| 分数维Vasicek利率模型下的欧式期权定价公式 |
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| 引用本文： | 黄文礼,陶祥兴,李胜宏.分数维Vasicek利率模型下的欧式期权定价公式[J].数学学报,2012(2):219-230. |
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| 作者姓名： | 黄文礼 陶祥兴 李胜宏 |
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| 作者单位： | 浙江科技学院数学系;浙江科技学院应用数学研究所;浙江大学数学系现代金融研究室 |
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| 基金项目： | 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) |
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| 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.
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| 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 |
Pricing Formulae for European Options under the Fractional Vasicek Interest Rate Model |
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| Institution: | Wen Li HUANG Institute of Applied Mathematics,Zhejiang University of Science and Technology, Hangzhou 310023,P.R.China Xiang Xing TAO Institute of Applied Mathematics,Zhejiang University of Science and Technology, Hangzhou 310023,P.R.China Shcng Hong LI Institute of Mathematical Finance,Department of Mathematics,Zhejiang University, Hangzhou 310027,P.R.China |
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| Abstract: | 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. |
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| Keywords: | fractional Brownian motion:fractional Vasicek model zero coupon bond option pricing |
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