38 FM14 Abstracts

IP1 debated. In response, an increasingly active field of re- No-arbitrage Under Model ambiguity and Funda- search focuses on model-free super/sub-hedging using the mental Theorems of underlying and Vanilla options. Explicit results often rely on pathwise inequalities and embedding techniques while We will present several recent versions of the Fundamen- pricing-hedging duality is obtained using martingale opti- tal Theorem of Asset Pricing for discrete and continuous mal transport methods. However, the resulting prices and time models under model ambiguity, with and without pro- hedges are often too expensive to be practically relevant. portional transaction costs. This talks is based on recent In this talk I show how to interpolate between the two collaborations with S. Biagini, K. Kardaras and M. Nutz. worlds. I argue that quoted prices should be incor- porated through distributional constraints while beliefs, or Bruno Bouchard past data, are most naturally included through pathwise CEREMADE, Universite Paris Dauphine restrictions. The resulting framework is robust and flexi- [email protected] ble. It allows for realistic outputs while quantifying the im- pact of making assumptions. I will present abstract results about pricing-hedging duality and then discuss examples of IP2 restrictions on future realised and future option Multi-Period Mean Variance Asset Allocation: Is prices. Based on joint works with Sergey Nadtochiy (Uni- It Bad To Win the Lottery? versity of Michigan) and Zhaoxu Hou and Peter Spoida (University of Oxford). We present semi-self-financing mean-variance (MV) dy- namic asset allocation strategies which are superior to Jan Obloj self-financing MV portfolio strategies. Our strategies are Mathematical Institute, University of Oxford built upon a Hamilton-Jacobi-Bellman (HJB) equation ap- and the Oxford-Man Institute of Quantitative Finance proach for the solution of the portfolio allocation prob- [email protected] lem. Under an HJB framework, our strategies have a sim- ple and intuitive derivation, and can be readily employed in a very general setting, namely continuous or discrete IP5 re-balancing, jump-diffusions, and realistic portfolio con- Long-Term Valuation and Misspecified Recovery straints. MV strategies are often criticized for penalizing the upside as well as the downside. However, under our Abstract TBD strategies, the MV portfolio optimization problem can be Lars Peter Hansen shown to be equivalent to maximizing the expectation of The University of Chicago a well-behaved utility function of the portfolio wealth. We [email protected] show that, for long term investors, the the use of dynamic MV strategies can achieve the same expected value with a much smaller standard deviation compared to a constant IP6 proportions strategy. Moral Hazard in Dynamic Risk Management

Peter Forsyth We consider a contracting problem in which a principal University of Waterloo hires an agent to manage a risky project. When the agent [email protected] chooses volatility components of the output process and the principal observes the output continuously, the princi- pal can compute the of the output, but IP3 not the individual components. This leads to moral hazard Bid-Ask Imbalance and Trade Arrival Modeling with respect to the risk choices of the agent. Using a recent theory of singular changes of measures for Ito processes, we We consider the dynamics of trade arrivals and best bid formulate a principal-agent problem in this context, and and ask order sizes in an electronic limit order book. The solve it in the case of CARA preferences. In that case, the joint evolution of these events is described by a three- optimal contract is linear in these factors: the contractible dimensional diffusion model. We show how to construct sources of risk, including the output, the quadratic vari- semi-analytical solutions for the probability of price move- ation of the output and the cross-variations between the ment prior to the arrival of an aggressive market order. output and the contractible risk sources. Thus, path- Finally, we calibrate the model to empirical limit order dependent contracts naturally arise when there is moral book data and discuss how it can be used to optimize or- hazard with respect to risk management. We also provide der execution at the tactical level. comparative statics via numerical examples, showing that the optimal contract is sensitive to the values of risk premia Michael Sotiropoulos and the initial values of the risk exposures. Bank of America Merrill Lynch [email protected] Jaka Cvitanic Caltech [email protected] IP4 Robust Meets Realistic: Interpolating Between Model-Specific and Model-Free Settings for Pric- IP7 ing and Hedging Adaptive Grids in Regression Monte Carlo Classical models in mathematical finance, even if highly Regression Monte Carlo has been enormously successful in complex, typically share important methodological weak- numerical solution of optimal stopping problems. It re- nesses: failure to account for model uncertainty and fail- lies on the statistical tool of regression and the probabilis- ure to incorporate market information in a consistent man- tic idea of a stochastic mesh to construct an approximate ner. In the wake of financial crisis these have been much stopping strategy. While the former has been extensively FM14 Abstracts 39

investigated, grid placement is typically prescribed by a ba- [email protected] sic simulation of underlying state process. We discuss the associated layers of inefficiency and introduce adaptive gen- eration of these grids using sequential design schemes. This SP1 accomplishes active learning of the classifiers partitioning SIAG/FME Junior Scientist Prize Lecture: Some the state space into the continuation and stopping regions. Financial Markets with Discontinuities As we show, adaptive refinement of the grids around the stopping boundaries can achieve an order of magnitude We shall discuss some systems of stochastic differential savings in gridding budgets. Moreover, sequential design equations with discontinuous and degenerate diffusion co- opens the door for other statistical approaches, including efficients with applications to stochastic portfolio manage- Bayesian methods, kriging, and multi-armed bandits for ment. The underlying model is tailor-made for the financial this class of control problems. We examine dynamic regres- systems with sadden changes. Allowing discontinuity in the sion algorithms that can implement such recursive estima- description of the system increases the range of phenomena tion of the stopping strategy, and present several numerical which might induce financial crisis. We examine long-time examples in the context of multi-dimensional Bermudan behaviors, and invariant distribution of large fi- option pricing. nancial markets, discuss some applications of Transporta- tion Cost Information inequalities to portfolio comparisons, Mike Ludkovski and propose some optimization problems. University of California at Santa Barbara [email protected] Tomoyuki Ichiba University of California, Santa Barbara Department of IP8 [email protected] The Value of Being Lucky: Option Backdating and Non-diversifiable Risk CP1 The Application of Kmv Model in Chinese Market The practice of executives influencing their option com- pensation by setting a grant date retrospectively is known According to the particularity of China’s ownership struc- as backdating. Since these options are usually granted at- ture of listed company and the macroeconomic conditions, the-money, selecting an advantageous grant date will be a flexible adjustment is introduced into KMV model about valuable to the executive. There is substantial evidence calculation method of default value setting and the value that backdating took place in the US, particularly prior to of equity .Using the adjusted KMV model to evaluate both the tightening of SEC reporting requirements. In this talk, ST (special treatment) companies and non ST companies we develop and solve a utility-indifference model to quan- to test whether the adjusted model works in China mar- tify the value of the opportunity to backdate options. We ket. The outcome show the adjusted KMV model is able to show that the magnitude of ex ante gains from backdat- differentiate between ST and non ST company in Chinese ing is significant. Our model can be used to explain why market. backdating was more prevalent at firms with highly volatile stock prices. Joint work with Jia Sun (China Credit Rat- Haoyun Chen ings) and Elizabeth Whalley (Warwick Business School) School of Statistics and Mathematics Central University of Finance and Economics [email protected] Vicky Henderson University of Warwick CP1 [email protected] Bank Liquidity Risk Management

The Basel III liquidity standard, the liquidity coverage ra- IP9 tio (LCR), is being officially implemented in 2015. As a The Value of Queue Position in a Limit Order Book consequence, it is imperative to understand the stochastic behaviour of this global liquidity standard and its compo- nents. In particular, the LCR is defined as the quotient of Many financial markets are organized as electronic limit high-quality liquid assets (HQLAs) to nett cash outflows order books operating under a price-time priority rule. In (NCOs). In this conference paper, we construct a stochas- practice, this creates a technological arms among high- tic model for the LCR that enables us to solve a stochastic frequency traders to establish advantageous early positions control problem with quadratic cost. In the sequel, we in the resulting FIFO queue. We develop a model for valu- introduce the LCR reference process in terms of which op- ing orders based on their queue position that identifies timal liquidity provisioning rate and HQLAs allocation are two components of positional value: a static component characterized. Furthermore, we propose an adjustment to that relates to the instaneneous trade-off between earning the provisioning rate per unit of the banks NCOs for deficit a spread and incurring adverse selection costs; and a dy- via cash injections. Also, the dynamic programming algo- namic component that captures future value that accrues rithm for stochastic optimization is used to verify the main by locking in given queue position. We empirically cal- results. Finally, we provide the conclusions about the LCR ibrated and test the model. Joint work with Kai Yuan modelling and optimization issues. (Columbia) Mmboniseni Mulaudzi Ciamac C. Moallemi University of South Africa Graduate School of Business Department of Decision Sciences Columbia University [email protected] 40 FM14 Abstracts

Mark Petersen, Janine Mukuddem-Petersen ter Analysis North West University [email protected], ja- We implement a parallelised covariance estimator using [email protected] graphics processor units to compute correlation matrices from large, unevenly sampled financial data sets, based on the Fourier coefficient method of Malliavan and Mancino. CP1 The parallelisation uses a vectorised form of the trigono- metric Fourier estimator and master-slave CPU-GPU pair- Capital Investment and Liquidity Management ing for efficient computation. The estimated sequence of with Collateralized Debt high-frequency trade data correlation matrices are used for high-speed visualisation of cluster dynamics. We analyze the interaction between dividend policy and investment decision of a cash constrained firm. We de- Dieter Hendricks, Tim Gebbie, Diane Wilcox part from the standard literature by allowing the firm to School of Computational and Applied Mathematics issue collateralized debt to invest in productive assets with University of the Witwatersrand decreasing return to scale. This leads us to study a bi- [email protected], dimensional singular control problem that we solve quasi- [email protected], [email protected] explicitly in some special cases and by means of viscosity solution in the general case. CP2 Erwan Pierre Statistically Significant Fits of Hawkes Processes EDF Lab to Financial Data [email protected] Most fits of Hawkes processes in financial literature Stephane Villeneuve are not statistically significant. Using parametric fits, Toulouse School of Economics Kolmogorov-Smirnov tests and assuming a constant exo- [email protected] geneous activity rate, FX trades activity can be fitted up to about one hour provided that the kernel consists of at Xavier Warin least two exponentials; the endogeneity factor is about 0.7. EDF Lab Significant fits of a full day can be achieved if one accounts [email protected] for intra-day variability of exogeneous activity, which yields a larger endogeneity factor (0.8).

CP1 Mehdi Lallouache, Damien Challet Ecole Centrale Paris Fund Management with Liquidity Con- [email protected], straint [email protected] We investigate a model for hedge funds with a liquid- ity constraint seeking to optimise the manager’s utility of CP2 wealth, with one and multiple period horizons. By using Regime Change in Dynamic Correlation Matrices stochastic control techniques we state the corresponding of Financial Data multi-dimensional HJB partial differential equation, which is solved numerically. We examine the manager’s risk- In light of recent trends in algorithmic trading of multi- taking profiles and compare the investor’s utility of wealth assets, this paper proposes a new computational method over different strategies (manager’s profile, risk-free and to estimate the correlation structure of high-dimensional Merton’s optimal) testing which is more beneficial. financial data. We use free random variable techniques and minimize the spectral distance between the theoret- Hugo E. Ramirez ical spectral density of a model and the spectral den- The University of Manchester sity obtained from data. By doing this, we estimate fac- [email protected] tor model parameters with moving windows, which shows regime changes in residual spaces. The mean-reversion Peter Duck time estimated from an Ornstein-Uhlenbeck model is re- The University of Manchester visited for comparison. We analyze a theoretical model School of Mathematics which accounts for system dynamics of correlated assets. [email protected] We return to discuss the applications of these techniques in algorithmic trading. Sydney Howell Joongyeub Yeo The University of Manchester Stanford University Business School [email protected] [email protected]? George C. Papanicolaou Paul Johnson Stanford University The University of Manchester Department of Mathematics School of Mathematics [email protected] [email protected]

CP2 CP2 Hawkes Processes and Applications in Finance High-Speed Fourier Method Estimation of Covari- ances from Asynchronous Data for Real-Time Clus- Hawkes process is a class of jump processes which has FM14 Abstracts 41

self-exciting and clustering effect and is in general non- ciated with global RBF methods, we employ a partition Markovian. Unlike Poisson process, Hawkes process has of unity approach. The free boundary is handled with a dependence across time and is a more realistic model in penalty term. Numerical experiments for one and two as- credit risk, high frequency trading, microstructure noise sets show that the RBF-PU approach is more cost effective etc. Hawkes process has rich behaviors in different regimes, than global RBF approximation. i.e. sublinear, subcritical, critical, supercritical and explo- sive regimes. Scaling limits in different regimes will be Victor Shcherbakov discussed, as well as some applications in finance. Uppsala University [email protected] Lingjiong Zhu University of Minnesota Elisabeth Larsson [email protected] Uppsala University, Department of Information Technology [email protected] CP3 Pricing ”Partial-Average” Asian Options with Bi- nomial Method CP3 Fredholm Expansions and Pde Methods Applied to An is path-dependent derivatives whose pay- Quadratic Functionals of the Ou Process off depends on the average of the underlying asset price over some prespecified period of time. Because there’s no In this paper we compute the bivariate Laplace transform closed-form solutions for the arithmetic Asian option, the of quadratic functionals of the form development of efficient and accurate numerical methods  T  T  becomes critical. In this paper, we present a modified bi- 2 XtdBt, Xt dt nomial method for pricing arithmetic Asian options with 0 0 ”partial-average”, which means the averaging of the asset is applied during some part of the life of the option. We where (Xt)t≥0 is a Ornstein-Uhlenbeck process driven by a extend a simple binomial method proposed by Moon and standard Brownian motion (Bt)t≥0.Ourmethodcombines Kim (2013) to choose the representative averages among PDE arguments with Carleman-Fredholm determinant of all the effective averages. Then, we use backward recur- associated Volterra operators that are computed by Fred- sion and spline interpolation to compute the price of the holm expansions. Classical and new bond pricing formulas option. We compare our results with . in the CIR model are obtained as particular cases. Hailing Wu, Nicolas Privault Erwinna Chendra Nanyang Technological University Institute Technology Bandung, Indonesia [email protected], [email protected] Parahyangan Catholic University, Indonesia [email protected] CP4 Kuntjoro Adji Sidarto, Dila Puspita Return-Volatility Correlation Implied by the Institute Technology Bandung, Indonesia Asymmetry in Options Trading Activity [email protected], [email protected] The author finds a possible cause of asymmetry in options trading activities from return-volatility correlation on the CP3 premise that traders set their net options exposure accord- ing to their anticipation of future correlation to increase Flexible Finite Element Method for Option Pricing the chance to benefit from both price and volatility move- in L´evy Models ments. Also proposed is a way to estimate return-volatility correlation implied by deep out-of-the-money options trad- For some models Finite Element Methods (FEM) for op- ing activities, near the region where the normalized Vega tion pricing have already proven to be efficient and of low is close to the absolute value of Delta. computational cost. The known results and implementa- tions require the system matrix in explicit form. This ex- Jungwoo Lee cludes various examples such as Normal Inverse Gaussian Yonsei University processes for which a standard procedure leads to an explo- [email protected] sion of the computation time. We present a FEM method that is flexible in the L´evy processes as well as efficient and of low computational and implementation cost. CP4 A Model Selection Method for Option Pricing Kathrin Glau Technische Universit¨at M¨unchen Empirical evidence on comparison of option pricing mod- [email protected] els shows that there is no consensus on a single dominat- ing model for all contract parameters and over different time periods. We propose a clustering method to find CP3 the relevant regions of contract parameters for model se- A Radial Basis Function Partition of Unity Penalty lection. Then, we use a decision rule to select the most Method for Pricing American Basket Call Options suitable model over these regions. Finally, we provide out- of-sample testing results using different assets and option Pricing of American options is a challenging problem due pricing methods over different time periods. to the free boundary arising from the early prop- erty. Radial basis function (RBF) approximation is used Berk Orbay, Refik Gullu, Wolfgang Hormann in space. To overcome the high computational cost asso- Bogazici University 42 FM14 Abstracts

