Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach

Abstract

Following the pioneering papers of Fournié, Lasry, Lebouchoux, Lions and Touzi, an important work concerning the applications of the Malliavin calculus in numerical methods for mathematical finance has come after. One is concerned with two problems: computation of a large number of conditional expectations on one hand and computation of Greeks (sensitivities) on the other hand. A significant test of the power of this approach is given by its application to pricing and hedging American options. The paper gives a global and simplified presentation of this topic including the reduction of variance techniques based on localization and control variables. A special interest is given to practical implementation, number of numerical tests are presented and their performances are carefully discussed.