An efficient implementation of a least squares Monte Carlo method for valuing American-style options

Abstract

Several methods for valuing high-dimensional American-style options were proposed in the last years. Longstaff and Schwartz (LS) have suggested a regression-based Monte Carlo approach, namely the least squares Monte Carlo method. This article is devoted to an efficient implementation of this algorithm. First, we suggest a code for faster runs. Regression-based Monte Carlo methods are sensitive to the choice of basis functions for pricing high-dimensional American-style options and, like all Monte Carlo methods, to the underlying random number generator. For this reason, we secondly propose an optimal selection of basis functions and a random number generator to guarantee stable results. Our basis depends on the payoff of the high-dimensional option and consists of only three functions. We give a guideline for an efficient option price calculation of high-dimensional American-style options with the LS algorithm, and we test it in examples with up to 10 dimensions.