[email protected], refi[email protected], hor- firm’s valuation and optimal operating strategies. [email protected] Mingliang Cheng University of Manchester CP4 School of Mathematics [email protected] Efficient Computation of Hedge-Sensitivities Via Automatic Differentiation Geoffrey Evatt Fast and accurate computation of is a pre-requisite The University of Manchester for reliable hedging of securities. We demon- geoff[email protected] strate the computation of such sensitivities through an approach called automatic differentiation. Based on the Paul V. Johnson source code of a finite difference solver of the Black Sc- University of Manchester holes equation, we apply the automatic differentiation tool School of Mathematics TAF to generate code for efficient evaluation of the sen- [email protected] sitivitiy of the derivative price with respect the the price of the underlying asset (Delta) and its volatility (Vega). Through second and third applications of TAF we gener- CP5 ate codes for efficient evaluation of the second (Gamma) Leveraged Investments and Agency Conflicts and third (Speed) derivatives of the derivative price with When Prices are Mean Reverting respect to the price of the underlying asset and the mixed derivative with respect to the asset price and the volati- We analyse the effect of mean reversion on the costs tily (Vanna). Since the derivative caculation is fully auto- of shareholder-bondholder conflicts arising from partially mated, it simplifies the maintenance of a modelling system debt-financed investments. We find that agency costs are for hedging/calibration. much lower under MR dynamics and, through a novel agency cost decomposition, we show that for a high speed Juergen T. Topper of mean reversion (and/or low expected growth in future University of Hannover profits) agency costs are driven mainly by suboptimal tim- d-fine GmbH ing decisions (default and investment) as opposed to sub- juergen.topper@d-fine.de optimal financing decisions. Kristoffer J. Glover, Gerhard Hambusch Thomas Kaminski University of Technology, Sydney FastOpt kristoff[email protected], ger- [email protected] [email protected]

MichaelB.Giles Mathematical Institute CP5 Oxford University An Explicit Formula for the Optimal Government [email protected] Debt Ceiling

We develop a stochastic control model to study the opti- CP4 mal ratio ceiling. We obtain an explicit Holding Period Information in Options Hedging solution for the government debt problem, that gives an explicit formula for the optimal debt ceiling. Moreover, we We examine the possibility of hedging downside risk for derive a practical rule for the optimal debt policy in terms European options, given information on the holding period of the optimal debt ceiling. This research provides the first of our position. Given a random but bounded liquidation theoretical model for the optimal government debt ceiling. date, we explore whether it is possible to effectively hedge a position at lower cost than by focusing on Δ-hedging Ricardo Huaman-Aguilar, Abel Cadenillas present-time sensitivities. Preliminary numerical results of University of Alberta this strategy are compared to standard Δ-hedging and are Department of Mathematical and Statistical Sciences leveraged in the formulation of a closed-form solution. [email protected], [email protected] E. Zambelli University of California, Los Angeles CP5 Anderson School of Management [email protected] On Linear Programing Approach to Inventory Con- trol Problems

This work deals with inventory control problems under the CP5 discounted and long-term average criteria. The objective The Optionality of a Financially Constrained Firm is to minimize the discounted or long-term average total holding and ordering costs. In contrast with the usual dy- We derive a model of a leveraged generic firm that is ex- namical programming approach, this work first imbeds the posed to uncertainties in the size of their future revenues. inventory control problem into an infinite-dimensional lin- In the face of these uncertainties, the firm must make de- ear program over a space of measures and then reduces the cisions that shall benefit its shareholders, such as expan- linear program to a simpler nonlinear optimization. This sion, dividend payments, borrowing levels, and closure. We approach not only determines the value of the inventory present a HJB and a numerical scheme for this class of op- control problem but also identifies an optimal impulse con- timisation problem, and investigate how cash affects the trol policy within restricted classes of control policies. Ad- FM14 Abstracts 43

ditional auxiliary and dual linear programs are introduced Methods: a Unified Approach for Some Interest to verify the optimality of the impulse control policy in the Rate Models general class of control policies. This is a joint work with Kurt Helmes and Richard Stockbridge. All parts of this research are focused on Whittaker func- tions. These functions are special cases of hypergeometric Chao Zhu functions and contrary to the general case they have known University of Wisconsin-Milwaukee asymptotic and analytic continuations laws. After some [email protected] specific change of variables we can obtain a unified struc- ture of Whittaker equation in all investigating models. All results are closed-form solutions and are represented in the CP6 terms of special functions and can be computed numeri- A General HJM Framework for Multiple Curve cally. Modeling Dmitry Muravey We propose a general HJM approach to the modeling of Geolab LLC multiple yield curves. In a general set- [email protected] ting, we model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive HJM drift and con- CP6 sistency conditions ensuring absence of arbitrage and we show how to construct models such that spreads are greater Bond Pricing under Regime Switching among Mul- than one and ordered with respect to the tenor’s length. tiple Short Rate Models When the driving semimartingale is an affine process, we obtain a flexible Markovian structure which allows for sim- We study the bond pricing problem under a regime switch- ple valuation formulas for most interest rate derivatives. ing environment where the dynamics of the short rate is switched among ones of several short rate models. This pa- per derives the solution to the system of partial differential Claudio Fontana equations in a form of recursive integrals by the homotopy University of Evry Val d’Essonne perturbation method. The solution has the same form as [email protected] the Adomian decomposition method to a system of mixed Volterra-Fredholm type integral equations. The price of an Christa Cuchiero European-type derivative on the short rate is also derived University of Vienna in the same form. [email protected] Keiichi Tanaka Alessandro Gnoatto Tokyo Metropolitan University LMU Munich [email protected] [email protected] CP7 CP6 Pricing and Hedging Exotic Options with Transac- Pricing with Counter- tion Cost under Jump-Diffusion Process party Risk and Funding Costs: A L´evy CVA Multiple-curve Model Numerical schemes often develop inaccuracies, when pric- ing financial derivatives with non-smooth payoff or its We propose a general framework for the valuation of in- derivatives have multiple discontinues. Averaging the ini- terest rate derivatives in the post-crisis setup. We first tial data, shifting the grid, and projection methods have develop a multiple-curve HJM-type model driven by L´evy been tried to deal with such discontinuities. Moreover, processes. To account for counterparty and funding risks, large error may occur in estimating the hedging param- the calibrated multiple-curve model is then used as an un- eters. A new class of Exponential Time Differencing derlying model for CVA computation. The problem of schemes are presented which are highly efficient and re- computing the counterparty risk and funding adjustments liable in dealing with path dependent exotic options with can be expressed via a pre-default Markovian BSDE, which transaction cost under jump-diffusion process. is solved by numerical methods. We discuss the impact of these adjustments on several examples. Waseem A. Khan Zorana Grbac CIIT, ISLAMABAD, PAKISTAN University Paris-Diderot [email protected] [email protected] Mohammad Rasras, Abdul Khaliq St´ephane Cr´epey, Nathalie Ngor Middle Tennessee State University University of Evry Val d’Essonne [email protected], [email protected] [email protected], [email protected] Mohammad Yousuf David Skovmand King Fahd University of Petroleum and Minerals Copenhagen Business School Saudi Arabia dgs.fi@cbs.dk [email protected]

CP6 CP7 Laplace Transform and Hypergeometric Functions Convergence of Monte-Carlo Computation on Var- 44 FM14 Abstracts

ious Exotic Options [email protected]

This paper develops approximation methods for path- CP8 dependent functionals, which have been used in many ap- plications involving path-dependent objective functions. In Systemic Risk with Jump-Diffusion Processes contrast to the traditional approach, this work provides a non-traditional convergence method in Monte Carlo anal- We illustrate what a systemic risk is by proposing an inter- ysis based on actual computations under the Skorohod bank borrowing and lending model using a stochastic flock- topology. Some examples such as the approximation of ing system with jump-diffusion processes. We use the discretely monitoring are considered. Laplace transform approach and the inversion formula in- stead to calculate the systemic risk. We then integrate a game feature with jumps where each bank controls its rate Qingshuo Song of borrowing/lending to a central bank. We have solved City University of Hong Kong an Nash equilibria with jumps in game theory with finitely [email protected] many banks.

Yi-Tai Chiu CP7 UCSB department of statistics and applied probability [email protected] Gaussian Markov Processes and Option Pricing Theory Jean-Pierre Fouque University of California at Santa Barbara I will discuss the development, testing, and implementation [email protected] of a less restrictive alternative to the Black-Scholes model for pricing derivatives. By relaxing the assumption of past independence but retaining the Markovian property, we CP8 are able to develop a less restrictive but equally efficient Dynamics of Trust in Networks and Systemic Risk model. This is achieved by replacing Black-Scholes’ under- lying process, Brownian motion, with a certain Gaussian Trust is a collective, self-fulfilling phenomenon that sug- Markov process. gests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in Mackenzie Wildman, Vladimir Dobric, Daniel Conus networks, which generically displays a first order transi- Lehigh University tion. The basic assumption of our model is that whereas Department of Mathematics trust begets trust, panic also begets panic, in the sense [email protected], [email protected], that sudden drops of trustworthiness may lead to sell-offs [email protected] that further decreases trust. We show, using both numer- ical simulations and mean-field analytical arguments, that there are extended regions of parameter space where two equilibrium states coexist: a well connected network where CP7 confidence is high, and a poorly connected network where Optimal Multiple Stopping with Negative Discount confidence is low. In these coexistence regions, sponta- Rate and Random Refraction Times under L´evy neous jumps between the two states can occur, correspond- Models ing to a sudden collapse of trust that is not caused by any major catastrophe. For large systems, spontaneous crises This paper studies a class of optimal multiple stopping are replaced by history dependence: whether the system is problems driven by L´evy processes. Our model allows for found in one state or in the other essentially depends on a negative effective discount rate, which arises in a num- initial conditions. ber of financial applications, including stock loans and real Joao DA GAMA BATISTA options, where the can potentially grow at a Ecole Centrale Paris higher rate than the original discount factor. Moreover, [email protected] successive exercise opportunities are separated by i.i.d. random refraction times. Under a wide class of two-sided L´evy models with a general random refraction time, we Jean-Philippe Bouchaud rigorously show that the optimal strategy to exercise suc- Capital Fund Management cessive call options is uniquely characterized by a sequence - of up-crossing times. The corresponding optimal thresh- olds are determined explicitly in the single stopping case Damien Challet and recursively in the multiple stopping case. Ecole Centrale Paris - Tim Leung Columbia University CP8 [email protected] Optimal Capital Reserve Strategies for a Bank and Its Regulator Kazutoshi Yamazaki Kansai University We present a general model of a deposit taking bank and [email protected] its regulator, where the bank’s loans are exposed to default risk. The bank’s objective is to maximise their market Hongzhong Zhang value of equity by appropriately controlling loan issuance, Department of Statistics dividend payments, and endogenous closure. The regu- Columbia University lator’s objective is to minimise the overall probability of FM14 Abstracts 45

bank closure by appropriately setting the bank’s capital arrivals of limit orders, market orders, and cancellations adequacy ratio, whilst simultaneously considering the im- are memoryless and stationary, but to account for some pact upon bank lending volumes. of the sparsity that has been observed empirically, a more realistic approach is pursued in a model which allows for Geoff Evatt both a variable spread and, more importantly, memory by University of Manchester keeping the information about the standing orders at the School of Mathematics opposite side of the book after a price change has occurred. geoff[email protected] In spite of the inherent model complexity, we are able to characterize the long-run behavior of the resultant mid- price process and, hence, our analysis shed further light on CP8 the relation between the observed macro price dynamics Financial Contagion with Heterogeneous Link- and the LOB features. The analysis is complemented with Weight Distributions a numerical procedure to simulate the order book with the given constraints. The recent financial crisis highlighted the importance of understanding the financial system as a complex interact- Jonathan A. Ch´avez Casillas,Jos´e Figueroa-L´opez ing system. In this paper, we focus on the contribution Purdue University of heterogeneity in link-weights of financial networks. We [email protected], fi[email protected] analyze how heterogeneous link-weight distributions affect contagion in different types of financial networks. Further- more, we explore the evolution of these networks in multi- CP9 ple shock scenarios. A Stochastic Free Boundary Problem and Limit Yuanying Guan Order Book Model Indiana University Northwest [email protected] We introduce a continuous model for the limit order book density with infinitesimal tick size, where the evolution of Micah Pollak buy and sell side is described by a semilinear SPDE and Indiana University Northwest the mid price defines a free boundary. Price changes are Department of Economics assumed to be determined by the bid-ask imbalance. We [email protected] transform the resulting stochastic free boundary problem into an evolution equation to study local existence, unique- ness and further properties. CP9 Optimal Liquidation in Limit Order Books under Marvin Mueller General Uncertainties Technical University Berlin [email protected] We consider the optimal strategy of a passive trader trad- ing in the limit order book wishing to maximize his ex- Martin Keller-Ressel pected utility, with the asset price following Geometric TU Dresden Brownian Motion. We reduce the resulting Hamilton- [email protected] Jacobi-Bellman PDE to a non-linear PDE with reduced di- mension and number of parameters. We numerically solve the PDE before asymptotically examining it in several vari- CP9 ables. We emphasize the adaptability of our methodologies Optimum Strategy in Market Order Execution As- by introducing a mean-reverting process for the asset price. sociated with the Poisson Cluster Process

James Blair We consider discrete optimal execution problem for market School of Mathematics order trading under different micro structure. Order flow University of Manchester can be viewed as occurring to a Poisson cluster process [email protected] with stochastic intensity. Interaction between price impact and price dynamics can model as a dynamic optimization with price impact as a function in the self-exciting process Paul V. Johnson dynamic. With constructing numeric boundaries on the University of Manchester order flow, we execute the amount of notional whenever School of Mathematics the bidding price hits or higher than the boundary. [email protected] Amirhossein Sadoghi Peter Duck Department of Computer Science University of Manchester Link¨oping University [email protected] [email protected]

CP9 Jan Vecer Columbia University Long-Run Price Dynamics under a Level-1 Lob Department of Statistics with Memory and Variable Spread [email protected] Motivated by Cont and de Larrard’s seminal Limit Or- der Book (LOB) model, a continuous-time queuing-based stochastic model is proposed. As in Cont and Larrard’s CP10 model, just one level in the order book is considered; the Set-valued Shortfall Risk Measures for Multi-asset 46 FM14 Abstracts

Markets case.

