分数维Vasicek利率模型下的欧式期权定价公式  

Pricing Formulae for European Options under the Fractional Vasicek Interest Rate Model

作　　者：黄文礼[1] 陶祥兴[2] 李胜宏[3] 

机构地区：[1]浙江科技学院数学系,杭州310023 [2]浙江科技学院应用数学研究所,杭州310023 [3]浙江大学数学系现代金融研究室,杭州310027

出　　处：《数学学报（中文版）》2012年第2期219-230,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10771110);教育部重大项目基金资助课题(309018);宁波市自然科学基金资助项目(2009A610084)

摘　　要：假定股票价格和利率的运动过程服从几何分数维布朗运动,利用风险对冲技术,分数维布朗运动随机分析理论与偏微分方程方法,得到了分数维Vasicek随机利率下欧式期权所满足的定价方程,获得了波动率是对间函数的情形下欧式看涨和看跌期权的一般定价公式以及它们的平价公式.Under the assuming of the stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with stochastic interest rate. At the same time, we get the explicit expression for the European option price with stochastic interest rat and the call-put parity. The results in this paper extend as well as improve previously known results.

关 键 词：分数维布朗运动 分数维Vasicek随机利率 零息票债券 期权定价 

分 类 号：O175.2[理学—数学] O211[理学—基础数学]