Malliavin Calculus for Monte Carlo Methods in Finance

LSE Working Paper

10 Pages Posted: 24 Jan 2002

See all articles by Eric Benhamou

Eric Benhamou

Université Paris Dauphine; AI For Alpha; EB AI Advisory; Université Paris-Dauphine, PSL Research University

Date Written: January 2002

Abstract

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, Likehood Ratio, Homogeneity, Heston, Stochastic volatility, Calibration

JEL Classification: G12, G13

Suggested Citation

Benhamou, Eric, Malliavin Calculus for Monte Carlo Methods in Finance (January 2002). LSE Working Paper, Available at SSRN: https://ssrn.com/abstract=298084 or http://dx.doi.org/10.2139/ssrn.298084

Eric Benhamou (Contact Author)

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775
France

AI For Alpha ( email )

35 boulevard d'Inkermann
Neuilly sur Seine, 92200
France

EB AI Advisory ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

Université Paris-Dauphine, PSL Research University ( email )

Place du Maréchal de Lattre de Tassigny
Paris, 75016
France

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