In a multi-asset market with frictions, existence of indi- Ludger Overbeck vidual utility functions for assets is assumed and the cor- Institute of Mathematics responding utility-based set-valued shortfall risk measures University of Giessen are studied. Their values are defined as the solutions of [email protected] certain convex set optimization problems. Using a recent set-Lagrange duality, dual problems are obtained and they give rise to multi-objective versions of optimized certainty CP10 equivalents. Examples include the entropic risk measure Shortfall Aversion and average value at risk. We solve the problem of optimal consumption and invest- Cagin Ararat, Birgit Rudloff ment, with a representative agent who is more sensitive Princeton University to declines than to increases in consumption (i.e., with [email protected], brudloff@princeton.edu shortfall aversion), and investment opportunities are con- stant. We solve the resulting free-boundary problem in Andreas Hamel closed form, using a combination of stochastic control and Free University of Bozen-Bolzano duality methods. Consumption remains constant over long [email protected] intervals, increases gradually as wealth is high relative to its current consumption, and falls below its last recorded maximum when wealth is low. The model implies that in CP10 bad times consumption is more volatile and investment is Dynamic Optimal Portfolio Choices for Robust higher. Preferences Paolo Guasoni This project considers an optimal dynamic portfolio choice Boston University problem for an ambiguity-averse investor. It introduces Dublin City University new preferences that allow the separation of risk and am- [email protected] biguity aversion. The novel representation is based on gen- eralized divergence measures that capture richer forms of Gur Huberman model uncertainty than traditional relative entropy mea- Columbia Business School sures. The novel preferences are shown to have a ho- [email protected] mothetic stochastic di?erential utility representation, and render a closed form solution for the investor with con- Dan Ren stant relative risk aversion. Based on this representa- University of Dayton tion, optimal portfolio policies are derived using numeri- [email protected] cal schemes with forward-backward stochastic di?erential equations and Monte Carlo simulation based on the Clark- Ocone presentation and . The optimal CP11 portfolio policy is shown to contain new hedging motives induced by the investors attitude toward model uncer- A Fast Calibrating Volatility Model for Option tainty. Ambiguity concerns introduce additional horizon Pricing e?ects, boost e?ective risk aversion, and overall reduce op- timal investment in risky assets. These ?ndings have im- We propose a new model, where the portant implications for the design of optimal portfolios in volatility has a deterministic term structure modified by the presence of model uncertainty. a scalar random variable. A closed-form approximation is derived for European option price using higher order Jingshu Liu, Marcel Rindisbacher Greeks. Through comprehensive numerical experiments Boston University on real data, we show that our model achieves accuracy [email protected], [email protected] comparable to the and Bates model in op- tion pricing, while being significantly cheaper to calibrate, and to simulate from, as compared to the aforementioned CP10 models. Classical Differentiability of Bsvies and Dynamic Capital Allocations Paresh Date Brunel University Capital allocations have been studied in conjunction with [email protected] static risk measures in various papers. The dynamic case has been studied only in a discrete-time setting. We ad- dress the problem of allocating risk capital to subportfolios CP11 in a continuous-time dynamic context. For this purpose we The Small Maturity Slope for introduce a classical differentiability result for backward Levy Models stochastic Volterra integral equations and apply this re- sult to derive continuous-time dynamic capital allocations. We consider the at-the-money strike derivative of implied Moreover, we study a dynamic capital allocation princi- volatility as the maturity tends to zero. Our main results ple that is based on backward stochastic differential equa- quantify the growth of the slope for infinite activity expo- tions and derive the dynamic gradient allocation for the nential Levy models. As auxiliary results, we obtain the dynamic entropic risk measure. As a consequence we fi- limiting values of short maturity digital call options, using nally provide a representation result for dynamic risk mea- a novel for . Finally, sures that is based on the full allocation property of the we discuss when the at-the-money slope is consistent with Aumann-Shapley allocation, which is also new in the static the steepness of the smile wings, as given by Lee’s moment FM14 Abstracts 47

formula. OTC derivative – for instance a double structure call op- tion based on exchange traded contracts on energy and Stefan Gerhold,IsmailG¨ul¨um weather. TU Wien [email protected], is- Nina Lange [email protected] Copenhagen Business School nl.fi@cbs.dk CP11 Fred Espen Benth Pricing American under University of Oslo Stochastic Volatility with Non Smooth Payoffs [email protected] We consider a two-pass free boundary PDE problem of pricing American Compound options under Heston’s CP12 stochastic volatility. A penalty method approach is used to deal with the free boundary. A linearly implicit scheme Optimal Writing of American Call Options on Elec- based on split Adams-Moulton formulas, is implemented tricity with Physical Delivery: A Free Boundary by treating the nonlinear penalty term explicitly, while Analysis of Optimal Entry maintaining superior accuracy and stability properties. We present the numerical experiments to demonstrate the com- We study American call options on electricity used in real- putational efficiency, accuracy and reliability of the method time balancing of electrical power systems. This involves for non-smooth payoffs. timing the purchase of electricity to be stored and deliv- ered in the contract and pricing of the itself. Kamran Kazmi We give a complete free boundary analysis for simple and Mathematics Department plausible models of the electricity spot price, characteris- University of Wisconsin Oshkosh ing stopping regions (with and without the smooth fit) and [email protected] value functions for both single and swing options. Jan Palczewski Mohammad Yousuf University of Leeds King Fahd University of Petroleum and Minerals [email protected] Saudi Arabia [email protected] John Moriarty University of Manchester Abdul Khaliq [email protected] Middle Tennessee State University [email protected] CP12 CP11 Enhancement of Practice-Based Methods for the Computation of the Delta of European Options un- Real Option Management of Commodity Storage der Stochastic Volatility Models Assets

The sensitivity analysis of options to the underlying param- The real option management of commodity storage assets eters is a fundamental area of research in financial model- is an important practical problem. Practitioners heuris- ing. For practitioners, the information the Greeks contain tically manage commodity storage assets using the rolling is widely used for measuring and managing risk. In this intrinsic and basket of spread options methods, which yield study we apply Malliavin calculus techniques to compute typically near optimal policies and, combined with Monte the delta of European type options in presence of stochastic Carlo simulation, lower bound estimates on the value of volatility. We define a general stochastic volatility model storage. This talk enhances these methods by developing and obtain a formula for the delta within. We conclude a simple, fast, and effective dual upper bound tailored for our work with some numerical results. them.

Yeliz Yolcu Okur, Bilgi Yilmaz, Alper Inkaya Nicola Secomandi Institute of Applied Mathematics, METU Carnegie Mellon [email protected], [email protected], Tepper School of Business [email protected] [email protected]

Tilman Sayer Fraunhofer Institute for Industrial Mathematics CP12 [email protected] Modeling Risks in Climate Change by Real Option Analysis

CP12 A large numbers of industries will experience climate Hedging of Quantity Risk in Energy Markets change related damages with the climate change processes over the coming years. In this paper, we treat the sea level In energy markets, quantity risk is inherent. An electric- and the temperature as the underlying assets and propose ity company has to deliver any demanded quantity at a a real option model to evaluate potential sea level rising fixed rate, thus facing an amplified risk due to positive risk management opportunities. The American real op- correlation between quantity and prices. We address the tion problem is formulated to a linear parabolic variational issue of correlation risk and show that sometimes, it is inequality. A so-called fitted finite volume method is pro- more efficient for an energy company to enter a structured posed to solve the nonlinear PDE and the convergence of 48 FM14 Abstracts

the fully discrete scheme is established. Numerical experi- ters will be presented. ments are given to illustrate the theoretical results. Slobodan Milovanovic Shuhua Zhang Uppsala University Tianjin University of Finance and Economics [email protected] Tianjin, China [email protected] Lina von Sydow Department of Information T Uppsala University CP13 [email protected] A Grid Based Optimization Algorithm to Select Intertwined Markets That Maximize Trading Re- turns CP13 Marginal Quantization of An Euler Diffusion Pro- Aset,{xi(t):1≤ i ≤ k},ofk price functions on a fi- cess and Its Application to Finance nite discrete time domain is intertwined if there is a linear combination, e(t)=α0 + α1x1(t)+α2x2(t)+...+ αkxk(t) We propose a new method to quantize the Euler diffusion such that e(t) has at least two zero crossings. We develop process. This raises new challenging questions as the anal- an algorithm to find an optimal e(t) which maximizes a ysis of the induced quantization error. We show that at nonlinear multi-objective of the total zero crossings and any tk, the error is bounded by the cumulative quantiza- trading returns on a grid based on αi values. We show tion errors (up to time tk) associated to the Euler operator. the results for pair (k = 2) and triple (k = 3) trading of For numerics, we restrict our analysis to the one dimen- markets. sional setting and show how to perform the optimal grids using the Newton algorithm. This allows us to quantize in Athula D. Gunawardena, William Dougan particular diffusion processes by reducing University of Wisconsin-Whitewater dramatically the computational complexity of the search [email protected], [email protected] of optimal quantizers while increasing their computational precision with respect to the algorithms commonly pro- Patrick Monaghan posed in this framework. Numerical tests are carried out Blackthorne Capital Management, LLC for the pricing of European options in a local volatility [email protected] model and a comparison with the MC simulations shows that the proposed method is more efficient (w.r.t. both computational precision and time complexity). CP13 Abass Sagna A Second Order Discretization Scheme for the Ex- LaMME, Evry University, French tended Cox-Ingersoll-Ross Process [email protected]

We propose a weak second order discretization scheme for Gilles Pag`es the extended Cox-Ingersoll-Ross process. In order to pre- LPMA, Universit´eParis6 serve the nonnegativity of the process, we use two different [email protected] approaches according to the current state of the scheme. When the scheme is far from the origin, we exploit the composition techniques of Ninomiya and Victoir. When CP14 the scheme approaches the origin, we generate a discrete random variable which matches the first two moments up Indifference Pricing of Variable Annuities to the second order terms. We extend our discretization We consider the pricing problem of variable annuities, scheme to the extended CIR process with jumps. We per- mainly GMDB (Guaranteed Minimum Death Benefit) and form numerical experiments to compare our schemes with GLWB (Guaranteed Lifetime Withdrawal Benefit). The others in terms of convergence. Hamilton-Jacobi-Bellman PDE (Partial Differential Equa- tion) is derived for the corresponding utility function, and Chulmin Kang the principle of equivalent utility is applied to derive the Departement of Mathematical Sciences, KAIST pricing PDE for the indifference price when we employ the Republic of Korea exponential utility function. Numerical examples are per- [email protected] formed when the mortality follows Gompertz law.

Jungmin Choi CP13 Florida State University Radial Basis Functions Generated Finite Differ- [email protected] ences (RBF-FD) for Solving High-Dimensional PDEs in Finance CP14 We consider RBF-FD methods for PDEs in option pricing. Regression-based Monte Carlo Methods for Thanks to being mesh-free and yielding sparse matrices, Stochastic Control Models: Variable Annuities these methods are expected to be advantageous for high- with Lifelong Guarantees dimensional problems compared to Monte Carlo (slow con- vergence), RBF (dense matrices) and FD methods (require We present the regression-based Monte Carlo simulation grids). Implementation has been made for Black-Scholes- algorithms for solving the stochastic control models asso- Merton equation with European call option payoff in 1D ciated with pricing and hedging of the Guaranteed Lifelong and 2D. Convergence and performance as a function of Withdrawal Benefit (GLWB) in variable annuities, where boundary conditions, basis functions and shape parame- the dynamics of the underlying fund value is assumed to FM14 Abstracts 49

evolve according to the stochastic volatility model. The Department of Banking and Financial Management GLWB offers a lifelong withdrawal benefit even when the [email protected] policy account value becomes zero while the policyholder remains alive. Upon death, the remaining account value Constantinos Kardaras will be paid to the beneficiary as a death benefit. The London School of Economics bang-bang control strategy analyzed under the assumption [email protected] of maximization of the policyholders expected cash flow reduces the strategy space of optimal withdrawal policies to three choices: zero withdrawal, withdrawal at the con- CP15 tractual amount or complete surrender. The impact on the GLWB value under various withdrawal behaviors of Asymptotics for Merton Problem with Capital the policyholder is examined. We also analyze the pricing Gain Taxes and Small Interest Rate properties of GLWB subject to different model parameter values and structural features. We consider the Merton problem with capital gain taxes. Since closed-form solutions are generally unavailable, we Yao Tung Huang, Yue Kuen Kwok provide asymptotic expansions with small interest rate and Hong Kong University of Science and Technology other parameters, and then obtain an explicit investment [email protected], [email protected] and consumption strategy that effectively approximates the optimal strategy. The expansions also offer qualita- tive and quantitative insights about the effects of various CP14 parameters on the optimal strategy. In addition, we find Constant Proportion Portfolio Insurance in De- that the optimal tax-deflated fraction of initial wealth in fined Contribution Pension Plan Management the risky asset is higher than the ”Merton line” provided that there is a positive interest rate. In this study, we focus on the optimal portfolio prob- lem in pension fund management under a portfolio insur- Min Dai ance methodology. By extending the ”Constant Proportion Dept of Math and Risk Management Institute Portfolio Insurance” method for defined-contribution pen- National University of Singapore sion plans, we solve stochastic optimal control problems for [email protected] each participant and obtain optimal portfolios. Assuming stochastic market dynamics, we define a stochastic lower bound on the portfolio wealth, based on the stochastic con- CP15 tribution payments. We also present simulation results on Tax-Aware Dynamic Asset Allocation the performance of our algorithms. We construct sub-optimal policies for dynamic portfolio Busra Z. Temocin optimization problems with taxes. We consider problems Institute of Applied Mathematics with all combinations of (i) full-use-of-losses vs. limited- Middle East Technical University use-of-losses and (ii) exact tax basis vs. average tax basis. [email protected] We show the dual versions of these problems based on infor- mation relaxations are generally easy to solve so that good Ralf Korn lower and upper bounds on the optimal objective function Department of Mathematics can be obtained. University of Kaiserslautern [email protected] Martin B. Haugh Department of IE & OR Sevtap Kestel Columbia University Institute of Applied Mathematics [email protected] Middle East Technical University [email protected] Garud N. Iyengar Columbia University Dept of Indust Eng & Oper Rsch CP15 [email protected] Equilibrium in Risk Sharing Games Chun Wang We study equilibrium sharing of investment risk among Columbia University agents whose random endowments constitute private in- [email protected] formation. Given the sharing rules that optimally allo- cate the submitted endowments, we propose a Nash game where agents’ strategic choices consist of the endowments CP15 to be submitted for sharing. It is proved that the best re- sponse problem admits a unique solution and differs from Mean Field Games and Systemic Risk: Heteroge- the agent’s true risk exposure. Then, we proceed in show- neous Grouping Models ing that the Nash equilibrium risk sharing admits a fi- nite dimensional characterization, and that it exists and In the previous paper “Mean Field Games and Systemic is unique in the case of two agents. Analysis shows that Risk”, we proposed a simple homogeneous model of inter- the game benefits the agents close to risk neutrality, since bank borrowing and lending. We now consider heteroge- their expected utilities are higher at the Nash risk sharing neous grouping cases where parameters are identical within equilibrium than the optimal risk-sharing one. their own groups but different between groups. Due to this heterogeneity, a central bank must keep deposits or pro- Michail Anthropelos vide extra cash flow instead of acting as a clearing house University of Piraeus and systemic risk happens in the more complicated manner 50 FM14 Abstracts

than the homogeneous case. swaps and S&P 500 options.

Li-Hsien Sun Dacheng Xiu Statistics and Applied Probability University of Chicago University of California Santa Barbara [email protected] [email protected] Dante Amengual Jean-Pierre Fouque CEMFI University of California at Santa Barbara amengual@cemfi.es [email protected] CP16 CP16 Market Option Prices and the Informational Con- Volatility, Risk-Premiums and Feedback Effect sistency The objective of the paper is to examine empirically a fun- We consider risk-premiums, volatility feedback effect and damental issue of informational consistency across options the leverage effect for stochastic and local volatility mod- prices with different for the same expiry. For els, including the GARCH family. The change in risk- this objective, we develop an option pricing model that de- premiums through time can be captured by identifying the pends solely on the return distribution of underlying asset change in the risk-neutral probability measure, which is at expiry and introduce a flexible return density function proportional to volatility of the price process. In some depicting up to the fourth moments of return. We find the cases, using Malliavin calculus, we investigate the relation different moneyness options share similar, but not exactly between the time-varying risk-premiums for various volatil- the same, structural parameter information. The options ity models and the asymmetric relation between return and with strike price far from the underlying asset price tend volatility. to exhibits economically larger volatility than the near at- Alper Inkaya the-money options. The result has a significant implication Institute of Applied Mathematics, METU on the VIX measure at CBOE. [email protected] Hongtao Yang University of Nevada, Las Vegas [email protected] CP16 Asian Option Pricing Using Mellin Transform for Seungmook Choi BN-S Models with Stochastic Volatility University of Nevada Las Vegas [email protected] In this talk, we consider a friction-less financial market driven by the generalized Barndorff-Nielsen and Shep- hard (BN-S) model which admits Ornstein-Uhlenbeck type CP17 stochastic volatility modeling. For such market a pricing Stochastic Target Problems with Controlled Prob- equation is derived for the floating strike put arithmetic ability of Success - A Probabilistic Approach Asian options. A solution procedure for the resulting par- tial differential equation is provided using the technique of We study a stochastic target problem with a controlled Mellin transforms. probability of success on a set of deterministic dates. We reduce the problem to a problem of super-replication of a Indranil Sengupta Bermudean option and study some important properties of Department of Mathematics the value function. We then apply our results to the so- North Dakota State University called quantile hedging problem when the constraint holds [email protected] on a set of deterministic dates and find an explicit solution under the framework of complete market.

