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

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Author Info
Eric Benhamou (Goldman Sachs International)

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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.

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File URL: http://129.3.20.41/eps/fin/papers/0212/0212003.pdf
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Publisher Info
Paper provided by EconWPA in its series Finance with number 0212003.

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Length: 126 pages
Date of creation: 21 Dec 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0212003

Note: Type of Document - PDF; prepared on windows; pages: 126
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Web page: http://129.3.20.41

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Related research
Keywords: Monte-Carlo Quasi-Monte Carlo Greeks Malliavin Calculus Wiener Chaos.

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
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  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. [Downloadable!] (restricted)
  2. 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 637-54, May-June. [Downloadable!] (restricted)
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