美式彩虹選擇權評價

Pricing American Rainbow Options

林嘉祐(Chia-Yu Lin)

指導教授 ： 王之彥

國立臺灣大學/管理學院/國際企業學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201600448

摘要

本篇論文延伸前向蒙地卡羅法 (Forward Monte Carlo Method) 來評價兩資產美式彩虹選擇權。先前已有學者成功發展出評價單資產美式選擇權的前向蒙地卡羅法，並大幅改善了評價效率。這個方法有別於其他評價方法，其優點在於它只需要判斷標的物價格是否落入提前履約的區域，而不需要使用逆推法。本篇論文將會提供兩資產美式彩虹選擇權的前向蒙地卡羅法與廣為人知的最小平方法 (Least Square Method) 的評價結果，在效率上，前向蒙地卡羅法擊敗了最小平方法。

關鍵字

BAW ； 美式彩虹選擇權 ； 平方逼近法 ； 假性關鍵價格 ； 前向蒙地卡羅法

並列摘要

This paper extends the forward Monte Carlo (FMC) method, which have been developed for the basic types of American options, to the valuation of two-asset American rainbow options.

The main advantage of this method is that it does not use backward induction as required by other methods. Instead, the proposed approach relies on a wise determination about whether a pair of simulated stock prices has entered the exercise region.

A series of numerical experiments are provided to compare the performance with the binomial tree model and least squares method and demonstrate the efficiency of the forward methods.

並列關鍵字

BAW ； American rainbow option ； Quadratic Approximation ； Pseudo critical price ； Forward Monte Carlo method

參考文獻

1. Barone-Adesi, G. and Whaley, R. (1987). ``Efficient Analytic Approximation of American Option Values'. Journal of Finance, 42, 301--320.

2. Chen, C.-Y., Wang, H.-C. and Wang, J.-Y. (2014). ``The Valuation of Forward-start Rainbow Options'. Review of Derivatives Research, 18, 145--188.

3. Hull, J. and A. White. (1994b). ``Numerical Procedures for Implementing Term Structure Models II: Two-Factor Models'. Journal of Derivatives, 2, 37--48.

4. Ju, N. (1998). ``Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function'. Review of Financial Studies, 11, 627-646.

5. Kim, I. J. (1990). ``The Analytic Valuation of American Options'. The Review of Financial Studies, 3, 547--572.