CP16 Geraldine Bouveret, Jean-Francois Chassagneux Resolution of Policy Uncertainty and Sudden De- Imperial College London clines in Volatility [email protected], [email protected] We introduce downward volatility jumps into a general non-affine modeling framework of the term structure of Bruno Bouchard variance. With both variance rates and the S&P 500 CEREMADE, Universite Paris Dauphine returns, we find that downward volatility jumps are asso- [email protected] ciated with a resolution of policy uncertainty, in particular through statements from Federal Open Market Commit- tee meetings and speeches of Federal Reserve chairmen, CP17 and that such jumps are priced with positive risk pre- Time Consistent Portfolio Selection under Short- mia, which reflect the premia for the “put protection” of- Selling Prohibition fered by the Federal Reserve. Ignoring downward volatility jumps may lead to an exaggeration of the negative variance In this talk, I shall introduce the time consistent strategies risk premia documented in the literature hence a biased- in the mean-variance portfolio selection with short-selling interpretation of the price of tail events. On the modeling prohibition. By applying the extended Hamilton-Jacobi- side, we find that log-volatility models with at least one Bellman equation (HJB), we obtain time consistent equi- Ornstein-Uhlenbeck factor with two-sided jumps are supe- librium control. In some numerical example, the equilib- rior in capturing volatility dynamics and pricing variance rium strategies in the model with short-selling prohibition FM14 Abstracts 51

can outperform the strategies without short-selling prohi- Department of Math & Stat Sciences bition. I will analyze this non-typical observation in both University of Alberta mathematical and economical aspects. [email protected]

Kwok Chuen Wong Abel Cadenillas Department of Mathematics, University of Alberta Imperial College London Department of Mathematical and Statistical Sciences [email protected] [email protected]

Alain Bensoussan The University of Texas at Dallas and MS1 City University of Hong Kong, Hong Kong Rationalizing Investors’ Choices [email protected] Assuming that agents’ preferences satisfy first-order Phillip S. Yam stochastic dominance, we show how the Expected Utility Department of Statistics paradigm can rationalize all optimal investment choices: The Chinese University of Hong Kong the optimal investment strategy in any behavioral law- [email protected] invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explic- Siu Pang Yung itly derived concave non-decreasing utility function. This Math. Dept., University of Hong Kong result enables us to infer the utility and risk aversion of [email protected] agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the ter- CP17 minal wealth and of the financial market. Specifically, we Turnpike Property and Convergence Rate for an show that DARA is equivalent to a demand for a terminal Investment Model with General Utility Functions wealth that has more spread than the opposite of the log pricing kernel at the investment horizon. In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high lev- Carole Bernard els of wealth: one is whether the turnpike property still University of Waterloo holds for a general utility that is not necessarily differen- [email protected] tiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be Jit Seng Chen estimated. We give positive answers to both questions. To GGY, Toronto achieve these results, we first show that there is a classical [email protected] solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution Steven Vanduffel to the dual HJB equation. We demonstrate the usefulness Vrije Universiteit Brussel, . of that representation with some nontrivial examples that steven.vanduff[email protected] would be difficult to solve with the trial and error method. We then combine the dual method and the partial differen- tial equation method to give a direct proof to the turnpike MS1 property and to estimate the error and the convergence Equilibrium Asset Pricing with Rational and Irra- rate of the optimal policy when the utility function is con- tional Investors tinuously differentiable and strictly concave. We finally re- lax the conditions of the utility function and provide some We study a multi-period asset pricing problem with ratio- sufficient conditions that guarantee the turnpike property nal investors having recursive utility preferences and irra- and the convergence rate in terms of both primal and dual tional investors having additional utility of trading gains utility functions. and losses represented by cumulative prospect theory. In the logarithmic utility case, we derive the unique equilib- Harry Zhang rium analytically and show the market dominance of the Imperial College rational investors in the long run. Moreover, we propose [email protected] a stock performance measure and show that the irrational investors hold less equities than the rational investors if and only if their loss aversion degree is higher than this CP17 measure. Finally, we develop an algorithm to compute the Optimal Investment and Risk Control Policies for equilibrium in the general case. An Insurer: Expected Utility Maximization Jing Guo Motivated by the AIG bailout case in the financial crisis Columbia University of 2007-2008, we consider an insurer whose risk is modeled [email protected] by a jump-diffusion process and is negatively correlated with the stock returns in the financial market. The in- surer wants to maximize her/his expected utility of termi- MS1 nal wealth by selecting optimal investment and risk control Rank Dependent Utility and Risk Taking in Com- policies. We apply the martingale approach to obtain ex- plete Markets plicit solutions of optimal policies for various utility func- tions. We analyze the portfolio choice problem of investors who maximize rank dependent utility in a single-period com- Bin Zou plete market. We propose a new notion of less risk taking: 52 FM14 Abstracts

choosing optimal terminal wealth that pays off more in bad Daniel Bauer states and less in good states of the economy. We prove Georgia State University that investors with a less risk averse preference relation Department of Risk Management and Insurance in general choose more risky terminal wealth, receiving a [email protected] risk premium in return for accepting conditional-zero-mean noise (more risk). Such general comparative static results do not hold for portfolio weights, which we demonstrate MS2 with a counter-example in a continuous-time model. Computation of Risk Measures for Variable Annu- ity Guaranteed Benefits Xuedong He Columbia University From the viewpoint of computational finance, variable an- Department of Industrial Engineering and Operations nuity guaranteed benefits are variations of path-dependent Research financial derivatives. However the quantification and as- [email protected] sessment of long-term liabilities pose difficult but intriguing technical challenges. It has been reported in recent indus- Roy Kouwenberg trial surveys that the current market practice of Monte Mahidol University Carlo simulations is often time-consuming and the cost Erasmus University Rotterdam is prohibitive. We developed several analytical solutions [email protected] and algorithms for the computation of risk measures using Xunyu Zhou eigenfunction expansion and numerical PDE methods. University of Oxford and The Chinese University of Hong Kong Runhuan Feng, Runhuan Feng [email protected] University of Illinois at Urbana-Champaign Department of Mathematics [email protected], [email protected] MS1 The Effect of Time Changing Risk Aversion on Hans W. Volkmer Equilibrium Pricing University of Wisconsin-Milwaukee Department of Mathematical Sciences In this paper, we propose an equilibrium pricing model [email protected] in a dynamic multi-period stochastic framework with uncertain income. There are one tradable risky asset (stock/commodity), one non-tradable underlying (temper- MS2 ature), and also a contingent claim (weather derivative) Hedging Costs for Variable Annuities under written on the tradable risky asset and the non-tradable Regime-Switching underlying in the market. The price of the contingent claim is priced in equilibrium by optimal strategies of represen- A general methodology is described in which policyholder tative agent and market clearing condition. The risk pref- behaviour is decoupled from the pricing of a variable an- erences are of exponential (CARA) type with a stochastic nuity based on the cost of hedging it, yielding two weakly coefficient of risk aversion. Both Nash subgame perfect coupled systems of partial differential equations (PDEs): strategies and naive strategies are considered. From the the pricing and utility systems. The utility system is used numerical result we examine how the equilibrium prices to generate policyholder withdrawal behaviour, which is in vary in response to changes in model parameters and high- turnfedintothepricingsystemasameanstodetermine light the importance of Nash equilibrium pricing principle the cost of hedging the contract. This approach allows us to incorporate the effects of utility-based pricing and factors such as taxation. As a case study, we consider the Guar- Traian A. Pirvu anteed Lifelong Withdrawal and Death Benefits (GLWDB) McMaster University contract. The pricing and utility systems for the GLWDB [email protected] are derived under the assumption that the underlying as- set follows a Markov regime-switching process. An implicit PDE method is used to solve both systems in tandem. MS2 Revisiting the Risk-Neutral Approach to Optimal Peter Forsyth Policyholder Behavior: a Study of Withdrawal University of Waterloo Guarantees in Variable Annuities [email protected]

Policyholder exercise behavior presents an important risk factor. However, presented approaches – building on Amer- MS2 ican option pricing – do not square with observed prices Optimal Initiation of a Glwb in a Variable Annuity: and exercise patterns. We show that including taxes into No Arbitrage Approach the valuation closes this gap between theory and practice. In particular, we develop a “subjective” risk-neutral valua- This paper offers a financial economic perspective on the tion methodology that accounts for differences in taxation. optimal time (and age) at which the owner of a Variable Applications to VAs with withdrawal guarantees show that Annuity (VA) policy with a Guaranteed Living Withdrawal tax advantages significantly affect the value and yields re- Benefit (GLWB) rider should initiate guaranteed lifetime alistic patterns and fees. income payments. Our main practical finding is that given current design parameters in which volatility (asset alloca- Thorsten Moenig tion) is restricted to less than 20%, while guaranteed pay- University of St. Thomas out rates (GPR) as well as bonus (roll-up) rates are less [email protected] than 5%, GLWBs that are in-the-money should be turned FM14 Abstracts 53

on by the late 50s and certainly the early 60s. Our method- pricing model with fractional diffusion. ology and results should be of interest to researchers as well as to the individuals that collectively have over $1 USD Cecile M. Piret trillion in aggregate invested in these products. Universit´e catholique de Louvain [email protected] Huaxiong Huang Department of Mathematics and Statistics, York University MS3 4700 Keele Street, Toronto, Ontario, Canada Efficient Pricing of Vanilla and Exotic Options with [email protected] Multiple Discrete Dividends using Finite-difference Method for Algorithmic Trading System Moshe Milevsky Schulich School of Business We calculate prices of European, American, barrier, turbo, York Univeresity and Asian options with multiple discrete dividends. The [email protected] framework is based on the finite-difference method for Black-Scholes equation. We apply analytical smoothing of final condition to improve properties of the numerical Tom Salisbury algorithm. The approach is efficient also for Asian options Department of Math & Stats with dividends beyond and within the averaging period. York University It is implemented as a pricing application for algorithmic [email protected] trading system and provides prices in real time.

Alexander Toropov MS3 TBricks AB Filtering and Parameter Estimation of Partially [email protected] Observed Diffusion Processes Using Gaussian RBFs Dmitry Ivanov Asset prices can be modeled as stochastic diffusion pro- ITMO University cesses involving a number of parameters. Based on market [email protected] observations, these parameters can be estimated. Prices are not uniquely determined due to the ask-bid spread. We Yuri Shpolyanskiy model the spread as additive noise, and show that Gaussian TBricks AB radial basis functions (RBFs), leads to a convenient math- [email protected] ematical representation. Furthermore, substantial parts of the computations can be performed analytically if RBFs are used for approximating transition densities. MS4 A Class of Fat-Tailed Residuals for Log-Returns Josef H¨o¨ok Consistent with Finite Asset Price Expectations Uppsala University, Sweden Dept. of Information Technology I investigate empirical performance of the generalized hy- [email protected] perbolic distribution in fitting log-returns of asset prices focusing on its three special cases: Students t distribution, Elisabeth Larsson normal inverse Gaussian distribution, and normal recip- Uppsala University, Sweden rocal inverse Gaussian distribution. Our results illustrate Department of Information Technology that there is no one overwhelmingly dominant in fitting the [email protected] data under GARCH or GJR-GARCH framework, although the NRIG distribution performs slightly better than the other two types of distribution. Some backtesting results Erik Lindstr¨om of the NRIG distribution from a risk management perspec- Lund University, Sweden tive are provided. Centre for Mathematical Sciences [email protected] Ziyi Guo Quantitative Risk Management Lina von Sydow Options Clearing Corporation Department of Information T [email protected] Uppsala University [email protected] MS4 Principal Components Analysis in Yield-Curve MS3 Modeling Option Pricing under Fractional Diffusion Using Radial Basis Functions Abstract not available at time of publication.

Diffusion processes in complex systems are often observed Carlos Tolmasky to deviate from standard laws and are better represented Institute for Mathematics and its Applications by fractional-order than by second-order diffusion models. University of Minnesota Such deviations have been observed in different contexts [email protected] such as dispersion of tracers in an aquifer, random dis- placements of living species in their search for food, or stock market volatility. We apply a new high order and MS4 efficient radial basis functions discretization to an option- Pricing and Hedging of Futures Contracts under 54 FM14 Abstracts

Multiple Stochastic Factors Order-2.0-weak-Taylor schemes, or by exact simulation. The conditional expectations appearing are approximated This paper focuses on two aspects of futures contracts: by using the characteristic function for these schemes and pricing and hedging. We first set up the pricing PDE for fu- Fourier-cosine series expansions. We apply the method to, tures contracts and provide the verification theorem. This among others, option pricing problems under the CEV and part is the routine work, although we consider the general CIR processes. stochastic differential equations for the underlying and N factors of the carry cost. Then, we introduce the concept Marjon Ruijter, Kees Oosterlee of a futures basis, present the necessary and sufficient con- CWI - Center for Mathematics and Computer Science ditions for a set of contracts to be the futures basis, and [email protected], [email protected] provide the hedging formulas by the future basis and the underlying. To our best knowledge, our results concerning hedging of futures contracts are new in the literature. MS5 Jinchun Ye The VIX-Heston Model for Asset Liability Man- Options Clearing Corporation agement [email protected] This article proposes a method of analyzing and modeling the real world dynamics of equity put/call option implied MS4 volatilities (IVs) using the risk neutral Heston model with Quantifying the Mutual Information Between In- specific parameter restrictions. In our modeling approach novations in the Prices of Security Options and we construct a stable and accurate calibration method for Their Underlyings calibrating the Heston model to historic market data. In this way the risk neutral Heston model is embedded in Abstract not available at time of publication. a real world scenario generator and can be used to gen- erate implied volatility structures, evaluate option invest- Lu Zhou ment strategies or to construct hedging strategies. The School of Statistics proposed methodology results in a stable valuation of em- University of Minnesota bedded options, which is in practice preferred by, among [email protected] others, insurance companies and pension funds.

Stefan Singor MS5 Ortec-Finance, Insurance Risk Management Credit Valuation Adjustment and the Stochastic Stefan.Singor@ortec-finance.com Grid Bundling Method

Valuation of Credit Valuation Adjustment (CVA) has be- MS5 come an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. The Time-Dependent FX-SABR Model: Efficient Exposure, which is defined as the potential future loss of Calibration based on Effective Parameters a default event without any recovery, is one of the key el- ements for pricing CVA. This paper provides a backward We present a framework for efficient calibration of the dynamics framework for assessing exposure profiles of Eu- time-dependent SABR model [3-5] in an FX context. In ropean, Bermudan and barrier options under the Heston a similar fashion as in [6] we derive effective parameters, and Heston Hull-White asset dynamics. We discuss the po- which yield an accurate and efficient calibration. On top of tential of an efficient and adaptive Monte Carlo approach, the calibrated FX-SABR model we add a non-parametric the Stochastic Grid Bundling Method (SGBM), which em- local volatility component, which naturally compensates ploys the techniques of simulation, regression and bundling. for possible calibration errors. By means of Monte Carlo Greeks of the exposure profiles can be calculated in the pricing experiments we show that the time-dependent same backward iteration with little extra effort. Assuming FX-SABR model enables an accurate and consistent independence between default event and exposure profiles, pricing of barrier options. We compare the results with we give examples of calculating exposure, CVA and Greeks prices implied by the constant-parameter SABR model for Bermudan and barrier options. and traditional Local Volatility model [1-2]. We also consider the role of the local volatility component in Qian Feng pricing barrier options. CWI - center for mathematics and computer science Amsterdam, the [1] E. Derman and I. Kani. Stochastic Implied Trees: [email protected] Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility. International Journal of Theoretical and Applied Cornelis W. Oosterlee Finance, 1(1):61-110, 1998. CWI, Centrum Wiskunde & Informatica, Amsterdam [2] B. Dupire. Pricing With a Smile. Risk Magazine, 7(1):18-20, [email protected] 1994. [3]J.Fern´andez, A. Ferreiro, J. Garca, A. Leitao, J. L´opez- Salas, and C. V´azquez. Static and Dynamic SABR Stochastic MS5 Volatility Models: Calibration and Option Pricing using GPUs. Second Order Weak Taylor Scheme and a Numer- Mathematics and Computers in Simulation, 94:55-75, 2013. ical Fourier Method for Backward Sdes [4] P. S. Hagan, D. Kumar, A. S. Lesniewski, and D. E. Woodward. Managing Smile Risk. Wilmott Magazine, pages We present a Fourier method to solve decoupled forward- 84-108, 2002. backward stochastic differential equations (FBSDEs) with [5] Y. Osajima. The Asymptotic Expansion Formula of Implied second-order accuracy. The FSDE is approximated by dif- Volatility for Dynamic SABR Model and FX Hybrid Model. ferent Taylor schemes, such as the Euler, Milstein, and Available at SSRN 965265, 2007. FM14 Abstracts 55

[6] V. Piterbarg. Time to Smile. Risk, 18(5):71-75, 2005. amount at bankruptcy is increasing, and its proportion rel- ative to the asset value is decreasing. The solution admits Anthonie W. Van der Stoep a semi-explicit form in terms of the scale function. Rabobank Int. Utrecht and CWI Amsterdam, the Netherlands Kazutoshi Yamazaki [email protected] Kansai University [email protected]

MS6 Budhi Surya Sequential Replacement under Uncertainty in the Bandung Institute of Technology Population Distribution [email protected] We study the impact of uncertainty in the problem of se- quential replacement of projects with unknown quality and MS6 unknown population distribution of quality. The decision- Optimal Multiple Stopping with Random Refrac- maker can operate one project at a time, observe the per- tion Times under Levy Models formance, update his belief on the quality and the popula- tion distribution, and replace it with another project from This paper studies a class of optimal multiple stopping the population. Our novel result: the real option value is problems driven by L´evy processes. Our model allows for decreasing in the uncertainty in the population distribu- a negative effective discount rate, which arises in a num- tion. ber of financial applications, including stock loans and real options, where the strike price can potentially grow at a Dharma Kwon higher rate than the original discount factor. Moreover, UIUC successive exercise opportunities are separated by i.i.d. College of Business random refraction times. Under a wide class of two-sided [email protected] L´evy models with a general random refraction time, we rigorously show that the optimal strategy to exercise suc- Steven Lippman cessive call options is uniquely characterized by a sequence UCLA of up-crossing times. The corresponding optimal thresh- [email protected] olds are determined explicitly in the single stopping case and recursively in the multiple stopping case.

