Correcting the bias in Monte Carlo estimators of American-style option values

Abstract

Existing Monte Carlo estimators of American option values are consistent but biased. This article presents a general bias reduction technique which corrects the bias due to making suboptimal exercise decisions. The derived asymptotic expression for the bias is independent of dimensionality, holds for very general underlying processes and option payoffs, and is easily evaluated. The bias is subtracted from the estimators at each exercise opportunity in order to produce bias-corrected estimators. We illustrate how to apply this technique to three methods of generating estimators - stochastic tree, stochastic mesh and least-squares Monte Carlo. Numerical results demonstrate that for a fixed sample size this technique significantly reduces the relative error for both high- And low-biased estimators. © Springer-Verlag Berlin Heidelberg 2009.