| Vasicěk随机利率模型下指数O-U过程的幂型期权鞅定价 |
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| 引用本文： | 刘敬伟.Vasicěk随机利率模型下指数O-U过程的幂型期权鞅定价[J].数学的实践与认识,2009,39(1). |
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| 作者姓名： | 刘敬伟 |
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| 作者单位： | 北京航空航天大学数学系,数学、信息与行为教育部重点实验室,北京,100191 |
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| 摘 要： | 研究了Vasicěk随机利率模型中一维标准Brown运动与资产价格服从指数Ornstein-Uhlenbeck过程中一维标准Brown运动的相关系数为ρ(-1≤ρ≤1)的情形下的幂型期权鞅定价问题.推广了基于Vasicěk随机利率模型下基于Black-Scholes公式的两种幂型期权定价问题.并利用Girsanov定理和等价鞅测度,给出了基于Vasicěk随机利率模型下服从指数Ornstein-Uhlenbeck过程的两种欧式幂型期权鞅定价公式.
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| 关 键 词： | 随机利率 Black-Scholes公式 指数Ornstein-Uhlenbeck过程 幂型期权 Girsanov定理 鞅方法 |
Pricing European Power-function Option Under Exponential Ornstein-Uhlenbeck Process and Vasicěk Interest Rate with Martingale Method |
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| LIU Jing-wei.Pricing European Power-function Option Under Exponential Ornstein-Uhlenbeck Process and Vasicěk Interest Rate with Martingale Method[J].Mathematics in Practice and Theory,2009,39(1). |
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| Authors: | LIU Jing-wei |
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| Abstract: | The martingale method of pricing European power-function option is investigated in this paper,where stochastic interest rate and risk asset′s price are under Vasicěk model and exponential Ornstein-Uhlenbeck process model respectively,with the correlation coefficient of standard Brown motions in Vasicěk model and Ornstein-Uhlenbeck process is ρ(-1≤ρ≤1).The pricing European option under Vasicěk model and Black-Scholes model is first extended to two kinds of power-function options,then the pricing European power-function option formula under Vasicěk model and exponential Ornstein-Uhlenbeck process model are derived,using Girsanov theorem and equivalent martingale measure. |
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| Keywords: | stochastic interest rate Black-Scholes formula exponential Ornstein-Uhlenbeck process Power-function option girsanov theorem martingale method |
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