We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging American options in high dimension. In particular, the comparison concerns the quantization method of Barraquand-Martineau and an algorithm based on Malliavin calculus. The (pure) Malliavin calculus algorithm improves the precision of the computation of the delta but, merely for pricing purposes, is unc...

The aim of these lectures is to provide an elementary introduction to Hörmanders famous results on linear diffusion equations from a probabilistic point of view, and to show how these results can be applied to computational finance in the context of advanced Monte-Carlo methods of diffusion models with stochastic volatility. The lectures are aimed at an audience with some modest knowledge of st...

We translate in semigroup theory Bismut’s way of the Malliavin calculus.

This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.