MS6 Hongzhong Zhang Optimal Mean Reversion Trading with Transaction Department of Statistics Cost and Stop-Loss Exit Columbia University [email protected] We study the optimal timing strategies for trading a mean- reverting price spread. An optimal double stopping prob- lem is formulated to analyze the timing to start and subse- MS7 quently liquidate the position subject to transaction costs Fundamental Theorem of Asset Pricing under and a stop-loss constraint. Modeling the price spread by Transaction Costs and Model Uncertainty an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously show that the entry region is We prove the Fundamental Theorem of Asset Pricing for a characterized by a bounded price interval that lies strictly discrete time financial market consisting of a money mar- above the stop-loss level. As for the exit timing, a higher ket account and a single stock whose trading is subject stop-loss level always implies a lower optimal take-profit to proportional transaction cost and whose price dynamic level. is modeled by a family of probability measures, possibly non-dominated. Under a continuity assumption, we prove Tim Leung using a backward-forward scheme that the absence of ar- Department of Operations Research and Industrial bitrage in a quasi-sure sense is equivalent to the existence Engineering of a suitable family of consistent price systems. A parallel Columbia University statement between robust no-arbitrage and strictly consis- [email protected] tent price systems is also obtained.

Erhan Bayraktar, Yuchong Zhang MS6 University of Michigan Optimal Capital Structure with Scale Effects under Department of Mathematics Spectrally Negative Levy Models [email protected], [email protected]

The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland MS7 and Toft (1996), and was later extended to the spectrally Portfolio Choice with Liquid and Illiquid Assets negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the We find dynamic portfolio strategies for long-term investors scale effects by allowing the values of bankruptcy costs with constant relative risk aversion, who trade in a market and tax benefits to be dependent on the firm’s asset value. with three assets, one safe, one risky and liquid, and one By using the fluctuation identities for the spectrally nega- risky and illiquid. Investment opportunities are constant tive Levy process, we obtain a candidate bankruptcy level and trading is continuous, but the illiquid asset incurs pro- as well as a sufficient condition for optimality. The opti- portional transaction costs. Optimal investment policies mality holds in particular when, monotonically in the as- entail infrequent trading in the illiquid asset compensated set value, the value of tax benefits is increasing, the loss by hedging activity in the liquid asset. Liquid hedging posi- 56 FM14 Abstracts

tions are nonlinear, and do not vanish even for independent in Continuous Time risky assets. This is a joint work with Paolo Guasoni. We consider a continuous-time financial market model un- Maxim Bichuch der a family of probability measures and show that there Department of Operations Research and Financial exists no free lunch with disappearing risk if and only if Engineering there exists an equivalent family of martingale measures. Princeton University [email protected] Patrick Cheridito Princeton University [email protected] Paolo Guasoni Boston University Dublin City University Michael Kupper, Ludovic Tangpi [email protected] Universitat Konstanz [email protected], [email protected]

MS7 MS8 Balancing Small Fixed and Proportional Transac- Market Making Via Acceptability Indices tion Cost in Trading Strategies We develop a general framework for determining dynamic We consider the finite horizon financial problem of optimal bid and ask prices of dividend paying securities. We use consumption under transaction cost. From the classical re- sub-scale invariant Dynamic Acceptability Indices (DAIs) sults, we know that there is a no-trade region outside which as the main tool in this study. We work with discrete time it is optimal to trade to change the position of portfolio to financial models, on a general probability space. We link some optimal point in the no-trade region. We assume a DAIs with Backward Stochastic Difference Equations and balance between fixed and proportional transaction cost, g-Expectation. One of the key feature of the proposed pric- such that none of them dominates the other, asymptoti- ing theory is non-homogeneity of prices in number of shares cally. We use a heuristic equilibrium argument to demon- traded - a desire property from practical point of view that strate that the deviation of transaction cost value function captures one aspect of liquidity risk. We also show that: from the Merton value function, without transaction cost, considered market models do not admit arbitrage; bid and 1 is of order  2 where  is the small fixed transaction cost. ask prices do shrink the super hedging pricing interval, the Based on this, we propose an expansion for the value func- prices are time consistent in some appropriate sense. Fi- 1 tion in terms of powers of  2 . In addition, we find the nally, we provide some practical examples. This is joint equilibrium distribution of the position of the portfolio in work with Tomasz R. Bielecki and Tao Chen. the no-trade region in two cases where we only have fixed Igor Cialenco transaction cost and where we have both fixed and propor- Illinois Institute of Technology tional transaction cost. [email protected] Arash Fahim Florida State University MS8 [email protected] Price and Risk in Discrete Time Market Models Subject to Model Misspecification Jose Alcala ITESO, Mexico In a model independent financial market, we introduce a [email protected] topological notion of Robust Arbitrage, without fixing an a-priori set of reference probability measures. This novel notion relies only on the market structure and admits a MS7 dual representation in terms of weakly open sets of prob- Trading with Small Price Impact ability measures. We show that the absence of Robust Arbitrage, with respect to an opportune filtration enlarge- An investor trades a safe and several risky assets with lin- ment, guarantees the existence of full support martingale ear price impact to maximize expected utility from termi- measures. Robust Arbitrage is also characterized by the nal wealth. In the limit for small impact costs, we explic- property that any polar set of the class of martingale mea- itly determine the optimal policy and welfare, in a general sures has empty interior. Markovian setting allowing for stochastic market, cost, and Marco Maggis preference parameters. These results shed light on the gen- Milano University eral structure of the problem at hand, and also unveil close [email protected] connections to optimal execution problems and to other market frictions such as proportional and fixed transac- tion costs. (Joint work with Ludovic Moreau and H. Mete MS8 Soner.) Distribution Based Risk Measures and Their Im- Johannes Muhle-Karbe plementation Departement Mathematik Banks and insurance companies typically use distribution- ETH Z¨urich based risk measures for the evaluation of their downside [email protected] risks. The statistical and numerical properties of these functionals are thus important. Recently, some authors emphasized the significance of the elicitability of risk mea- MS8 sures, a notion closely related to Huber’s M-estimators A Robust Fundamental Theorem of Asset Pricing and quantile regression. The talk characterizes elicitable FM14 Abstracts 57

distribution-based risk measures, analyzes their general- Stanford University ized Hampel-robustness, and explains their relationship to [email protected] stochastic approximation theory. Ciamac C. Moallemi Stefan Weber Graduate School of Business Leibniz Universit¨at Hannover Columbia University sweberstochastik.uni-hannover.de [email protected]

MS9 MS9 Systemic Risk with Central Counterparty Clearing Institutional Investors and the Dependence Struc- ture of Asset Returns Abstract not available at time of publication. We propose a model of a financial market with multiple as- Hamed Amini sets, which takes into account the impact of a large institu- ´ Swiss Finance Institute, Ecole polytechnique f´ed´erale de tional investor rebalancing its positions, so as to maintain La a fixed allocation in each asset. We show that feedback hamed.amini@epfl.ch effects can lead to significant excess realized correlation between asset returns and modify the principal component structure of the (realized) correlation matrix of returns. MS9 Our study naturally links, in a quantitative manner, the Networks of Overlapping Portfolios: Aggregation properties of the realized correlation matrix – correlation and Measures of Vulnerability between assets, eigenvectors and eigenvalues – to the sizes and trading volumes of large institutional investors. In This paper quantifies the interrelations induced by overlap- particular, we show that even starting with uncorrelated ping portfolios. A network representation emerges, where ’fundamentals,’ fund rebalancing endogenously generates a nodes represent portfolios and edge weights aggregate the correlation matrix of returns with a first eigenvector with common asset holdings and the liquidity of these holdings. positive components, which can be associated to the mar- As a building block, we introduce a simple model of or- ket, as observed empirically. der imbalance that estimates price impacts due to liquidity shocks. In our model, asset prices are set by a competi- Lakshithe Wagalath tive risk-neutral market maker and the arrival rates for the Universite de Paris VI, France buyers and sellers depend on the common asset holdings. [email protected] We illustrate the relevance of our aggregation method and the resulting network representation using data on mutual fund asset holdings. We introduce three related measures MS10 of vulnerability in the network and demonstrate a strong On the Connection Between Mean Field Games dependence between mutual fund returns and these mea- and Symmetric N-Player Games sures. Mean field games, as introduced by J.M. Lasry and P.- Braverman, Andreea Minca L. Lions and, independently, by M. Huang, R.P. Malham, Cornell University and P.E. Caines, are limit models for symmetric N-player [email protected], [email protected] games with interaction of mean field type as N →∞.The limit relation is often understood in the sense that a solu- tion of a mean field game allows to construct approximate MS9 Nash equilibria for the corresponding N-player games. The Welfare Analysis of Dark Pools opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean We investigate the role of a class of alternative market field game? In this direction, rigorous results are mostly structures known as electronic crossing networks or ‘dark available for stationary problems with ergodic costs. The pools’. Relative to traditional ‘lit’ intermediated dealer aim here is to identify limit points of sequences of approx- markets, dark pools offer investors the trade-off of reduced imate Nash equilibria as solutions to mean field games for transaction costs in exchange for greater uncertainty of problems with Itˆo-type dynamics and costs over a finite trade. In an equilibrium setting, we analyze the choice time horizon. Limits are studied through weak conver- between dark and lit venues, and illustrate how this criti- gence of associated occupation measures and identified us- cally depends on the information available to each investor. ing a probabilistic notion of solution for mean field games. We establish that while dark pools attract relatively unin- formed investors, they still experience implicit transaction costs in the form of adverse selection. We quantify the ef- Markus Fischer fect of the presence of a dark pool on the transaction costs University of Padua in the lit market, as well as on the overall welfare of the fi[email protected] market. In particular, for specific model parameter values, we show that the introduction of a dark pool can increase the transaction costs in the lit market and diminish the MS10 overall welfare. Wealth Distribution and the Business Cycle: The Role of Private Firms Krishnamurthy Iyer Cornell University Recent recessions have been characterized by extraordinar- [email protected] ily slow recoveries, a fact that is hard to explain with stan- dard business cycle models. Most business cycle models Ramesh Johari assume that firm ownership is irrelevant, either by pos- 58 FM14 Abstracts

tulating that there is a representative firm or that own- then define time consistency for DPM such that the po- ership is perfectly diversified. But in contrast to this as- sitions which are considered good tomorrow are already sumption, the majority of economic activity in the United considered good today. Under some mild continuity as- States is accounted for by privately held firms, rather than sumption on the DPM we prove the equivalence between publicly traded ones. Motivated by this fact, we study time consistency for the DPM and weak acceptance con- an economy with heterogeneous privately held firms, col- sistency for the induced family of dynamic risk measures. lateral constraints and indivisibilities in production, cali- brated to the United States. We find that the presence of private firms affects how the economy responds to aggre- Jocelyne Bion-Nadal gate shocks in important ways, and in particular that our CMAP, Ecole Polytechnique model economy has the potential to explain the observed [email protected] slow recoveries. The slow dynamics of the wealth distribu- tion are key to this result. A methodological contribution of our paper is to show how heterogeneous agent rational MS11 expectation models with aggregate shocks can be approx- OntheModel-freeHedgingDuality imated numerically even when “approximate aggregation” fails due to important nonlinearities. Based on new representation results for monotone convex functionals we discuss a generalized version of the trans- Yves Achdou port duality. As an application we focus on model-free University of Paris VII versions of the fundamental theorem asset pricing and the Mathematics corresponding hedging duality. The talk is based on joint [email protected] work with Patrick Cheridito and Ludovic Tangpi. Michael Kupper Jean-Michel Lasry Universitat Konstanz University of Paris Dauphine [email protected] [email protected]

Pierre-Louis Lions MS11 Coll`ege de France A Fourier Approach to the Computation of Risk [email protected] Measures

Benjamin Moll We consider the class of risk measures associated with op- Princeton University timized certainty equivalents. This class includes several [email protected] popular examples, such as Expected Shortfall (also known as CV@R) or the entropic risk measures. Beyond explicit formulas to compute them, they also provide a handy way MS10 to compute risk contributions in portfolio. We develop nu- Tba (Waiting for Answer of Y. Achou) merical schemes for the computation of such risk measures using Fourier transform methods. This leads to a very Abstract not available at time of publication. competitive method for the calculation of CV@R for in- stance, which is comparable in computational time to the TBA TBA calculation of V@R. We also address the computation of IBM Corporation risk contributions in a portfolio of risks, for which Fourier TBA transform methods are particularly efficient.

Antonis Papapantoleon MS10 TU Berlin Mean Field Games with Major and Minor Players [email protected]

Abstract not available at time of publication. MS11 Geoffrey Zhu A Recursive Algorithm for Dynamic Multivariate Princeton University Risk Measures and a Set-Valued Bellman’s Princi- [email protected] ple

A method for calculating multi-portfolio time consistent MS11 multivariate risk measures in discrete time is presented. Correspondence Between Dynamic Quasi Concave Market models for d assets with transaction costs or illiq- Performance Measures and Parametric Families of uidity are considered. The set of risk compensating portfo- Dynamic Risk Measures lio vectors at each time and state is calculated recursively backwards in time along the event tree. We motivate why In order to optimize asset allocation, some performance the proposed procedure can be seen as a set-valued Bell- criterion must be selected. To achieve this goal, we in- man’s principle. We give conditions under which the back- troduce the notion of Dynamic quasi-concave Performance wards calculation reduces to solving a sequence of linear, Measure (DPM), on random variables bounded from below. respectively convex vector optimization problems. Numer- This notion encompasses a wide variety of cases, from dy- ical examples include superhedging under illiquidity, the namic expected utility and dynamic certainty equivalent to entropic set-valued risk measure, and the composed set- dynamic acceptability indexes. We establish a one-to-one valued average value at risk. relation between DPMs and parametric families of dynamic convex risk measures. In the case of dynamic acceptabil- Birgit Rudolff ity indexes these dynamic risk measures are coherent. We Princeton University FM14 Abstracts 59

brudloff@princeton.edu relative performance compared to their peers into account. Finding equilibria in this setting is related to multidimen- Zachary Feinstein sional backward stochastic differential equations (BSDEs). Washington University in St. Louis We introduce a new notion of local solution by splitting [email protected] multidimensional BSDEs over time. From this, we deduce that there exist local but no global equilibria in our model of a financial market. MS12 The Master Equation of Mean Field Games and Christoph Frei Controlled McKean Vlasov Dynamics University of Alberta [email protected] Abstract not available at time of publication.

