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Importance sampling is a promising variance reduction technique for MonteCarlo simulation based derivative pricing. Existing importance sampling methodsare based on a parametric choice of the proposal. This article proposes analgorithm that estimates the optimal proposal nonparametrically using amultivariate frequency polygon estimator. In contrast to parametric methods,nonparametric estimation allows for close approximation of the optimalproposal. Standard nonparametric importance sampling is inefficient forhigh-dimensional problems. We solve this issue by applying the procedure to alow-dimensional subspace, which is identified through principal componentanalysis and the concept of the effective dimension. The mean square errorproperties of the algorithm are investigated and its asymptotic optimality isshown. Quasi-Monte Carlo is used for further improvement of the method. It iseasy to implement, particularly it does not require any analytical computation,and it is computationally very efficient. We demonstrate through path-dependentand multi-asset option pricing problems that the algorithm leads to significantefficiency gains compared to other algorithms in the literature.

Nonparametric Partial Importance Sampling for Financial Derivative Pricing