Malliavin Calculus and Its Application in Finance

Abstract

<p> In recent years, some efficient methods have been developed for calculating derivative price sensitivities, or the Greeks, using Monte Carlo simulation. However, the slow convergence, especially for discontinuous payoff functions, is well known for Monte Carlo simulation. In this project, we investigate the Malliavin calculus and its application in computation of the Greeks. Malliavin calculus and Wiener Chaos theory are introduced. The theoretical framework of the Malliavin weighted scheme of computation of the Greeks is explored in details, and the numerical implementation of the one-dimensional case and an example of the two-dimensional case are presented. Finally, the results are compared with those of finite difference scheme.</p>