Rene Carmona MS13 Princeton University Various Aspects of Incomplete Equilibrium Theory Dpt of Operations Research & Financial Engineering [email protected] In this talk we will present recent progress related to the theory of incomplete equilibrium theory incl. open prob- lems. MS12 Mean Field Games with Congestion Kasper Larsen Dept. of Mathematical Sciences In this talk, we consider mean field games with conges- Carnegie Mellon University tion effects. Such models were originally considered by [email protected] Lions who established uniqueness of solutions. We present a new class of a-priori estimates, which yield the existence of smooth solutions. MS13 Quadratic BSDEs Arising from a Price Impact Diogo Gomes Model with Exponential Utility King Abdullah Univeristy of Science and Technology [email protected] We analyze a price impact model where an influential in- vestor wants to trade illiquid assets with a representative market maker who quotes prices for these securities. In MS12 our model, the market maker’s preferences are modeled Coalescence of Hysteresis in a Large Population: through an exponential utility function and the price im- Mean Field Stackelberg Games pact of the trading strategy of the influential investor is derived endogenously through an equilibrium mechanism. In this talk, I shall introduce an N-player interacting strate- We establish a relationship between the equilibrium mecha- gic game in the presence of a (endogenous) dominating nism and a multidimensional BSDE with quadratic growth. player, who gives direct influence on individual agents, This allows us to show that an equilibrium exists under cer- through its impact on their control in the sense of Stackel- tain conditions on the final payoffs of the traded assets, the berg game, and then on the whole community. Each indi- risk aversion coefficient of the market maker and the trad- vidual agent is subject to a delay effect on collecting infor- ing strategy of the influential investor. The relationship mation, specifically at a delay time, from the dominating between the equilibrium mechanism and the multidimen- player. The size of his delay is completely known by the sional quadratic BSDE also allows us to study stability and agent; while to others, including the dominating player, his asymptotic behavior with respect to the parameters of the delay plays as an hidden random variable coming from a model. At the same time, the structure of the equilibrium common fixed distribution. problem allows us to prove novel results for the correspond- ing BSDE. This is a joint work with Dmitry Kramkov. S.C.P Yam The Chinese University of Hong Kong Sergio Pulido [email protected] Swiss Finance Institute EPFL, Switzerland sergio.pulido@epfl.ch MS12 Linear-Quadratic Optimal Control Problems for Dmitry Kramkov Mean-Field Stochastic Differential Equations — Carnegie Mellon University Time-Consistent Solutions Pittsburgh Abstract not available at time of publication. [email protected]

Jiongmin Yong University of Central Florida MS13 [email protected] Existence of Close to Pareto Optimal Incomplete Radner Equilibrium

MS13 We consider an equilibrium model between exponential in- Finding Local Equilibria by Splitting Multidimen- vestors whose random endowments cannot be spanned by sional BSDEs the traded asset. We first characterize the set of endow- ments which induce Pareto optimal equilibrium. For en- We consider a model of a financial market where investors dowments close to this set, we establish three existence take not only their own absolute performance, but also the results of equilibria which are not Pareto optimal. In a 60 FM14 Abstracts

non-Markovian setting, the first existence result is estab- [email protected] lished by analysing a system of coupling quadratic BSDEs, via the techniques introduced by Tevzadze (2008). Then Sergei Levendorskii the first result is improved by a BMO-norm estimate in University of Leicester the second result. In a Markovian setting, equilibrium is [email protected] established using partial regularity results for system of parabolic PDEs with quadratic nonlinearity in gradient. MS14 Hao Xing, Kostas Kardaras Underexposed Risk Snapshots - The Dangers of London School of Economics and Political Science Risk-Neutral Exposures [email protected], [email protected] As per regulations and common risk management practice, Gordan Zitkovic the credit risk of a portfolio is managed via its potential fu- Department of Mathematics ture exposures (PFEs), expected exposures (EEs), and re- The University of Texas at Austin lated measures, the expected positive exposure (EPE), ef- [email protected] fective expected exposure (EEE) and the effective expected positive exposure (EEPE). Notably, firms use these expo- sures to set economic and regulatory capital levels. Their MS14 values have a big impact on the capital that firms need Valuation and Hedging of Contracts with Funding to hold to manage their risks. Due to the growth of CVA Costs and Collateralization computations, and the similarity of CVA computations to exposure computations, firms find it expedient to compute The research presented in this work is motivated by re- these exposures under the risk neutral measure. Here we cent papers by Brigo et al. (2011), Burgard and Kjaer show that exposures computed under the risk neutral mea- (2009), Cr´epey (2012), Fujii and Takahashi (2010), Piter- sure are essentially arbitrary. They depend on the choice of barg (2010) and Pallavicini et al. (2012). Our goal is to num´eraire, and can be manipulated by choosing a different provide a sound theoretical underpinning for some results num´eraire. Even when restricting attention to commonly presented in these papers by developing a unified frame- used num´eraire exposures can vary by a factor of two or work for the non-linear approach to hedging and pricing more. As such, it is critical that these calculations be done of OTC financial contracts. We introduce a systematic ap- under the real world measure, not the risk neutral measure. proach to valuation and hedging in nonlinear markets, that is, in markets where cash flows of the financial contracts may depend on the hedging strategies. Our systematic ap- Harvey Stein proach allows to identify primary sources of and quantify Bloomberg LP various adjustment to valuation and hedging, primarily the [email protected] funding and liquidity adjustment and credit risk adjust- ment. We propose a way to define no-arbitrage in such nonlinear markets, and we provide conditions that imply MS14 absence of arbitrage in some specific market trading mod- Dynamic Replication Strategies under Funding and els. Accordingly, we formulate a concept of no-arbitrage Collateral Costs price, and we provide relevant (non-linear) BSDE that pro- duces the no-arbitrage price in case when the contract’s We develop a framework for dynamic hedging of collateral- cash flows can be replicated. ized claims in presence of funding costs. We derive closed form expressions for the total valuation adjustment as well Marek Rutkowski as for the super-hedging strategy of an European claim, University of Sydney under a framework where corporate bonds referencing in- [email protected] vestor and counterparty may be used to hedge CVA and DVA risk. We decompose the XVA in terms of default- Tomasz Bielecki and collateralization free price under funding constraints, Applied Mathematics funding-adjusted CVA, funding-adjusted DVA and funding Illinois Institute of Technology costs of the collateralization procedure. We numerically il- [email protected] lustrate the impact of counterparty risk and funding costs on the total adjustment.

MS14 Stephan Sturm Efficient Options Pricing under Levy Processes ORFE Department with CVA and FVA Princeton University [email protected] We generalize the CVA-FVA model of Piterbarg (2010) by introducing jumps in the dynamics of the underlying as- Agostino Capponi set. We develop an efficient explicit-implicit scheme for Johns Hopkins University European options, barrier options with CVA-FVA. The [email protected] advantage of the scheme is that one only needs an ex- plicit analytic formula for the characteristic exponent of theprocess.TheschemeiseasytoimplementusingFFT MS15 as the main computational tool. Numerical results are pro- Price Contagion Through Balance Sheet Linkages vided for some common Levy models like KoBoL, Variance Gamma, double exponential jump diffusion. We study price linkages between assets held by financial in- stitutions that maintain fixed capital structures over time. Justin Shek We consider a market consisting of a banking and nonbank- Bank of China International ing sector. Firms in the banking sector actively manage FM14 Abstracts 61

their leverage ratios to conform with pre-specified target Chen Chen levels. We find that if leverage targeting banks become too Berkeley large relative to the nonbanking sector, as measured by [email protected] elasticity-weighted assets, the financial system may enter a regime of excess volatility and correlation. Our analysis Garud Iyengar suggests that regulatory policies aimed at stabilizing the Columbia University, USA system by imposing capital constraints on banks may have [email protected] unintended consequences: banks’ deleveraging activities may amplify asset return shocks and lead to large fluctua- tions in realized returns. The same mechanism can cause MS15 spill-over effects, where assets held by leverage targeting banks can experience hikes or drops caused by shocks to Large Portfolio Asymptotics and Fluctuation Anal- otherwise unrelated assets held by the same banks. We ysis for Losses from Default show that these effects can be mitigated by encouraging banks to implement asset allocation strategies with higher The past several years have made clear the need to bet- exposure to liquid, rather than illiquid, assets. ter understand the behavior of risk in large interconnected financial networks. Interconnections often make a system Agostino Capponi robust, but they can act as conduits for risk. In this talk, Johns Hopkins University I will present recent results on modeling the dynamics of [email protected] correlated default events in the financial market. An em- pirically motivated system of interacting point processes is Martin Larsson introduced and we study how different types of risk, like Cornell University contagion and exposure to systematic risk, compete and [email protected] interact in large-scale systems. A for the loss from default is proven and used for approximating the distribution of the loss from default in large, poten- MS15 tially heterogeneous portfolios. Fluctuation analysis and Systemic Risk and the Macroeconomy: An Empir- conditional Gaussian approximations are used to improve ical Evaluation the approximations

We propose an empirical criterion for evaluating systemic Konstantinos Spiliopoulos risk measures based on their ability to predict quantiles of Boston University future macroeconomic shocks. We construct 17 measures Department of Mathematics and Statistics of systemic risk in the US and Europe spanning several [email protected] decades. We propose dimension reduction estimators for constructing systemic risk indexes from the cross section of measures and prove their consistency in a factor model set- MS16 ting. Empirically, systemic risk indexes provide significant Optimally Thresholded Realized Power Variations predictive information for the lower tail of future macroe- for Levy Jump Diffusion Models conomic shocks, even out-of-sample.

Stefano Giglio Thresholded Realized Power Variations are some of the University of Chicago most popular nonparametric estimators for continuous- [email protected] time processes with jumps. A common practical issue in their application lies in the necessity of choosing a suitable Bryan Kelly threshold for the estimator, a problem which so far has not The University of Chicago fully been addressed. In this talk, an objective selection [email protected] method for the threshold is proposed based on desirable op- timality properties of the estimators. Concretely, we intro- duce a well-posed optimization problem which, for a fixed Seth Pruitt sample size and time horizon, selects a threshold that mini- Arizona State University mizes the expected total number of jump misclassifications [email protected] committed by the thresholding mechanism associated with these estimators. The leading term of the optimal thresh- MS15 old sequence is shown to be proportional to the Levy’s modulus of continuity of the underlying Brownian motion, A Structural Model for Asset Price Contagion and hence theoretically justifying and sharpening several selec- Systemic Risk tion methods previously proposed in the literature based on power functions or multiple testing procedures. Further- We develop a structural model for the analysis of systemic more, building on the aforementioned asymptotic charac- risk in financial markets based on asset price contagion. terization, we develop an estimation algorithm, which al- Specifically, we describe a mechanism of contagion where lows for a feasible implementation of the newfound optimal exogenous random shocks to agents in an economy force sequence. portfolio rebalancing. This creates an endogenous chain reaction as agents trade in reaction to price changes. Our approach allows us to quantify the effect of attributes such Jose E. Figueroa-Lopez as leverage and portfolio diversity on asset price contagion. Purdue University fi[email protected] Ciamac C. Moallemi Graduate School of Business Jeff Nisen Columbia University Purdue University [email protected] Statistics Department 62 FM14 Abstracts

[email protected] [email protected]

MS16 MS17 Convergence Rate of the Truncated Realized Co- Bertrand & Cournot Mean Field Games variance When Prices Have Infinite Variation Jumps We study how continuous time Bertrand and Cournot com- petitions, in which firms producing similar goods compete We consider two processes driven by Brownian motions with one another by setting prices or quantities respec- plus drift and jumps with infinite activity. Given discrete tively, can be analyzed as continuum dynamic mean field observations it is possible to separately estimate the in- games. Interactions are of mean field type in the sense tegrated covariation IC between the two Brownian parts that the demand faced by a producer is affected by the and the sum of the co-jumps by using a threshold princi- others through their average price or quantity. Motivated ple (truncated realized covariance) allowing to isolate the by energy or consumer goods markets, we consider the set- jumps over a given threshold. This gives insight into the ting of a dynamic game with uncertain market demand, dependence structure of the processes and has important and under the constraint of finite supplies. The continuum applications in finance. We establish here the speed of con- game is characterized by a coupled system of partial dif- vergence of ICˆ when the small jump components of the two ferential equations: a backward HJB PDE for the value processes are L´evy. We find that such a speed is heavily function, and a forward Kolmogorov PDE for the density influenced by the small jumps dependence structure other of players. Asymptotic approximation enables us to de- than by their jump activity indices. This work follows duce certain qualitative features of the game in the limit Mancini and Gobbi (2011) and Jacod (2008), where the of small competition. We find that, in accordance with the two-player game, a large degree of competitive interaction asymptotic normality of ICˆ was obtained when the jump causes firms to slow down production. components have finite activity or finite variation. Patrick Chan Cecilia Mancini Princeton University University of Florence [email protected] Italy cecilia.mancini@unifi.it MS17 MS16 Uniqueness of Random Equilibriums in Large Pop- ulation Stochastic Control Short-Time Expansions for Close-to-the-Money Options under a Levy Jump Model with Stochastic Uniqueness of equilibriums in large population stochastic Volatility control, such as mean-field games, may be a challenging question. We here discuss the case when agents are sub- A second order short maturity approximation for ATM op- mitted to a common noise, which renders the equilibriums tion prices is presented for a large class of exponential L´evy random. It turns out that randomness of the equilibriums models, with or without a Brownian component. We also may restore uniqueness on the model. Specific examples show that the formulas can be extended to include the are discussed. case of “close-to-the-money” strike prices, and to the case where the continuous Brownian component is replaced by Fran¸cois Delarue an independent stochastic volatility process with leverage. Universit´e Nice Sophia Antipolis Laboratoire J.A. Dieudonn´e Sveinn O. Olafsson [email protected] Purdue University - Department of Statistics USA [email protected] MS17 Mean Field Games Systems with Local Coupling MS16 We present some recent results on systems of mean field Asymptotic Methods for Portfolio Risk Manage- games with local coupling between the value function and ment the mean field distribution. Under general structure con- ditions on the Hamiltonian and coupling, we prove exis- We present sharp asymptotics for the left tail of the dis- tence and uniqueness of the weak solution, characterizing tribution function of the sum of exponentials of compo- this solution as the minimizer of some optimal control of nents of a multidimensional time-changed Brownian mo- Hamilton-Jacobi and continuity equations. We also prove tion. These results have a wide range of applications in risk that this solution converges in the long time average to the analysis of long only portfolios, such as variance reduction solution of the associated ergodic problem. methods for precise estimation of tail event probabilities by Monte Carlo, asymptotic formulas for implied volatility Jameson Graber of basket options and systematic design of stress tests for ENSTA Paristech long-only portfolios. [email protected]

Peter Tankov Pierre Cardaliaguet Universit´e Paris-Diderot (Paris 7) University of Paris Dauphine FM14 Abstracts 63

[email protected] system acceptable, it is natural to consider systemic risk measures as set-valued risk measures.

MS17 Zachary Feinstein On a Boltzmann Type Price Formation Model Washington University in St. Louis [email protected] In 2007 Lasry & Lions introduced a price formation model that describes the evolution of price by a system of parabolic equations for the trader densities (as functions of MS18 the bid-ask price), with the agreed price entering as a free Stochastic Intensity Models of Wrong Way Risk: boundary. The authors motivated the model using mean Wrong Way CVA Need Not Exceed Independent field game theory, but the detailed microscopic origin re- CVA mained unclear. In this talk we provide a simple agent based trade model with standard stochastic price fluctua- Wrong way risk can be incorporated in Credit Value Ad- tions together with discrete trading events. By modeling justment (CVA) calculations in a reduced form model. Hull trading events between vendors and buyers as kinetic colli- and White [2012] introduced a CVA model that captures sions we obtain a Boltzmann-type model for the densities. wrong way risk by expressing the stochastic intensity of a Then we prove rigorously that in the limit of large trading counterparty’s default time in terms of the financial insti- frequencies, the proposed Boltzmann model converges to tutions credit exposure to the counterparty. We consider a the Lasry and Lions free boundary problem. We also ana- class of reduced form CVA models that includes the formu- lyze other asymptotic limits beyond the scales that the free lation of Hull and White and show that wrong way CVA boundary model can describe and illustrate our analytical need not exceed independent CVA. results with numerical simulations. Samim Ghamami Marie-Therese Wolfram Federal Reserve Bank Johan Radon Institute for Computational and Applied [email protected] Mathematics (RICAM) [email protected] MS18 Martin Burger Likelihood Inference for Large Financial Systems University of Muenster Muenster, Germany We consider the problem of parameter estimation for large [email protected] interacting stochastic systems. Maximum likelihood esti- mation is computationally intractable due to the scale and Luis Caffarelli complexity of such systems. Weak convergence results are University of Texas at Austin exploited to develop approximate maximum likelihood es- Department of Mathematics timators for such systems. An important application is caff[email protected] systemic risk in banking systems and other large financial systems. Peter Markowich University of Cambridge Justin Sirignano [email protected] Stanford University [email protected]

MS18 Gustavo Schwenkler Boston University The Systemic Effects of Benchmarking [email protected] I analyze the portfolio construction problem for a group of risk-neutral investors with two sets of goals. On one Kay Giesecke hand, they wish to maximize the return on their invest- Stanford University ments within the boundaries of their risk aversion. On Dept. of Management Science and Engineering the other hand, they wish to outperform a market bench- [email protected] mark. Benchmarking induces excessive risk-taking behav- ior among certain types of investors. I study the impli- cations of this excessive risk-taking behavior for systemic MS19 risk. BarrierOptions,CDSandQuantoCDSinL´evy Models with Stochastic Interest Rate Gustavo Schwenkler, Diogo Duarte,KeithLee Boston University Recently, advantages of conformal deformations of the con- [email protected], [email protected], [email protected] tours of integration in pricing formulas for European op- tions have been demonstrated in the context of wide classes of L´evy models, the Heston model and other affine models. MS18 Similar deformations were used in one-factor L´evy models, Risk Measures for Financial Networks where the Wiener-Hopf factorization is applicable, to price options with barrier and lookback features and CDSs. In We define systemic risk measures for a network of intercon- the present paper, we generalize this approach to models nected banks to be the risk of the system to the obligations of structural default with the stochastic interest rate, and the financial firms have to the outside economy. Since the design an algorithm which is almost as fast as in the case value that is of interest to a regulator is the capital re- of the constant interest rate. Similar results are obtained quirements for each financial firm which makes the overall for quanto CDS, where an additional stochastic factor: the 64 FM14 Abstracts

exchange rate is introduced. electricity derivatives.

