Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options

Abstract

American-Asian options are average-price options that allow early exercise. In this paper, we derive structural properties for the optimal exercise policy, which are then used to develop an efficient numerical algorithm for pricing such options. In particular, we show that the optimal policy is a threshold policy: The option should be exercised as soon as the average asset price reaches a characterized threshold, which can be written as a function of the asset price at that time. By exploiting this and other structural properties, we are able to parameterize the exercise boundary, and derive gradient estimators for the option payoff with respect to the parameters of the model. These estimators are then incorporated into a simulation-based algorithm to price American-Asian options. Computational experiments carried out indicate that the algorithm is very competitive with other recently proposed numerical algorithms.