Improved Variance Reduced Monte-Carlo Simulation of in-the-Money Options

Abstract

Pricing derivatives with Monte-Carlo simulations involve standard errors that typically decrease at a rate proportional to where N is the sample size. Several approaches have been discussed to reduce the empirical variance for a given sample size. This article analyzes the joint application of the put-call-parity approach and importance sampling to variance reduced option pricing. For this purpose, we examine non-path-dependent and path-dependent options. For European options, we observe dramatic variance reduction, especially for in-the-money options. Also for arithmetic Asian options, a significant variance reduction is achieved.