A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks
FMG Discussion Paper No. 0350
26 Pages Posted: 27 Apr 2001
Date Written: May 2000
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: Suggested Citation