Prof. Henry Schellhorn (Claremont Graduate University)

Title: An Algorithm for the Pricing of Path-Dependent American Options Using Malliavin Calculus

Abstract: We propose a recursive scheme to calculate backward the values of conditional expectations of functions of path values of Brownian motion. This scheme is based on the Clark-Ocone formula in discrete time. We construct an algorithm based on our scheme to efficiently calculate the price of American options on securities with path-dependent payoffs. Our algorithm can be combined with regression-based Monte Carlo methods, like the Longstaff-Schwartz algorithm. In this case, our algorithm remedies the decrease of performance experienced by regression-based methods when the number of basis functions, or regressands, needs to be quite large, because of path-dependence.