美式賣權在改良式三項式模型下的最適執行區間

AN OPTIMAL EXERCISE BOUNDARY OF A MODIFIED EQUAL-PROBABILITY TRINOMIAL MODEL IN AMERICAN PUT OPTION

葉志峯(Chih-Feng Yeh)

指導教授 ： 陳軒基

共同指導教授 ： 曾芳美

元智大學/管理學院/國際企業學系/碩士(2006年)

摘要

本文提出兩個命題與一個推測來改良機率相等三項模型，得出美式賣權的最適執形區間，發現此法所得之最適執行界線較平滑，非鋸齒狀；且因為這改良，使得我們在評價上可以較一般機率相等三項式 模型節省百分之三十的時間。而本文亦用平方根相對誤差(root-mean-squared relative error)與最小收斂步驟(the minimum convergence step)來比較二項式與三項式的評價效率與準確度，結論與之前學者一樣，三項式評價模型均優於二項式評價模型。

關鍵字

美式賣權；三項式評價

並列摘要

This paper develops a modified equal-probability trinomial model to obtain the optimal exercise boundary in American put option and finds the optimal exercise boundary gotten in this paper is smoother than the optimal exercise boundary gotten by Kim and Byun’s (1994) modified binomial model. The optimal exercise boundary of this modified equal-probability trinomial model non-decreases as the option approaches maturity and not toothed shape. In addition, by using the modified equal-probability trinomial lattice, we can reduce 30% of computing time, compared to the equal-probability trinomial lattice. Furthermore, I adopt the root-mean-squared (RMS) relative error and the minimum convergence step (MCS) to evaluate the accuracy and efficiency for these two models. The computational results show that the modified equal-probability trinomial model outperforms Kim and Byun’s modified binomial model.

並列關鍵字

Optimal Exercise Boundary ； American Put ； Trinomial Model

參考文獻

Barone-Adesi, G. (2005). The saga of the American put. Journal of Banking & Finance, 29, 2909-2918.

Carr, P., Jarrow, R., & Myneni, R. (1992). Alternative characterizations of American put options. Mathematical Finance, 2, 87-106.

Cox, J., Ross, S., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229-264.

Chen, H-C., Chen, D., & Chung, S-L. (2002). The accuracy and efficiency of alternative option pricing approaches relative to a log-transformed trinomial model. The Journal of Futures Markets, 22, 557-577.

Jacka, R. (1911). Optimal stopping and the American put. Mathematical Finance, 1, 1-14.