Svetlana Boyarchenko Rafael Mendoza-Arriaga Department of Economics, University of Texas at Austin, University of Texas at Austin [email protected] [email protected]

Sergei Levendorskii Lingfei Li University of Leicester Chinese University of Hong Kong [email protected] Systems Engineering & Engineering Management lfl[email protected]

MS19 Ghost Calibration and Pricing Barrier Options and MS20 CDSs in Spectrally One-Sided L´evy Models: the Model Uncertainty and Its Impact on the Pricing Parabolic Laplace Inversion Method of Derivative Instruments

Recently, the advantages of conformal deformations of the Abstract not available at time of publication. contours of integration in pricing formulas were demon- strated in the context of wide classes of L´evy models and Rama Cont the Heston model. In the present paper we construct effi- Imperial College London cient conformal deformations of the contours of integration Department of Mathematics in the pricing formulas for barrier options and CDS in the [email protected] setting of spectrally one-sided L´evy models. We demon- strate that the proposed method is more accurate than the standard realization of Laplace inversion in many cases. MS20 We also exhibit examples in which the standard realiza- Martingale Optimal Transport in the Skorokhod tion is so unstable that it cannot be used for any choice Space of the error control parameters. This may lead to a ghost calibration: a situation where a parameter set of a model The dual representation of the martingale optimal trans- is declared to be a “good fit’ to the data only because the port problem in the Skorokhod space of multi dimensional errors of calibration and of the numerical method used for cadl` ag` processes is proved. The dual is a minimization pricing (almost) cancel each other out. problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal Sergei Levendorskii transport problem. The constraints are required to hold University of Leicester for very path in the Skorokhod space. This problem has [email protected] the financial interpretation as the robust hedging of path dependent European options.

MS19 Yan Dolinsky On Additive Subordination with an Application in Department of Statistics Cross Commodity Modeling Hebrew University of Jerusalem [email protected] We study additive subordination, which is a natural gen- eralization of Bochner’s subordination, and show that it Mete Soner is a useful technique for constructing time-inhomogeneous Department of Mathematics Markov processes with analytical tractability. As an appli- ETH Zurich cation, we develop the first analytically tractable model for [email protected] crack spread option valuation in the literature that is able to calibrate the implied volatility surface of each commod- ity. Moreover, our model can generate implied correlation MS20 patterns that are consistent with market observations and Model Uncertainty and Optimal Transport economic intuitions. Abstract not available at time of publication. Lingfei Li Chinese University of Hong Kong Marcel Nutz Systems Engineering & Engineering Management Department of Mathematics lfl[email protected] Columbia University [email protected] Rafael Mendoza-Arriaga University of Texas at Austin [email protected] MS20 On Arbitrage and Duality under Model Uncer- tainty and Portfolio Constraints MS19 Modeling Electricity Prices: A Time Change Ap- We consider the fundamental theorem of asset pric- proach ing (FTAP) and hedging prices of options under non- dominated model uncertainty and portfolio constrains in We develop a new framework for modeling electricity spot discrete time. We first show that no arbitrage holds if prices by time changing the basic affine jump diffusion, and only if there exists some family of probability mea- which successfully captures seasonal spikes. Our model is sures such that any admissible portfolio value process is easy to estimate from data and it is tractable for pricing a local super-martingale under these measures. We also FM14 Abstracts 65

get the non-dominated optional decomposition with con- to one another and outside depositors. Within this frame- straints. From this decomposition, we get duality of the work, we analyze how incomplete information about the super-hedging prices of European options, as well as the viability of bank assets affects the fragility of the system. sub- and super-hedging prices of American options. Fi- In particular, we show that fluctuations in expectations and nally, we get the FTAP and duality of super-hedging prices higher-order beliefs can be amplified and lead to systemic in a market where stocks are traded dynamically and op- risk. Fragility depends both on the topology of the network tions are traded statically. as well as the structure of higher-order beliefs. Our results have implications for regulatory policies such as mandatory Zhou Zhou disclosure policies and stress tests. Department of Mathematics University of Michigan Jennifer La’O, Alireza Tahbaz-Salehi [email protected] Columbia University [email protected], [email protected] Erhan Bayraktar University of Michigan MS22 Department of Mathematics [email protected] Convergence of ADI Schemes for Two-dimensional Convection-diffusion Equations with Mixed Deriva- tive Term MS21 Alternating Direction Implicit (ADI) schemes are well- Interconnected Balance Sheets, Market Liquidity, known in the numerical solution of multidimensional time- and the Amplification Effects in a Financial System dependent partial differential equations (PDEs) arising in financial mathematics. The Craig-Sneyd (CS), Mod- Abstract not available at time of publication. ified Craig-Sneyd (MCS) and Hundsdorfer-Verwer (HV) Nan Chen schemes form three popular ADI schemes. A structural The Chinese University of Hong Kong analysis of their fundamental properties, notably conver- [email protected] gence, is of main interest. Up to now, however, a con- vergence result is only known in the literature for the HV scheme and only in the case of one-dimensional PDEs. In MS21 this talk we shall present a new analysis revealing that, Rehypothecation and Systemic Risk under natural stability and smoothness conditions, the CS, MCS and HV schemes all possess a temporal order of con- Abstract not available at time of publication. vergence equal to two, uniformly in the spatial mesh width, whenever they are applied to two-dimensional convection- Alex Shkolnik diffusion equations with mixed derivative term. The ob- Stanford University tained convergence results will be illustrated by numerical [email protected] experiments for contemporary stochastic volatility models.

MS21 Karel In ’t Hout, Maarten Wyns Department of Mathematics and Computer Science Efficient Risk Analysis for Mortgage Pools and University of Antwerp Mortgage-backed Securities [email protected], Typical mortgage pools of interest are very large and com- [email protected] putationally expensive to simulate. We develop a dynamic law of large numbers and a dynamic central limit theorem MS22 in order to tractably calculate pool loss and prepayment distributions for a broad class of models. Importantly, this High-Order Splitting Methods for Forward PDEs large pool approximation is not a ”top-down or reduced- and PIDEs form model” but instead takes full advantage of the rich We construct finite-difference schemes for forward and information available from the high-dimensional loan-level backward PIDEs such that option prices obtained by solv- data. Computational cost is often several orders of magni- ing both the forward and backward equations are consis- tude less than simulation of the actual pool with a similar tent. This approach is partly inspired by Andreassen, Huge level of accuracy. 2011 who reported a pair of consistent finite-difference Justin Sirignano schemes of first-order approximation in time for an uncor- Stanford University related local stochastic volatility model. We extend this to [email protected] the second-order in both space and time and also take into account correlations, jumps and discrete dividends.

Kay Giesecke Andrey Itkin Stanford University New York University Dept. of Management Science and Engineering [email protected] [email protected]

MS22 MS21 Efficient Implicit Predictor-Corrector Methods for Information Contagion in Financial Networks Pricing American Options under Regime Switching This paper studies the effect of incomplete information An implicit predictor-corrected method is presented for one within a banking network, in which banks have obligations and two assets American options under multi-state regime 66 FM14 Abstracts

switching. The method is based on exponential time dif- [email protected] ferencing approach which makes it highly efficient while maintaining excellent stability and convergence properties in each regime with different interest rates. The impact of MS23 regime switching on option prices for different jump rates Algorithmic Trading with Learning is illustrated. Numerical experiments on American options with convex and nonconvex payoffs demonstrate reliability Abstract not available at time of publication. of the method. Damir Kinzebulatov Abdul M. Khaliq The Fields Institute Middle Tennessee State University [email protected] Department of Mathematical Sciences [email protected] MS23 Mohammad Yousuf Simulating and Analyzing Order Book Data: The King Fahd University of Petroleum and Minerals Queue-Reactive Model Saudi Arabia Abstract not available at time of publication. [email protected] Mathieu Rosenbaum Ruihua Liu CMAP - Ecole Polytechnique Paris University of Dayton mathieu.rosenbaum@polytechnique [email protected]

MS23 MS22 Title Not Available at Time of Publication

Pricing Options under Stochastic Volatility Models Abstract not available at time of publication. with Jumps Sasha F. Stoikov We consider partial integro-differential equation (PIDE) Cornell University formulations for pricing options under the Bates and SVCJ [email protected] models. The time discretization is performed using the two-step implicit-explicit scheme called IMEX-CNAB. We treat the differential operator implicitly and the integral MS24 operator explicitly. For American options, we employ an Parametric Inference and Dynamic State Recovery operator splitting method to decouple the early exercise from Option Panels constraint. Numerical experiments demonstrate the good efficiency of the proposed methods. We develop a new parametric estimation procedure for op- tion panels observed with error. We exploit asymptotic Jari Toivanen approximations assuming an ever increasing set of option Stanford University prices in the moneyness (cross-sectional) dimension, but [email protected] with a fixed time span. We develop consistent estimators for the parameters and the dynamic realization of the state vector governing the option price dynamics. The estima- Santtu Salmi tors converge stably to a mixed-Gaussian law and we de- University of Jyvaskyla velop feasible estimators for the limiting variance. We also santtu.salmi@jyu.fi provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted Lina von Sydow from the options and one constructed nonparametrically Department of Information T from high-frequency data on the underlying asset. Fur- Uppsala University thermore, we develop new tests for model fit over specific [email protected] regions of the volatility surface and for the stability of the risk-neutral dynamics over time. A comprehensive Monte Carlo study indicates that the inference procedures work MS23 well in empirically realistic settings. In an empirical ap- plication to S&P 500 index options, guided by the new When Option Pricing Meets Optimal Execution diagnostic tests, we extend existing asset pricing models by allowing for a flexible dynamic relation between volatil- In this talk, we show how ideas coming from optimal ex- ity and priced jump tail risk. Importantly, we document ecution models la Almgren-Chriss can be used to solve that the priced jump tail risk typically responds in a more specific option pricing problems. We present a model to pronounced and persistent manner than volatility to large price and hedge call options (with physical settlement or negative market shocks. cash settlement) when liquidity costs matter, that is when the underlying is illiquid and/or when the nominal is large. Torben G. Andersen We also briefly discuss the case of Accelerated Share Re- Northwestern University purchase contracts in the same modeling framework. [email protected]

Olivier Gueant Universit´e Paris-Diderot MS24 UFR de Math´ematiques Simulated Likelihood Estimators for Discretely Ob- FM14 Abstracts 67

served Jump-Diffusions T . We then investigate several tractable approximations that are shown to be quite accurate. This paper develops an unbiased Monte Carlo approxima- tion to the transition density of a jump-diffusion process Michael Ludkovski, Kyle Bechler with state-dependent drift, volatility, jump intensity, and UC Santa Barbara jump magnitude. The approximation is used to construct a [email protected], [email protected] likelihood estimator of the parameters of a jump-diffusion observed at time intervals that need not be short. The estimator is asymptotically unbiased for any sample size. MS26 It is consistent and has the same limiting normal distri- A Class of Distributions with Analytic Character- bution as the true but uncomputable likelihood estimator. istic Functions Numerical results illustrate our approach. In this talk, we consider a class of distributions with char- Kay Giesecke acteristic functions that are analytic in a horizontal strip Stanford University in the complex plane. Distributions in this class can be Dept. of Management Science and Engineering inverted from their characteristic functions very efficiently [email protected] using simple rules with exponentially decaying approxima- tion errors. The results can be used for accurate valuation Gustavo Schwenkler of option contracts in models with jumps and stochastic Boston University volatility. Numerical examples illustrate the effectiveness [email protected] of the schemes.

Liming Feng MS24 Department of Industrial and Enterprise Systems Nonparametric Tests for Constant Betas in Jump- Engineering Diffusions University of Illinois at Urbana-Champaign [email protected] PlWe derive a nonparametric test for constant beta over a fixed time interval from high-frequency observations of a bivariate Ito semimartingale. Beta is defined as the ratio of MS26 the spot continuous covariation between an asset and a risk A martingale approach to long term risk and Ross factor and the spot continuous variation of the latter. The recovery: theory test is based on the asymptotic behavior of the covariation between the risk factor and an estimate of the residual com- We start with a general pricing kernel in the semimartin- ponent of the asset, that is orthogonal (in martingale sense) gale asset pricing framework and study existence of the to the risk factor, over blocks with asymptotically shrink- long-term forward measure, the long-term limit of T- ing time span. Rate optimality of the test over smoothness maturity forward measures. We then show that in the classes is derived. ergodic Markovian environment the Hansen-Scheinkman factorization of the pricing kernel into the permanent and Viktor Todorov transitory components naturally emerges, and Ross recov- Kellogg School of Management ery emerges as the special case. The strength of our semi- Northwestern University martingale approach is that we naturally extend these con- [email protected] cepts to non-Markovian models.

Vadim Linetsky MS24 Northwestern University Assessment of Uncertainty in High Frequency [email protected] Data: The Observed Asymptotic Variance

No text MS26 Sticky Reflecting Ornstein-Uhlenbeck Processes Per Mykland and Interest Rate Modeling with Zero Lower The University of Chicago Bound Department of Statistics [email protected] We study sticky reflecting Ornstein-Uhlenbeck processes which are solutions to SDEs with sticky boundary condi- Lan Zhang tions. We construct sample paths of the solution by means University of Illinois at Chicago of time change and represent the transition semigroups in lanzhang at uic dot edu terms of spectral expansion. As an application, we pro- pose a Markovian short rate model with zero lower bound based on sticky OU processes under which zero coupon MS25 bond and interest rate derivative prices have analytical so- Optimal Execution and Order Flow Imbalance lutions though eigenfunction expansion.

