A New Modified Binomial Approach to Pricing American Put Option

美式賣權二項模式之新計算法

10.6545/JFS.2002.10(2).3

蔡宏洲(Hung-Chou Tsai)；陳欣得(Hsin-Der Chen)

美式賣權 ； 最適停止時間 ； 二項樹 ； American put option ； optimal stopping time ； binomial tree

財務金融學刊

10卷2期（2002 / 08 / 31）

63 - 78

英文

本文發展美式賣權二項模式的另一種計算法，根據此計算法，我們可以將美式賣權的二項樹狀圖分割為零值區（null region）、持有區（continuation region）與停止區（stopping region），並且，我們祇須計算落在持有區中之每一節點的美式賣權價格。由於需要計算美式賣權價格的節點數明顯地減少，以MATLAB執行計算的結果，此一新計算法的平均計算時間比傳統的二項計彪法快16倍，並且也比最近Kim and Byun（1994）提出之修正的二槓計算法快了約4倍。

This paper develops a new computational method of the binomial model for pricing American put option. The binomial tree can be partitioned by null region, continuation region, and stopping region. The new method is to compute the value of American put option only at the nodes in the continuation region. In this approach, the number of nodes for computing the value of put option is significantly reduced. The computational experiment is performed in MATLAB . The performance of our new modified binomial approach is measured by the average computing time (in flops) , and it is found that our new modified binomial approach is about four times faster than the modified binomial approach of Kim and Byun (1994), and sixteen times faster than the conventional binomial method.

1. Carr, P.,Jarrow, R.,Myneni, R.(1992).Alternative Characterizations of American Put Options.Mathematical Finance,2(2)
2. Cox, J. C.,Ross, S. A.,Rubinstein, M.(1979).Option Pricing: A Simplified Approach.Journal of Financial Economics,7(3)
3. Cox, J.,Rubinstein, M.(1985).Options Markets.Englewood Cliffs, NJ:Prentice Hall.
4. Jacka, S.(1991).Optimal Stopping and the American Put.Mathematical Finance,1
5. Kim, I.(1990).The Analytic Valuation of American Options.Review of Financial Studies,3
6. Kim, I.,Byun, S.(1994).Optimal Exercise Boundary in a Binomial Option Pricing Model.The Journal of Financial Engineering,3
7. McKean, H.(1965).Appendix: Free Boundary Problem for the Heat Equation Arising from a Problem of Mathematical Economics.Industrial Management Review,6

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