PricingMulti-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 respectivly. 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.