Pricing Contingent Claims & Evaluating Market Risk

GUEST LECTURER
Professor Roger J-B Wets

AFFILIATION
University of California, Davis

ABSTRACT
We consider contingent claims pricing model with continuous distributions, discrete and continuous time. By formulating such problems as stochastic optimization problems and resorting to stochastic optimization and variational convergence techniques, one can obtain constructive procedures in situations that go much beyond the classical Black-Scholes framework. In the process, one derives some important properties such as no-arbitrage and nearly no-arbitrage conditions, equivalent martingale measures, equilibrium equation, etc. Implementation of this strategy requires an, as good as possible, estimate of the price process. A novel estimation approach, that relies on Levy's characterization of a Wiener process, is suggested and implemented experimentally.