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.