Smart Monte Carlo: Various tricks using Malliavin calculus

Eric Benhamou ()

Finance from University Library of Munich, Germany

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 Fournié et al. (1999), we explain how to tackle this issue using Malliavin calculus to smoothen the payoff to estimate. We discuss the relationship with the likelihood ration 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; Quasi-Monte Carlo; Greeks; Malliavin Calculus; Wiener Chaos. (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Pages: 126 pages
Date: 2002-12-21
Note: Type of Document - PDF; prepared on windows; pages: 126
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpfi:0212004

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