樹狀模型對美式亞式選擇權評價之比較研究

Abstract

本論文主要研究樹狀模型對美式亞式選擇權之評價結果。本文針對三個樹狀模型進行比較：Hull-White(1993)、Chalasani-Jha-Egriboyun-Varikooty(1998)和Costabile-Massabó-Russo(2006)。針對這三個模型的運算時間及評價結果之關係進行比較與探討。 本文除了以上所提到的樹狀模型之外，在比較評價結果的部分還加入Dai-Huang-Lyuu(2005)及Dai-Wang-Wei(2007)之樹狀模型以及Longstaff-Schwartz (2001)的最小平方蒙地卡羅模擬方法一同進行比較，使本文的結論更具完整性。 根據本文的研究結果指出，在執行速度的部分，Hull-White(1993)樹狀模型的表現相較另外兩個模型優異。但是隨著二元樹之階段數(steps)的增加，Chalasani-Jha-Egriboyun-Varikooty(1998)、Costabile-Massabó-Russo(2006)的樹狀模型卻能提供相較Hull-White(1993)之評價模型更穩定之評價結果。 最後我們在實做的過程之中發現Costabile-Massabó-Russo(2006)文中對其評價結果的解釋可能有誤，本文則針對Costabile-Massabó-Russo(2006)之評價結果給予一個更合適的解釋。

This paper compares the results of the three different models which are Hull-White(1993), Chalasani et al.(1998) and Costabile-Massabó-Russo(2006). We compare the CPU time needed for each model and try to explain the relationship of their valuation.

To make our result more reasonable, we add another three models for our study when comparing the price. They are Dai-Huang-Lyuu(2005), Dai-Wang-Wei(2007) and Longstaff-Schwartz (2001).

Finally, in this paper, we conclude that Hull-White model performs the best in CPU time, but the other models provide relatively stable price when the number of the steps of a tree is larger.