Enhancing the Computational Efficiency for the Monte-Carlo Simulation Approach

Abstract

Before 1993, there were only few papers using the Monte Carlo simulation approach to value American options. Since then, a number of articles developed alternative computational skills for the Monte Carlo simulation to value these options. Recently, Grant, Vora and Weeks (1996) successfully developed a technique which can simply and directly determine ”whether early exercise is optimal or not for American options when a particular asset value is reached at a given time using the Monte Carlo approach”. In this paper we first use the Geske and Johnson (1984) method to improve the computational efficiency for the Grant, Vora and Weeks method for valuing plain vanilla American options. We then extend our computational algorithm to the case of American options on maximum or minimum of two risky assets, whose prices are jointly lognormal distributions. We also show how to calculate the hedge ratios using the Monte Carlo simulations. Furthermore, we investigate how the key parameters affect the values of options on maximum or minimum of two risky assets.