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数学计算

《数学计算》(Mathematical Computation) (年刊)是IVY出版社旗下的一本关注数学理论与计算应用发展的国际期刊,是数学理论与现代工业技术相结合的综合性学术刊物。主要刊登有关理论数学、应用数学,及其在自然科学、工程技术、经济和社会等各领域内的最新研究进展的学术性论文和评论性文章。旨在为该领域内的专家、学者、科研人员提供一个良好的传播、分享和探讨数学理论进展的交流平台,反映学术前沿水平,促进学术交流,推进数学理论和应用方法的发展。本刊可接收中、英…… 【更多】 《数学计算》(Mathematical Computation) (年刊)是IVY出版社旗下的一本关注数学理论与计算应用发展的国际期刊,是数学理论与现代工业技术相结合的综合性学术刊物。主要刊登有关理论数学、应用数学,及其在自然科学、工程技术、经济和社会等各领域内的最新研究进展的学术性论文和评论性文章。旨在为该领域内的专家、学者、科研人员提供一个良好的传播、分享和探讨数学理论进展的交流平台,反映学术前沿水平,促进学术交流,推进数学理论和应用方法的发展。

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ISSN Print:2327-0519

ISSN Online:2327-0527

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Paper Infomation

Study on Timing of Expiration Time in Binomial Tree Option Pricing

Full Text(PDF, 353KB)

Author: Guanyu Li

Abstract: In this paper, we take the call option with stock as stock as an example. On the basis of the binary tree model, we convert the fluctuation process of stock price into random walk on the straight line. Furthermore, the results of H. Kesten, M.V. Kozlov and F. Spitzer in 1979 were used to show that the first arrival time of random walks can be characterized by the population of a branching process. Based on this, this paper calculates the probability generation function of the first (or nth) rise time of the stock, and performs Taylor expansion on the generated function to obtain different probabilities of different times used in the first arrival, and then analyzes its probability characteristics. .Based on this, the study guides the selection of the option expiration time.

Keywords: Binary Tree Model, First Arrival Time, Branching Proces

References:

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[3] Kesten, H., Kozlov, M.V., Spitzer, F., A limit law for random walk in a random environment. Composition Mathematic, 1979, 30, 145-168

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[5] Asmussen, S., Hering, H. Branching Processes, Birkhauser, Boston,1983

[6] Campos, L., Gonzalez, A., A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems, 1989, 29, 145-153

[7] Dubois, D., Prade, H., Possibility theory: an approach to computerized processing of uncertainty. New York: Plenum, 1988

[8] Cox, J., Ross, S., Rubinstein, M., Option pricing: A simplified approach. Journal of Financial Economics, 1979, 7(3), 229-263

[9] Loeve, M. Probability theory. New York: Springer-Verlag,1977

[10] Hualing Min. Stochastic Process[M], Tongji University Press.1987

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