本文利用蒙地卡羅模擬法評價美式選擇權與衍生性金融商品 Before 1993, only a few papers used 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. Grant, Vora and Weeks (1996) successfully developed a technique recently, 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 Johoson (1984) method to improve the computational efficiency for the Grant, Vora and Weeks method when valuing plain vanilla American options. We then extend our computational algorithm to the case of American options on the 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 and investigate how the key parameters affect the values of options on maximum or minimum of two risky assets.
