Smart Monte Carlo: Various tricks using Malliavin calculus
AbstractCurrent 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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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0212004.
Length: 126 pages
Date of creation: 21 Dec 2002
Date of revision:
Note: Type of Document - PDF; prepared on windows; pages: 126
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Monte-Carlo; Quasi-Monte Carlo; Greeks; Malliavin Calculus; Wiener Chaos.;
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- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- T. R. Cass & P. K. Friz, 2006. "The Bismut-Elworthy-Li formula for jump-diffusions and applications to Monte Carlo pricing in finance," Papers math/0604311, arXiv.org, revised May 2007.
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