Pricing American options: a comparison of Monte Carlo simulation approaches

Abstract

A number of Monte Carlo simulation-based approaches have been proposed within the past decade to address the problem of pricing American-style derivatives. The purpose of this paper is to test some of these algorithms empirically on a common set of problems in order to be able to assess the strenghts and weaknesses of each approach as a function of the problem characteristics. In addition, the authors introduce another simulation-based approach that parametrizes the early exercise curve and casts the valuation problem as an optimization problem of maximizing the expected payoff (under the martingale measure) with respect to the associated parameters, the optimization problem being solved using a simultaneous perturbation stochastic approximation (SPSA) algorithm.