Weighted Monte Carlo for Equity Derivatives: Theory and Practice
Marco Avellaneda
Workshop on Multi-Asset Options,  Paris, November 2002

This talk describes the method of Weigted Monte Carlo (WMC), or Maximum-Entropy Monte Carlo, in the context of multi-dimensional models for equity derivatives. We show that WMC represents a turnkey solution for calibrating Monte Carlo simulations to option markets in situations where there are multiple underlying instruments. We prove rigorously that, under mild regularity assumptions, WMC gives rise to a numerically feasible numerical algorithm for computing the minimal martingale measure (least-relative-entropy martingale measure) consistent with options markets on the underlying stocks. Finally, we compare the predictions of WMC for pricing index options with the recently-derived steepest-descent approximation (RISK, Oct 2002) and actual market quotes using real market data.