随机利率下股票价格服从指数O-U过程的期权定价  

Option pricing with the underlying stock price driven by Ornstein-Uhlenbeck process under stochastic interest rates

作　　者：李美蓉[1,2] 

机构地区：[1]合肥师范学院数学系,安徽合肥230061 [2]合肥工业大学数学系,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2009年第4期598-600,共3页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校省级自然科学重点研究资助项目(KJ2008A37ZC);合肥师范学院教学研究资助项目(2008jyy09)

摘　　要：文章建立了股票价格服从指数O-U过程的随机微分方程,在风险中性的假设下利用Girsanov定理找到了该模型的唯一等价鞅测度;利用期权定价的鞅方法,得到了随机利率情形下股票价格服从指数O-U过程,并且影响利率的因素与影响股票价格的因素相关时欧式期权的定价。The paper constructs the stochastic differential equation of the stock price whose process is driven by the exponential Ornstein-Uhlenbeck process. Under the risk-neutral hypothesis, the equiva- lent martingale measure is found by means of Girsanov theorem. The European option pricing on stocks is obtained as the price is driven by the exponential Ornstein-Uhlenbeck process under stochastic interest rates and the factors affecting the interest rate and the price of the stocks are correlative.

关 键 词：ORNSTEIN-UHLENBECK过程 随机利率 GIRSANOV定理 期权定价 

分 类 号：O211.6[理学—概率论与数理统计]