Pricing Multi-Dimensional Options with Importance Sampling for Moment Reduction

Pricing multi-dimensional options is a challenging problem in financial mathematics. In this paper, we price these options with importance sampling for moment reduction. That is, instead of minimizing the second moment or relative variance of an estimator, the optimal parameters of a candidate measure are obtained by minimizing the relative centered moment of order p and the relative origin moment of order p respectively. We investigate the use of different importance sampling for moment reduction techniques to improve the efficiency of the Monte Carlo estimators. Some numerical experiments on multi-dimensional options are used to investigate the performance of these approaches.