Confirmed Speakers

Abstracts

Wen Cheng (JP Morgan):

Title: Analytical Green's Function Approximation and its applications in Counterparty credit Risk Management

Abstract: Since the credit crisis in 2008 and the failures of large financial institutions such as Bear Sterns, Lehman Brothers, etc., counterparty risk has been considered by most market participants the key financial risk. For the purpose of pricing and hedging counterparty risk, one usually needs to calculate Credit Valuation Adjustment (CVA). However, calculation of CVA is more complicated than ordinary derivative pricing in the sense that first, interest rate cannot be considered constant; second, in many cases we have to do forward pricing. Consequently, many pricing models do not admit closed-form solutions any more, and analytical approximation methods are needed. In this talk we will discuss the newly developed Dyson-Taylor Commutator method that analytically approximates the Green's functions of second order parabolic equations with coefficients dependent on both time and space. We show how this method can give an approximation of the solution for any fixed time and within any given tolerance. For applications in CVA calculation, we will discuss how this method can be used in equity derivative pricing, FX volatility surface merging, basket option pricing, etc.

Igor Cialeco (Illinois Institute of Technology):

Title: Dynamic Conic Finance

Abstract: We develop a framework for narrowing the theoretical spread between ask prices and bid prices of derivative securities in models of discrete time markets with transaction costs using dynamic coherent acceptability indices studied in Bielecki, Cialenco, and Zhang (2010). Aside from the use of acceptability indices as a tool, our approach is very much rooted in the literature studying good deal bounds as a vehicle to narrow the no-arbitrage interval. We first formulate and prove a no-good-deal version of the fundamental theorem of asset pricing (FTAP) using a family of dynamic coherent risk measures. The obtained results generalize to dynamic market model set-up the version of FTAP proved in Cherny and Madan (2010) in the static conic finance framework. We use the market model setup found in Bielecki et al (2012), which is suitable for dividend-paying securities in markets with transaction costs. Finally, we discuss some applications of this theory to path dependent options and compute the good-deal ask and bid prices generated by dynamic gain-loss ratio (a particular dynamic acceptability index).

Manfred Denker (Penn State):

Title: Richter's local limit theorem and Black-Scholes type formulas

Abstract: The talk reviews Richter's local limit theorem for multinomial distributions and its extension to dependent variables by S. Fares. Due to Kan's work one can formulate a European option price based on a 'conditional arbitrage free' argument. This leads to new types of the option pricing in accordance with the Black-Scholes formula. Last, the talk will make some comments on the space-time approximation of financial derivatives using extensions of the Jakubowski-Memin-Pages approach for weak convergence of stochastic integrals (see also Kurtz and Protter for a similar result).

Erich Walter Farkas (University and ETH, Zurich):

Title: Risk Measures and Capital Requirements with Multiple Eligible Assets

Abstract: We discuss risk measures associated with general acceptance sets for financial positions allowing for capital injections to be invested in a pre-specified eligible asset with an everywhere positive payoff. Risk measures play a key role when defining required capital for a financial institution. We address three critical questions: when is required capital a well-defined number for any financial position? When is required capital a continuous function of the financial position? Can the eligible asset be chosen in such a way that for every financial position the corresponding required capital is lower than if any other asset had been chosen? In addition we discuss the possibility of allowing for multiple eligible assets. We show that the multiple eligible asset case can be reduced to the single asset case, provided that the set of acceptable positions can be properly enlarged. This is the case when acceptability arbitrage is not possible, i.e. when it is not possible to make every financial position acceptable by adding a zero-cost portfolio of eligible assets. In contrast to most of the literature our approach is not limited to convex or coherent acceptance sets and allows for eligible assets that are not necessarily bounded away from zero. This generality uncovers some unexpected phenomena and opens up the field for applications to acceptance sets based both on Value-at-Risk and Tail Value-at Risk. This talk is based on two recent papers, jointly written with Pablo Koch-Medina (SwissRe) and Cosimo-Andrea Munari (ETH Zurich).

