Optimal Malliavin Weighting Function for the Computation of the Greeks

Source abstract

This paper reexamines the Malliavin weighting functions introduced by Fournié et al. (1999) as a new method for efficient and fast computations of the Greeks. Reexpressing the weighting function generator in terms of its Skorohod integrand, we show that these weighting functions have to satisfy necessary and sufficient conditions expressed as conditional expectations. We then derive the weighting function with the smallest total variance. This is of particular interest as it bridges the method of Malliavin weights and the one of likelihood ratio, as introduced by Broadie and Glasserman (1996) . The likelihood ratio is precisely the weighting function with the smallest total variance. We finally examine when to use the Malliavin method and when to prefer finite difference.