Engineering More Effective Weighted Monte Carlo Option Pricing Models

Abstract

The Weighted Monte Carlo (WMC) method (Avellaneda (1998) and Avellaneda et al. (2001)) is a practical and robust method for calibrating a contingent claim pricing model that is consistent with the prices of liquid market instruments. We discuss new, tractable instances of the WMC method that make use of underlying asset prices that evolve with Student t (rather than, for example, Gaussian) innovations, relative U-entropy (rather than Kullback-Leibler relative entropy), and constraints that force model prices to lie within the bid-ask bands together with penalties on the discrepancies from the mid-market prices. We demonstrate the effectiveness of these WMC instances via benchmarking exercises on SPX option and LIBOR swaption data. In particular, we find that our WMC instances can be successfully calibrated to more liquid options (in our benchmarking exercises, our WMC instances reduced calibration failure rates – SPX options and LIBOR swaptions priced outside the bid-ask band – by a factors of over 2,000 and 38, respectively), and are more accurate on “out-of-sample” options than previously described WMC instances, particularly short-dated options and highly out-of-the-money options, where our instances are less prone to underpricing.