Computational tools in modern finance are often classified as either numerical or simulation methods. While the former provide fast and accurate answers in less complex problem, the latter offer the only viable tools for pricing instruments contingent on several assets. In the talk, we present a framework that allows combining these apparently different approaches. This is possible by introducing a smooth Monte Carlo estimator of transition density functions for stochastic differential equations. The estimator, though nonparametric, is unbiased and exhibits a rate of convergence that is typical to parametric problems. When used to approximate functionals of terminal prices, it reduces variance by a factor that depends on the ``smoothness" of the density estimate. We illustrate some possible applications of the method using European and American style financial instruments. For the latter, we focus on methods based on regression techniques, like the one considered recently by Longstaff and Schwartz, and on the low discrepancy mesh method (Boyle et al.).