Smart Monte Carlo: Various Tricks Using Malliavin Calculus
11 Pages Posted: 2 Mar 2002
Date Written: January 2002
Current Monte Carlo pricing engines may face computational challenge for the Greeks, because of not only their time consumption but also their poor convergence when using a finite difference estimate with a brute force perturbation. The same story may apply to conditional expectation. In this short paper, following Fournie et al. (1999), we explain how to tackle this issue using Malliavin calculus to smooth the payoff to estimate. We discuss the relationship with the likelihood ratio method of Broadie and Glasserman (1996). We show on numerical results the efficiency of this method and discuss when it is appropriate or not to use it. We see how to apply this method to the Heston model.
Keywords: Monte-Carlo, Greeks, Conditional expectation, Malliavin Calculus, Likelihood Ratio, Homogeneity, Heston
JEL Classification: G13
Suggested Citation: Suggested Citation