Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis

Background: This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing. The standard approach in the option pricing literature is to choose the basis arbitrarily. By comparing four different polynomial basis we show that the choice of basis interferes in the option's price. Methods: We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis: Power, Laguerre, Legendre and Hermite A. To every American Asian Option priced, three sets of parameters are used in order to evaluate it properly. Results: We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths. In the case of an Amerasian call option, for example, we find that the preferable polynomial basis is Hermite A. For an Amerasian put option, the Power polynomial basis is recommended. Such empirical outcome is theoretically unpredictable, since in principle all basis can be indistinctly used when pricing the derivative. Conclusion: In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters. Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option. Theoretically all basis can be indistinctly used when pricing the derivative. However, our results does not confirm these. We find that when pricing an American Asian put option, Power A is better than the other basis we have studied here whereas when pricing an American Asian call, Hermite A is better.