Function-approximation-based importance sampling for pricing American options

Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multidimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance importance sampling measure for American options. We then discuss how function approximation may be used to approximately learn this measure; we test this idea in simple examples. We also note that the zero-variance measure is fundamentally connected to a duality result for American options. While our methodology is geared towards developing an estimate of an accurate lower bound for the option price, we observe that importance sampling also reduces variance in estimating the upper bound that follows from the duality.