Out-of-the-money monte carlo simulation option pricing: the joint use of importance sampling and descriptive sampling

Abstract

As in any Monte Carlo application, simulation option valuation produces imprecise estimates. In such an application, descriptive sampling (DS) has proven to be a powerful variance reduction technique. However, this performance deteriorates as the probability of exercising an option decreases. In the case of out-of-the-money options, the solution is to use importance sampling (IS). Following this track, the joint use of IS and DS is deserving of attention. Here, we evaluate and compare the benefits of using standard IS method with the joint use of IS and DS. We also investigate the influence of the problem dimensionality in the variance reduction achieved. Although the combination IS+DS showed gains over the standard IS implementation, the benefits in the case of out-of-the-money options were mainly due to the IS effect. On the other hand, the problem dimensionality did not affect the gains. Possible reasons for such results are discussed.