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