Nonparametric Partial Importance Sampling for Financial Derivative Pricing

Efficient variance reduction is crucial to Monte Carlo simulation based derivative pricing. Importance sampling is one of the most promising approaches for variance reduction but typically neither the optimal importance sampling distribution itself nor a reliable approximation is available. We suggest an algorithm that applies a multivariate frequency polygon to estimate the optimal importance sampling distribution nonparametrically. Nonparametric importance sampling is inefficient in high-dimensional problems due to the curse of dimensionality. We tackle this problem by restricting our procedure to a low-dimensional subspace. We apply Quasi Monte Carlo techniques for the further improvement of our method. We demonstrate our method's potential to reduce Monte Carlo variance through path-dependent and multi-asset option pricing problems.