Mathematical Finance Seminar

April 26, 2001 , 5:30 PM to 7:00 PM

Thomas Bielicki, Northeast Illinois University

Recent Results on Evaluating Functionals of Several Random Times, with Applications to Valuation of Basket Credit Derivatives

In this talk we shall discuss the issue of evaluating certain functionals of several random times using intensity based approach. The idea is to convert formulas involving stochastic integration with respect to point processes, to formulas involving only ordinary (Lebesgue) integrals. This can be done if, for example, one knows intensity processes of the underlying random times with respect to the underlying filtrations (information F-fields). In particular, we shall provide calculations and formulas for the functionals corresponding to the minimum, and to the maximum of two random times. A martingale technique is typically used for such calculations. Respective formulas may be applied to valuation of the first-to-default and to valuation of the last-to-default basket credit derivatives, or, in more generality, to valuation of the ith-to-default basket credit derivatives. It will be shown that the assumption of conditional independence of random times leads to considerable simplification in calculations (whenever such an assumption may be justified).