Paul Feehan (Rutgers University):

Title: Degenerate Obstacle Problems in Mathematical Finance

Abstract: ABSTRACT: Degenerate elliptic and parabolic obstacle problems arise in mathematical finance when valuing American-style options on an underlying asset modeled by a degenerate diffusion process. We will describe our work on existence, uniqueness, and regularity of solutions to stationary and evolutionary variational inequalities and associated obstacle problems when the underlying asset is modeled by a degenerate diffusion process. This is joint work with Panagiota Daskalopoulos (Department of Mathematics, Columbia University) and Camelia Pop (Department of Mathematics, Rutgers University)

Jingzhi (Jay) Huang/Zhan Shi (Penn State):

Title: Understanding Term Premia on Real Bonds

Abstract: Real bonds are a very important asset class but there has been little research on the dynamic behavior and economic determinants of risk premia on such bonds. In this paper we investigate these issues both empirically and theoretically. First, we document empirically that the real bond risk premium changes over time and fluctuates between positive and negative values, an evidence against the expectation hypothesis for real bonds. We then examine the potential link between the real risk premium and macro variables. We find that macro factors associated with real estate and consumer income and expenditure can capture a large portion of forecastable variations in excess returns on real bonds. Finally, we propose a long-run risk type model of the real term structure that allows for nonseparable preferences over housing services and other consumption. We show that the model can quantitatively explain almost all the stylized facts about the real term structure documented in our empirical analysis.

Robert Huitema (ETH, Zurich):

Title: Optimal Trade Execution using Market and Limit Orders

Abstract: We investigate trade execution strategies that maximize expected exponential utility. In contrast to existing literature our strategy makes use of both market and limit orders. We derive a Hamilton-Jacobi-Bellman equation for the optimal combination of these order types and solve it numerically. We show that limit orders have a significant impact on the optimal strategy, and discuss the utility gains with respect to pure market order strategies. Our findings indicate an inverse relation between the speed by which market orders are submitted and the likelihood of limit orders being filled. Furthermore, we find that the optimal limit price moves away from the market price when any of the following holds: i) trade execution is not urgent, ii) the asset position relatively small, iii) the agent not very risk averse.

Jenny Li (PSU):

Title: Optimal Intermediated Investment in a Liquidity-Driven Cycle

Abstract: A general equilibrium model of a financial intermediary extends the model first introduced by \citet{diamondDybvig1983} to an infinite-horizon environment. This extension offers a plausible explanation for the fluctuation of the asset composition in the U.S. banking sector. As in the Diamond-Dybvig model, the bank is an optimal financial intermediary coalition here. Moreover, the bank's optimal policy involves decisions about liquidity that vary systematically over the business cycle.

John Liechty (Penn State):

Title: Beyond the Office of Financial Research

Abstract: The financial system is struggling to escape a credit-confidence trap.  What type of feedback could be given to markets in order to make them more self-stabilizing?  The financial crisis cycle starts with the buildup of leverage in the financial system, which allows prices to be pushed up by a smaller and smaller set of optimistic buyers; leaving markets vulnerable to a cascade of losses as optimistic investors are wiped out driving prices down and wiping out additional highly, leveraged investors.  The interaction between having to sell at fire prices and a contraction in the short-term lending markets can result in market panic.  Innovation in the financial markets have outpaced the ability to regulate and to price these crisis risks. Regulators must insist on transparency and exercise broad corrective actions when needed.  Investors need to develop ways of sharing system-wide data so they can measure these risks and ultimately price them.

Camelia Pop (Rutgers University):

Title: Degenerate- parabolic partial differential equations with unbounded coefficients, martingale problems, and a mimicking theorem for Ito processes

Abstract: We solve four intertwined problems, motivated by mathematical finance, concerning diffusion processes. First, we consider a parabolic differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which becomes degenerate along the boundary of the half-space. We establish existence and uniqueness of solutions in weighted Holder spaces which incorporate both the degeneracy at the boundary and the unboundedness of the coefficients. Second, we show that the martingale problem associated with differential operator with unbounded, locally Holder continuous coefficients on a half-space is well-posed in the sense of Stroock and Varadhan. Third, we prove existence, uniqueness, and the strong Markov property for weak solutions to a stochastic differential equation with degenerate diffusion and unbounded coefficients with suitable Holder continuity properties. Fourth, for an Ito process with degenerate diffusion and unbounded but appropriately regular coefficients, we prove existence of a strong Markov process, unique in the sense of probability law, whose one-dimensional marginal probability distributions match those of the given Ito process. (Joint work with Paul Feehan.)

Dan Pirjol (JP Morgan Chase):

Title: Normal Local Volatility Model (based on work with Viorel Costeanu)

Abstract: An alternative formulation of the local volatility model is proposed, the normal local volatility model, which is appropriate for problems where the normal implied volatility is a more natural choice for quoting option prices than the commonly used log-normal Black-Scholes implied volatility. This is the case for example for assets which are not positive definite, such as spreads between two positive definite assets. We study the dynamics of the normal implied volatility in this model, using a small-time expansion in powers of maturity T.