We examine optimal execution models that consider infor- Yutian Nie mational costs to the trader. Most existing optimal exe- Northwestern University cution literature ignores the traders order side relative to Industrial Engineering and Management Sciences the prevailing order flow. We model the influence on the [email protected] flow imbalance process and develop an indefinite-horizon stochastic control problem which allows the trader to react Vadim Linetsky to changing order flow by endogenizing the trading horizon Northwestern University 68 FM14 Abstracts

[email protected] the cost of hedging a contingent claim with given expected success ratio, by semi-static strategy in stocks and options. We prove duality results that link this quantile hedging MS26 price to a randomized composite hypothesis testing prob- A martingale approach to long term risk and Ross lem, and obtain the optimal hedging strategy in complete recovery: examples markets. In incomplete markets, an approximation proce- dure is proposed, by discretization of the path space. We give explicit treatment of a number of asset pricing models where the long-term bond process and the long- Gu Wang term forward measure exist, including affine diffusions, as University of Michigan, Department of Mathematics well as non-Markovian Heath-Jarrow-Morton models. [email protected]

Likuan Qin Erhan Bayraktar Northwestern University University of Michigan Industrial Engineering and Management Sciences Department of Mathematics [email protected] [email protected]

Vadim Linetsky Northwestern University MS27 [email protected] Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion

MS27 We study the robust stochastic control problem of an in- Optimal Transport and Skorokhod Embedding dividual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she Model-independent pricing has grown into an independent does not have perfect confidence in the drift of the risky field in during the last 15 years. A asset. In analyzing the HJB equation, we establish the driving inspiration in this area has been the fruitful con- existence and uniqueness of viscosity solution using Per- nection to the Skorokhod embedding problem. We dis- rons method, and then upgrade regularity by working with cuss a more recent approach to model-independent pric- an equivalent convex problem obtained via the Cole-Hopf ing, based on a link to Monge-Kantorovich optimal trans- transformation. port. Based on a similar technique in optimal transport we derive a ”monotonicity principle” that is applicable to Yuchong Zhang, Erhan Bayraktar model-independent pricing. This transport-viewpoint also University of Michigan sheds new light on Skorokhod’s classical problem. Department of Mathematics [email protected], [email protected] Mathias Beiglb¨ock University of Vienna (Universit¨at Wien) math department [email protected] MS28 Rare Event Simulations using shaking transforma- tions on stochastic processes MS27 Model-Independent Hedging under Portfolio Con- Based on reversible transformation on the state space (such straints as continuous or cadlag paths), we introduce different Markov chains that enter in the design of two different We study model-independent superhedging of exotic op- methods for estimating rare event probability. One is based tions under portfolio constraints. The hedging portfolio on interacting particle systems (IPS) and the other on time- contains static positions in liquidly traded options, and a average on a single path (POP) using ergodic theorem. dynamic trading strategy, subject to constraints, on the We discuss the associated convergence rates and provide risky asset. By the theory of optimal transport, we estab- numerical experiments. Our examples cover situations re- lish a superhedging duality, which admits a connection to lated to insurance and finance among others. Both algo- convex risk measures. We also derive a model-independent rithms are accurate, with a seemingly advantage to POP. fundamental theorem of asset pricing. Our method covers a large class of Delta constraints and Gamma constraint. Emmanuel Gobet Arash Fahim Ecole Polytechnique Florida State University France [email protected] [email protected]

Yu-Jui Huang, Yu-Jui Huang Gang Liu School of Mathematical Sciences Ecole polytechnique Dublin City University [email protected] [email protected], [email protected]

MS28 MS27 Global Ranking Problems, Sequential Design and Quantile Hedging in a Semi-Static Market with Applications to Real Options Model Uncertainty We consider sequential design approaches to the problem With model uncertainty characterized by a convex, non- of determining the pointwise index of the largest function dominated set of probability measures, investors minimize among a family of N maps x → fi(x), i =1, 2,...,N, FM14 Abstracts 69

over a multi-dimensional domain x ∈X.Thefi’s are un- [email protected], [email protected], edgard- known but can be noisily sampled. Our context is moti- [email protected] vated by the extension of the sequential Regression Monte Carlo approach to optimal switching problems. Applica- tions to valuation of real options for irreversible capacity MS30 expansion will be presented. On the Sensitivity of Calibrated American Put Val- ues to Short Rate Volatility Ruimeng Hu, Michael Ludkovski UC Santa Barbara We demonstrate that for a wide class of Equity-Interest [email protected], [email protected] rate hybrid models the price of the American put decreases with increasing interest rate volatility. Specifically we as- sume the Equity volatility is local in spot and spot-rate MS28 correlation is non-negative. The model is required to cal- Improved Greeks for American Options Using Sim- ibrate perfectly to vanillas and zero coupons. We deduce ulation that the price of American put is maximal when interest rate volatility is zero and the model reduces to Dupire local This paper revisits the estimation and approximation of volatility. the Greeks for American style options and compares vari- ous methods in term of bias, convergence and overall per- Aleksey Polishchuk formance. Using the constrained Monte Carlo Bloomberg, NY method of L´etourneau and Stentoft (2014) a new, simple [email protected] and computationally efficient method is proposed, which is based on differentiating the holding value function. The MS30 proposed method is shown to perform well compared to existing methods. A New Hybrid Monte Carlo-Finite Difference Method to Obtain Counterparty Exposure Profiles Lars Stentoft and Sensitivities Western University [email protected] After the credit crunch, financial institutions are more and more interested in the Expected Exposure (EE) of their derivatives. This EE is also needed to compute the Credit MS28 Valuation Adjustment (CVA). To measure EE we intro- duce the Finite Difference Monte Carlo (FDMC) method. An Iterative Simulation Approach for Solving By combining two well-known methods in options pricing, Stochastic Control Problems in Finance highly accurate probability densities of future option prices can be obtained. In this presentation we show how FDMC We develop a variable sample size, iterative, contraction can be extended to compute CVA and its sensitivities of a method to solve stochastic optimization problems with con- portfolio. Next to that, we show that it can be applied to tinuous choice variables, and study its asymptotic conver- higher dimensional (n ≥ 2) models. gence. We use the method to solve first order optimal- ity conditions for high-dimensional discrete-time stochastic Kees de Graaf control problem under general constraints, in a framework University of Amsterdam that employs Monte-Carlo simulation in every step. We the Netherlands illustrate the method using applications from Finance. [email protected]

Chunyu Yang Drona Kandhai BI School of Business University of Amsterdam [email protected] ING Bank [email protected] Stathis Tompaidis McCombs School of Business Peter Sloot UT Austin University of Amsterdam [email protected] [email protected]

MS30 MS30 A Robust Spectral Method for Pricing Options un- Dimension Reduction Techniques in Space and der Local Volatility Discontinuous Galerkin in Time to Price High- Dimensional Options We constructed a spectral method for solving PDEs mod- elling standard European and American options under lo- A multi-dimensional Black-Scholes equation to price basket cal volatility. In the case of European options, the PDE options is solved using adaptive finite differences. These is discretised directly in space, whereas the free boundary problems suffer from the ”curse of dimensionality” which problem arising from American options is reformulated as is here tackled by using a dimension reduction technique; a a variational inequality which is then transformed into a principal component analysis together with an asymptotic nonlinear PDE on fixed boundaries by adding a penalty expansion. In time we employ a discontinuous Galerkin term. The resulting nonlinear PDE is discretised using an scheme. We will present the favorable properties of this adaptive rational spectral method. methodology in terms of accuracy and computational time.

Pindza Edson, Kailash C. Patidar, Edgard Ngounda University of the Western Cape Lina von Sydow 70 FM14 Abstracts

Department of Information T ter (2013). In particular it gives an affirmative answer to a Uppsala University problem posed in that paper in the case of the 3/2 stochas- [email protected] tic volatility model. We also give precise conditions (not based on asymptotics) when the discrete fair strike of the Erik Lehto is higher than the continuous one and dis- Department of Mathematics cuss the convex order conjecture proposed by Griessler and Royal Institute of Technology Keller-Ressel (2014) in this context. [email protected] Carole Bernard University of Waterloo Paria Ghafari [email protected] Uppsala University [email protected] Zhenyu Cui Department of Mathematics Mats W˚angersj¨o Brooklyn College of the City University of New York Department of Information Technology [email protected] Uppsala University [email protected] Don McLeish Department of Statistics and MS31 University of Waterloo [email protected] Asymptotic Approximations for Some Path- Dependent Contracts MS32 We give asymptotic formulas for approximate valuation of some path-dependent contracts. Robust Nash Strategies in Mean Field LQG Games Weconsiderameanfieldgameinalinear-quadratic- Roger Lee Gaussian (LQG) setting. All agents’ dynamics are affected University of Chicago by a common disturbance signal in the drift term, as an un- [email protected] known L2 function of time, which models the uncertainty in the decision environment. Each agent wishes to mini- MS31 mize its worst case cost where the disturbance acts first to maximize. We obtain a set of decentralized strategies as a Explicit Implied Vols for Multifactor Local- robust -Nash equilibrium in an N player game. The so- Stochastic Vol Models lution is based on open-loop information and is character- ized by a system of forward backward stochastic differential We consider an asset whose risk-neutral dynamics are equations (FBSDEs). described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for Jianhui Huang European-style option prices and implied volatilities. Our Department of Applied Mathematics implied volatility expansions are explicit; they do not re- The Hong Kong Polytechnic University quire any special functions nor do they require numerical [email protected] integration. To illustrate the accuracy and versatility of our method, we implement it under five different model Minyi Huang dynamics: CEV local volatility, quadratic local volatility, Carleton University Heston stochastic volatility, 3/2 stochastic volatility, and [email protected] SABR local-stochastic volatility.

Matthew Lorig MS32 Princeton University ORFE Department Mean Field Models for Dynamic Matching Markets [email protected] We present recent progress in the application of mean field models to dynamic matching markets. In particular Stefano Pagliarani we consider a decentralized two-sided matching market in Ecole Polytechnique which agents arrive and depart asynchronously. As a re- [email protected] sult, it is possible that an agent on one side of the market (a buyer) identifies an agent on the other side of the mar- Andrea Pascucci ket (a seller) who is a suitable match, only to find that the Universita di Bologna seller is already matched. We find using a mean field ap- [email protected] proach that lack of knowledge about availability can create large welfare losses to both buyers and sellers. We consider a simple intervention available to the platform: limiting MS31 visibility of sellers. We find that this intervention can sig- Convergence of the Discrete Variance Swap in nificantly improve the welfare of agents on both sides of Time-Homogeneous Diffusion Models the market; sellers pay lower application costs, while buy- ers are less likely to find that the sellers they screen have In stochastic volatility models based on time-homogeneous already matched. Somewhat counterintuitively, the bene- diffusions, we provide a simple necessary and sufficient con- fits of showing fewer sellers to each buyer are greatest in dition for the discretely sampled fair strike of a variance markets in which there is a shortage of sellers. In this talk, swap to converge to the continuously sampled fair strike. It we describe the nonasymptotic model, its formal mean field extends Theorem 3:8 of Jarrow, Kchia, Larsson and Prot- limit, and some of the key techniques employed to establish FM14 Abstracts 71

an approximation theorem. [email protected]

Nick Arnosti, Ramesh Johari Stanford University MS33 [email protected], [email protected] Asymptotic Single Risk Factor Model of Credit Risk: Empirical Evidence from Australia Yash Kanoria Columbia Business School Prevailing states of the Australian economy recovered from [email protected] the asymptotic single risk factor model implemented by the Basel II internal ratings-based approach find general agree- ment with macroeconomic indicators. Since the depths of the financial crisis of 2007-09 were reached after the im- MS32 plementation of Basel II, our analysis measures the impact Mean Field Games with a Common Noise of the crisis on the Australian banking sector. Access to internal bank data collected by the prudential regulator This talk presents some recent results on stochastic differ- distinguishes our research from other empirical studies on ential mean field games (MFGs) with common noise. The the recent crisis. concepts of strong and weak solutions are introduced in Silvio Tarca,MarekRutkowski analogy with the theory of stochastic differential equations, University of Sydney and existence of weak solutions for MFGs holds under very [email protected], general assumptions. Using an analog of the famous result [email protected] of Yamada and Watanabe, existence and uniqueness of a strong solution can be shown to hold in some cases. Fi- nally, it turns out that the notion of weak solution is the MS33 right one from the perspective of the n-player games: Ev- ery sequence of approximate Nash equilibria in the n-player Short Rate Models with Stochastic Volatility games admits certain limits as n tends to infinity, and ev- We look at a class of non-affine short rate models with ery limit is a weak solution of the MFG. Conversely, every lognormal stochastic volatility as a low-dimensional alter- weak solution of the MFG can be obtained as the limit of native to LIBOR Market Model. For efficient calibration to a sequence of approximate Nash equilibria in the n-player vol grids, we first obtain asymptotic expansions of games. zero bond price in the presence of time-dependent param- eters and in multi-dimensional setting. We then formulate Daniel Lacker the problem of calibrating to market-consistent SABR pa- ORFE, Princeton University rameter matrix as an optimal projection of forward swap [email protected] rate process onto the SABR process.

Rene Carmona Andrew Lesniewski Princeton University Baruch College Dpt of Operations Research & Financial Engineering Department of Mathematics [email protected] [email protected]

Fran¸cois Delarue Heng Sun Universit´e Nice Sophia Antipolis Bank of New York Mellon Laboratoire J.A. Dieudonn´e [email protected] [email protected] Qi Wu Columbia University, Applied Mathematics MS33 [email protected] Perturbation Analysis on Decision-Making for In- vestment Portfolios Under Partial Information MS33 Optimal Consumption With Habit Formation In It is well-known that solving the Markowitz problem will Markets with Transaction Costs And Unbounded result in portfolio weights that don’t resemble the weights Random Endowment used in real-life investment. The Black-Litterman is a prac- tical solution to this problem, wherein investors’ views on This paper studies the utility maximization problem on upcoming performance are incorporated into the optimiza- consumption with addictive habit formation in the mar- tion along with any degree of uncertainty that the investor kets with proportional transaction costs and unbounded may have in these views. In this paper we consider a random endowment. To model the proportional transac- Merton-type portfolio problem wherein the framework is tion costs, we adopt Kabanov’s multi-asset framework with adapted to incorporate filtering and the views of market a cash account. At the terminal time t=T, the investor can experts. Our results use perturbation theory to analyze receive an unbounded random endowment for which we a partial information HJB equation, from which we find propose a new definition of acceptable portfolio processes an intuitive interpretation of the model parameters and of depending on the strictly consistent price system (SCPS). how stochasticity in expected returns affects optimal in- We prove a type of super-hedging theorem for a family vestment. of workable contingent claims using the acceptable port- folios and random endowment which enables us to obtain Andrew Papanicolaou, Andrew Papanicolaou the consumption budget constraint result under the mar- University of Sydney ket frictions. With the path dependence reduction and the [email protected], alpa- embedding approach, the existence and uniqueness of the 72 FM14 Abstracts

optimal consumption are proved using the auxiliary primal eliminates implausible scenarios for rates and FX produced and dual processes and the convex duality analysis by flat reversion models.

Xiang Yu Alexander Sokol Department of Mathematics, CompatibL University of Michigan [email protected] [email protected] MS35 MS34 Integral Representation Theorems for Martingales Wrong Way and Gap Risks Modeling: A Marked Motivated by the Problems of Endogenous Com- Default Time Approach pleteness and Market Completeness with Deriva- tive Securities We use marked stopping times to model the defaults of two counterparties. The role of the mark is to convey some in- We present conditions, which guarantee the endogenous formation about the defaults, in order to account for vari- completeness of a dynamic equilibrium market and the ous possible wrong-way risk and gap risk scenarios and fea- completeness of markets in which, in addition to stocks, tures. The corresponding CVA, DVA and FVA equations one may also trade derivative securities. From a purely and studied. Specific tools are required to analyze the cure mathematical point of view we prove the following inte- Q P period (time interval between the default and the liquida- gral representation theorem: let and be two equivalent Q tion) and the ensuing gap risk of diverging evolutions of probability measures, SF a martingale under , ψ avector B EQ |F the portfolio and of its collateral. In particular, the liq- of random variables and let St = [ψ t]. We present uidation time is predictable (as announced by the default conditions on model primitives which guarantee that every under Q can be represented as a stochastic time), which modifies the nature of the pricing problems. F B The case of counterparty risk on credit derivatives, a major integral with respect to the martingale S =(S S ) . wrong-way and gap risk concern, poses specific dependence Daniel Schwarz modeling and dimensionality challenges. To address these, Carnegie Mellon University we resort to dynamic copula models of portfolio credit risk [email protected] and we apply the above-mentioned approach in these se- tups. Dmitry Kramkov Stephane C. Crepey Carnegie Mellon University Evry University, France Pittsburgh [email protected] [email protected]

MS34 Derivative Pricing under Collateralization and Dif- ferential Rates

The increasing practice of collateralization has a deep im- pact on the valuation of derivatives. Assuming cash col- lateral, and that collateral posting occurs in continuous time, Piterbarg (2010) derived an option pricing formula under the assumption of an unsecured funding rate that is different than the collateral rate. In this talk, we extend Piterbarg’s (2010) result on European-style derivative pric- ing under collateralization, by relaxing the assumption of a single unsecured funding rate. Introducing different lend- ing and borrowing rates has the effect of producing non- linear price functionals for general claims. Buyer and seller prices diverge, and values of derivative portfolios are not the sum of the individual deal values. Conditions under which no-arbitrage price bounds can be derived explicitly are given and numerical examples showcased.

Fabio Mercurio Bloomberg LP [email protected]

MS34 Joint Measure Calibration and Mean Reversion Skew for Interest Rates

We propose a model for interest rates which produces both risk neutral and real world distributions. The model is cal- ibrated to market implied prices and historical regressions of rates of different maturity. The interest rate mean rever- sion estimated using the model is found to depend on rate level and increase rapidly for rates above 10 percent, which