基于O-U过程的具有不确定执行价格的期权定价  

Option pricing with change exercise price driven by the Ornstein-Uhlenback process

作　　者：郑晓阳[1] 刘兆鹏 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2008年第11期1232-1235,共4页Journal of Harbin Engineering University

基　　金：哈尔滨工程大学基础研究基金资助项目(HEUF04022)

摘　　要：为了更深入探讨鞅方法在期权定价中的应用,并使股票模型更加接近市场实际情况,主要研究了能反映股票预期收益率波动变化的指数O-U(Ornstein-Uhlenback)过程来刻画期权的标的股票价格的变化规律.利用随机微分方程和鞅方法,在无风险利率依赖于时间参数的情况下,考虑了在有效期内股票有红利支付和无红利支付2种情况下具有不确定执行价格的欧式期权定价问题,其主要结果为获得了股票价格遵循指数O-U过程且具有不确定执行价格的欧式看涨期权及欧式看跌期权的定价公式.In order to study the martingale method of pricing options more deeply in a way that makes the stock market model closer to the actual situation, the pricing option on a stock was considered with the price process driven by an exponential Ornstein-Uhlenback process, which can reflect fluctuations in the appreciation rate of the underlying stock＇s price. By means of the stochastic differential equation and the martingale method respectively, we analyzed the European option pricing issues with changing exercise prices stocks for the cases with dividend paying and without dividend paying during the effective time period. In addition, both the cases are in a special ones that the risk-free rate depends on the time parameter. From the research outcome, we know that the stock prices obey an exponential O-U process; by the way, the pricing formulas of European put option pricing and call option pricing formulas with changing exercise prices were obtained.

关 键 词：期权 指数Ornstein—Uhlenback过程 鞅方法 定价模型 

分 类 号：F830.91[经济管理—金融学]