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A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks

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Listed:
  • Eric Benhamou

    (Goldman Sachs International)

Abstract

This paper presented a new technique for the simulation of the Greeks (i.e. price sensitivities to parameters), efficient for strongly discontinuous payo¤ options. The use of Malliavin calculus, by means of an integration by parts, enables to shift the differentiation operator from the payo¤ function to the diffusion kernel, introducing a weighting function.(Fournie et al. (1999)). Expressing the weighting function as a Skorohod integral, we show how to characterize the integrand with necessary and sufficient conditions, giving a complete description of weighting function solutions. Interestingly, for adapted process, the Skorohod integral turns to be the classical Ito integral.

Suggested Citation

  • Eric Benhamou, 2002. "A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks," Finance 0212003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0212003
    Note: Type of Document - PDF; prepared on windows; pages: 126
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    References listed on IDEAS

    as
    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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    5. 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.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Monte-Carlo; Quasi-Monte Carlo; Greeks; Malliavin Calculus; Wiener Chaos.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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