Random Path Sampling in Local Volatility Models

A backward Monte Carlo approach to exotic option pricing

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variancereduction when pricing exotic options.The new algorithm relies on theconstruction of a discrete multinomial tree.We characterize the tree in two alternative ways : in terms of the optimal gridsoriginating from the recursive marginal quantization algorithm and following anapproach inspired by the finite difference approximation of the diffusion s infinitesimal generator.We assess the reliability of the new methodology by comparing the performance of both approaches and benchmarking them with competitor monte carlo methods.