Enhancing the Computational Efficiency for the Monte-Carlo Simulation Approach

強化蒙地卡羅模擬法之計算效率

10.6295/TAMJ.2004.0402.01

張傳章(Chuang-Chang Chang)；張森林(San-Lin Chung)；林忠機(Chung-Gee Lin)

蒙地卡羅模擬法 ； 美式選擇權 ； 最小值選擇權 ； 最大值選擇權 ； Monte Carlo simulation approach ； American options ； Values of options on maximum or minimum of two risky assets

台灣管理學刊

4卷2期（2004 / 08 / 01）

123 - 140

英文

於1993年以前，只有少數論文探討如何利用蒙地卡羅模擬法來對美式選擇權訂價，此後即有許多學者企圖提出各式各樣的蒙地卡羅模擬法來對美式選擇權訂價。Grant-Vora-Weeks(1996)成功地發展出一種簡單的蒙地卡羅模擬法，其可以決定美式選擇權在各個時點的提早履約價值，進而可以計算出美式選擇權的價格。本文首先以Geske-Johnson的Richardson外插法，來增進Grant-Vora-Weeks(1996)之蒙地卡羅美式選擇權訂價法之計算效率，並將此法擴展至最小值或最大值選擇權的訂價，同時本文亦執行敏感度分析，來探討一些重要模型參數之變動，如何影響最小值或最大值選擇權的價格。

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.

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