Smart Monte Carlo: Various Tricks Using Malliavin Calculus

11 Pages Posted: 2 Mar 2002  

Eric Benhamou

A.I. Square Connect; LAMSADE- Paris Dauphine University

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

Benhamou, Eric, Smart Monte Carlo: Various Tricks Using Malliavin Calculus (January 2002). Goldman Sachs Working Paper; EFA 2002 Berlin Meetings Discussion Paper. Available at SSRN: or

Eric Benhamou (Contact Author)

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200

LAMSADE- Paris Dauphine University ( email )

Place du Marechal de Lattre de Tassigny
Pais, 75016

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