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Smart Monte Carlo: Various tricks using Malliavin calculus

Listed author(s):
  • Eric Benhamou

    (Goldman Sachs International)

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.

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Paper provided by EconWPA in its series Finance with number 0212004.

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Length: 126 pages
Date of creation: 21 Dec 2002
Handle: RePEc:wpa:wuwpfi:0212004
Note: Type of Document - PDF; prepared on windows; pages: 126
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