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A generalisation of Malliavin weighted scheme for fast computation of the Greeks

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  • Benhamou, Eric

Abstract

This paper presented a new technique for the simulation of the Greeks (i.e. price sensitivities to parameters), efficient for strongly discontinuous payoff options. The use of Malliavin calculus, by means of an integration by parts, enables to shift the differentiation operator from the payoff 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

  • Benhamou, Eric, 2000. "A generalisation of Malliavin weighted scheme for fast computation of the Greeks," LSE Research Online Documents on Economics 119105, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119105
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    References listed 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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