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研究生:葉志峯
研究生(外文):Chih-Feng Yeh
論文名稱:美式賣權在改良式三項式模型下的最適執行區間
論文名稱(外文):AN OPTIMAL EXERCISE BOUNDARY OF A MODIFIED EQUAL-PROBABILITY TRINOMIAL MODEL IN AMERICAN PUT OPTION
指導教授:陳軒基陳軒基引用關係
指導教授(外文):Hsuan-Chi Chen
學位類別:碩士
校院名稱:元智大學
系所名稱:國際企業學系
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
畢業學年度:94
語文別:英文
論文頁數:28
中文關鍵詞:美式賣權三項式評價
外文關鍵詞:Optimal Exercise BoundaryAmerican PutTrinomial Model
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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。
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.
TITLE.....................................................I
ABSTRACT IN CHINECE..................................................II
ABSTRACT IN ENGLISH.................................................III
ACKNOWLEDGE..............................................IV
LIST......................................................V
FIGURES..................................................VI
TABLES............................................VII
I.INTRODUTION.............................................1
II. KIM AND BYUN’S OPTIMAL EXERCISE BOUNDARY IN BINOMIAL MODEL.....................................................4
III.THE EQUAL-PROBABILITY TRINOMIAL MODEL................8
IV. THE MODIFIED EQUAL-PROBABILITY TRINOMIAL MODEL....................................................10
V.COMPUTATIONAL RESULTS..................................................13
VI.CONCLUSION............................................16
APPENDIX Ⅰ: PROOFS OF PROPOSITION 1 AND 2...............17
APPENDIX Ⅱ: ALGORITHMS FOR EXAMINING MY HYPOTHESIS...............................................18
BIBLIOGRAPHY.............................................20
BIBLIOGRAPHY
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.
Kim, I., & Byun, S. (1994). Optimal exercise boundary in a binomial option pricing model. The Journal of Financing Engineering, 3, 137-158.
McKean, H. (1965). Appendix: A free boundary problem for the heat equation arising from a problem of mathematical economics. Industrial Management Review, 6, 32-39.
Parkinson, M. (1977). Option pricing: The American put. Journal of Business, 50, 21-36.
Tian, Y. (1993). A modified lattice approach to option pricing. The Journal of Futures Markets, 13, 563-577.
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