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Smart Monte Carlo: Various tricks using Malliavin calculus


  • 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.

Suggested Citation

  • Eric Benhamou, 2002. "Smart Monte Carlo: Various tricks using Malliavin calculus," Finance 0212004, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0212004
    Note: Type of Document - PDF; prepared on windows; pages: 126

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    References listed on IDEAS

    1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
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    Cited by:

    1. 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,, revised May 2007.
    2. repec:eee:apmaco:v:264:y:2015:i:c:p:21-43 is not listed on IDEAS
    3. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.

    More about this item


    Monte-Carlo; Quasi-Monte Carlo; Greeks; Malliavin Calculus; Wiener Chaos.;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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