive closed form solu-tions for the forward price of the renewable resource andstudy its dynamics. In contrast to Black (1976) we showthat forward prices do not evolve according to a geomet-ric Brownian motion, but follow a more complex process.For the case of an option we show that the Black (1976)formula needs to be adapted in such a way, that the nor-mal distribution is replaced by a reciprocal Γ-distribution,to get at least a very good approximation of the true op-tion price. We include numerical evidence to underline thisstatement. Finally, we derive pricing formulas for optionswritten on forward contracts, and show how forward con-tracts can be hedged under the assumption that there isa spanning asset. The full paper is available at SSRN:http://ssrn.com/abstract=1469135 The presentation willalso include material from a second working paper, whichincludes more empirical analysis.

Christian EwaldDepartment of Economics, University of [email protected]

MS28Adaptations of Least-squares Methods to ConvexControl Problems


Juri Hinz

158 FM12 Abstracts

ETH Zurich, Department of Mathematics,Institute for Operations [email protected]

MS28Dark Pools and Hidden Markets


Ulrich HorstHumboldt [email protected]

MS28A Feedback Model for the Financialization of Com-modity Prices


Ronnie SircarORFEPrinceton [email protected]

MS29A Flexible Matrix Libor Model with Smiles

We present a flexible approach for the valuation of inter-est rate derivatives based on Affine Processes. We extendthe methodology proposed in Keller-Ressel et al. (2009) bychanging the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. Wethen show that it is possible to price swaptions in a multi-factor setting with a good degree of analytical tractability.This is done via the Edgeworth expansion approach devel-oped in Collin-Dufresne and Goldstein (2002). A numeri-cal exercise illustrates the flexibility of the Wishart Libormodel in describing the movements of the implied volatilitysurface.

Alessandro GnoattoLMU [email protected]

Jose Da FonsecaAuckland University of [email protected],

Martino GrasselliUniversity of [email protected]

MS29The Explicit Laplace Transform for the WishartProcess

We derive the explicit formula for the joint Laplace trans-form of the Wishart process and its time integral which ex-tends the original approach of [Bru, M. F. (1991): Wishartprocesses. Journal of Theoretical Probability, 4:725751].We compare our methodology with the alternative resultsgiven by the variation of constants method, the lineariza-tion of the Matrix Riccati ODEs and the Runge-Kutta al-gorithm. The new formula turns out to be fast, accurateand very useful for applications when dealing with stochas-tic volatility and stochastic correlation modelling.

Martino Grasselli

University of [email protected]

MS29Generalized Affine Transform Formulae and ExactSimulation of the WMSV Model

The aim of this talk is to introduce transform formulaefor linear functionals of affine processes and their bridgeswhose state space is a set of positive semidefinite matrices.Particularly, we investigate the relationship between suchtransforms and certain integral equations. We are, then,able to derive analytic expressions for Laplace transformsof some functionals of Wishart bridges. As an application,we suggest an exact simulation method of Wishart multi-dimensional stochastic volatility model.

Chulmin Kang, Wanmo KangDepartement of Mathematical Sciences, KAISTRepublic of [email protected], [email protected]

MS29Calibration of Multivariate Affine StochasticVolatility Models

We provide a new calibration algorithm for multivariateaffine stochastic covariance models using both option andtimeseries data. The option data is used to recover the pa-rameters determining the drift of the covariance process,while the timeseries allows us to identify the volatility ofthe covariance process and its correlation to the price pro-cesses. The procedure relies only on the knowledge of thefirst moments of log-prices and an estimation of volatilityusing Fourier series.

Christa CuchieroUniversity of Vienna, Faculty of [email protected]

Elisa NicolatoUniversity of [email protected]

David SkovmandAarhus University, Department of Economics [email protected]

Josef TeichmannDepartment of MathematicsETH [email protected]

MS30Calibrating Volatility Surfaces for CommodityDerivatives

Commodities and their derivatives have become key playersin the portfolios of many corporations, especially for thoseworking in the energy sector. In this talk we shall discussthe calibration of local volatility surfaces for commodityderivatives. In order to obtain stable and robust resultswe shall make use of regularization techniques to handlethe inverse problem. In particular we shall present someresults with Brent oil (WTI) and Natural Gas (HH) data.

