Hedging Exotic Derivatives Through Stochastic Optimization

Patrick Hénaff
Banque Internationale de Placement, Dresdner Bank Group
Henaff@bip.fr

Abstract

In this paper, we develop methods for hedging financial instruments through stochastic optimization. We first concentrate on the proper formulation of such problems. Indeed one may consider artibrage-free prices, which are theoretical prices consistent with a model of the risk factors in the economy, or the observed market prices, which may not be consistent with any theoretical model. We define the roles that these two sets of prices may play in order to obtain a well-formulated model. Next, we present efficient solution algorithms which are derived naturally from the formulations presented earlier. Finally, we apply the method to the hedging of ``exotic options", both in the framework of a single period model, and of a multi-period model with recourse.