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Efficient Control Variates for Monte-Carlo Valuation of American Options

In this paper we consider the application of control variates to the Monte-Carlo valuation of American options. The main idea of the paper is to sample control variates at the exercise time of the American option rather than at expiry, which would be the case for the corresponding European option valuation. We show that the reduction of variance benefits the computation of both lower and upper bound estimates of the American option value. Numerical examples are given for the American versions of the single-asset put option, and for the geometric and arithmetic Asian option, as well as for the max-call option in the multi-asset Black-Scholes model. The increased accuracy obtained in the valuation requires additional work in the determination of the exercise strategy, performed for instance by the Least-Squares Monte-Carlo approach of Longstaff & Schwartz (2001), in order to balance the overall accuracy.