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Does the Derivatives Market Still Look Backward to Move Forward

USC Mathematical Finance Colloquium Special Lecture SeriesTitle: "Does the Derivatives Market Still "Look Backward to Move Forward?" Speaker: Nicole El Karoui, Université de Paris VI and Ecole Polytechnique, France Date/Time/Location: Friday, February 26, 2010, Lecture 3:30-4:30, Ethel Percy Andrus Gerontology Center (GER), Leonard Davis AuditoriumReception: 4:30-5:30 PM Outside GER AuditoriumAbstract: In the Black-Scholes theory of 1973, the message was that the derivatives market "looks backward to move forward". More precisely, the theory indicates that to price and hedge option contracts, one looks backward from the maturity and the pay-off of the contract for very short time periods, and then calculate from dates to dates the best hedge to the residual risk exposure. The minimal investment to implement the hedging strategy is then the market price of the derivative. The theory of Backward Stochastic Differential Equations was introduced by E. Pardoux and S. Peng in1990 originally without links with finance. It has, in particular the associated Monte Carlo methods, become a ubiquitous mathematical tool in finance exactly for such thinking. During the past two decades, with the increasing market liquidity, large classes of derivatives, such as vanilla options on stocks or currency or interest rates have been used as hedging instruments. Since the seminal paper of Heath, Jarrow, Morton (1987) on the forward dynamics of yields curve, the desire to understand the forward dynamics of some derivatives has grown significantly. The problems become increasingly complex, from the dynamics of the yields curve, to that of the implied volatility surface, and now to that of the implied volatility cubes. While the calibration issues seem to be the main reasons for this evolution, the asymptotic problems are particularly challenging both in theory and practice. In this talk I will present some of the problems in this new development.Bio: Nicole El Karoui is Professor of Applied Mathematics at both University of Paris VI and Ecole Polytechnique, France. She is well known for her many contributions on probabilistic aspects of stochastic control and their applications to partially observable optimization problems. In 1989, after a sabbatical semester in a bank, she started working on various mathematical problems in finance. She has been the leader in many fields of mathematical finance and related stochastic analysis. In 1990, with H. Geman, she founded one of the first graduate programs in quantitative finance at University of Paris VI, co-accredited with the Ecole Polytechnique. The program has been highly successful, and was widely reported in the French and US media (e.g., Le Monde and Wall Street Journal in 2006), which has greatly increased the visibility of French Quants in the world. There will be a reception after Prof. El Karuoi's talk, outside the Ethel Percy Andrus Gerontology Center (GER).

Location: Ethel Percy Andrus Gerontology Center (GER) - Auditorium

Audiences: Everyone Is Invited

Contact: Georgia Lum