分数布朗运动下的亚式重置期权定价
Fractional Brownian Motion under the Asian Reset Option Pricing
DOI: 10.12677/PM.2019.94073, PDF,   
作者: 程斯吉：广西师范大学数学与统计学院，广西 桂林
关键词: 分数布朗运动；亚式期权；重置期权；Fractional Brownian Motion； Asian Period； Reset Option
摘要: 本文主要利用等价鞅方法，给出在分数布朗运动环境下，几何平均亚式重置期权的定价公式，并利用MATLAB软件分析了初始股票价格、波动率和Hurst参数与期权价格的关系。
Abstract: This paper mainly uses equivalent martingale method to give the pricing formula of the geometric mean Asian reset option under fractional Brownian motion, and the relationship between the initial stock price, volatility and Hurst parameters and option price is analyzed by MATLAB.
文章引用：程斯吉. 分数布朗运动下的亚式重置期权定价[J]. 理论数学, 2019, 9(4): 551-556. https://doi.org/10.12677/PM.2019.94073

参考文献

[1] 约翰赫尔. 期权、期货及其他衍生产品[M]. 北京: 机械工业出版社, 2014.
[2] 姜礼尚. 期权定价的数学模型和方法[M]. 北京: 高等教育出版社, 2003.
[3] Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-654.
[Google Scholar] [CrossRef] 
[4] Peters, E.F. (1994) Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. John Wiley & Sons, New York.
[5] Elliott, R.J. and Hoek, J.V.D. (2010) A General Fractional White Noise Theory and Applications to Finance. Mathematical Finance, 13, 301-330.
[Google Scholar] [CrossRef] 
[6] Hu, Y. and Ksendal, B. (2003) Fractional White Noise Calculus and Applications to Finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6, 1-32.
[Google Scholar] [CrossRef] 
[7] 孙玉东, 师义民, 谭伟. 分数布朗运动环境下亚式期权定价的新方法[J]. 工程数学学报, 2012, 2(2): 173-178.
[8] 刘邵跃, 方秋莲, 王剑君. 多个分数布朗运动影响时的混合期权定价[J]. 系统工程, 2005, 23(6): 110-114.
[9] Deng, G. and Xi, H. (2011) Pricing Reset Option in a Fractional Brownian Motion Market. Chinese Academic Journal Electronic Publishing House, 7, 22-24.
[10] 刘邵容, 朱晖. 一种亚式重置期权的定价[J]. 南华大学报, 2011, 25(2): 49-51.

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