A nonparametric method for pricing and hedging American options

In this paper, we study the problem of estimating the price of an American option and its price sensitivities via Monte Carlo simulation. Compared to estimating the option price which satisfies a backward recursion, estimating the price sensitivities is more challenging. With the readily-computable pathwise derivatives in a simulation run, we derive a backward recursion for the price sensitivities. We then propose nonparametric estimators, the k-nearest neighbor estimators, to estimate conditional expectations involved in the backward recursion, leading to estimates of the option price and its sensitivities in the same simulation run. Numerical experiments indicate that the proposed method works well and is promising for practical problems.