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

FMG Discussion Paper No. 0350

26 Pages Posted: 27 Apr 2001  

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

Date Written: May 2000

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.

JEL Classification: G12, G13

Suggested Citation

Benhamou, Eric, A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks (May 2000). FMG Discussion Paper No. 0350. Available at SSRN: https://ssrn.com/abstract=265277 or http://dx.doi.org/10.2139/ssrn.265277

Eric Benhamou (Contact Author)

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

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