FM12 Abstracts 159

Vinicius AlbaniIMPARio de Janeiro, [email protected]

MS30Volatility Surface Calibration andRelative-Entropy Minimization

In this talk we will survey the research developed jointlywith a number of collaborators during the past few yearsin connection with the calibration of Black-Scholes modelsunder stochastic volatility. We shall start with the rela-tion between uncertain volatility models, Hamilton-Jacobiequations, and the Kullback-Leibler distance. Then, weshall discuss calibration and entropy. Finally we will dis-cuss weighted Monte Carlo methods and applications.

Marco AvellanedaCourant InstituteNew York [email protected]

MS30Calibrating Self-exciting Marked Point Processesfor Algorithmic Trading

Recently, marked point processes have been used to modelthe dynamics of assets at ultra-high frequencies. Cartea,Jaimungal and Ricci (2011) develop a multi-factor self-exciting model accounting for the arrival of market ordersthat influence activity, trigger one- and two-sided cluster-ing of trades, and induce temporary changes in the shape ofthe LOB. The classification of trades as influential versusnon-influential induces hidden state variables and makesonline calibration a necessity in high frequency trading achallenging endeavor. Here, we develop quasi-maximum-likelihood parameter estimators and a Sequential MonteCarlo estimator of the activity path for use in algorithmictrading strategies.

Sebastian JaimungalUniversity of Toronto, [email protected]

Jason RicciUniversity of [email protected]

MS30An Overview of Calibration Methods of LocalVolatility Surfaces

Local volatility models are extensively used and well rec-ognized for hedging and pricing in financial markets. Theyare frequently used, for instance, in the evaluation of exoticoptions so as to avoid arbitrage opportunities with respectto other instruments. Yet, the ill-posed character of localvolatility surface calibration from market prices requiresthe use of regularization techniques either implicitly or ex-plicitly. Such regularization techniques have been widelystudied for a while and are still a topic of intense research.In this talk we shall review different attempts that havebeen made in order to tackle the local volatility calibrationproblem. In particular, we shall discuss convex regulariza-tion tools and recent inverse problem advances to deal with

the calibration problem.

Jorge P. [email protected]

PP1Adjoint Monte-Carlo Technique for Calibration ofFinancial Market Models

We present a Monte-Carlo based adjoint technique for solv-ing calibration problems of financial market models like theHeston model with time-dependent parameters. Any effi-cient optimization method for calibration requires at leastgradient information. The major advantage of the adjointtechnique lies in the fact that the calculation time requiredfor a gradient computation stays nearly constant, indepen-dent of the number of parameters. Our numerical resultsconfirm this improved speed-up.

Bastian GrossUniversity of [email protected]

Ekkehard W. SachsUniversity of TrierVirginia [email protected]

PP1On Efficient Option Pricing Under Jump Diffusion

Merton’s jump-diffusion model leads to partial-integro dif-ferential equations (PIDE), which can be solved in orderto price options. Discretization of the integral in the PIDEleads to non-local terms and dense matrices. The presen-tation will discuss ways to solve the PIDE, avoiding densematrices. This is applied to European-style options.

Ruediger U. SeydelUniversity of CologneMathematical [email protected]

PP1The Impact of Constraints on the Views of theBlack-Litterman Model

The Black-Litterman model is a Bayesian portfolio opti-mization model that allows investors to impose prior viewson the expected returns of assets in the portfolio. Con-straints can be considered as prior views on the optimalportfolio weights. Constraints distort the views expressedby the investor, resulting in sub-optimal portfolio weights.Our research shows that a mild relaxation of the long-onlyconstraint results in Black-Litterman views that are moreefficiently represented in the portfolio weights.

Byron WilsonUniversity of Cape [email protected]

Gareth Q. WittenUniversity of Cape TownPontificia Universidad Catolica del Per, [email protected]

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