| 随机利率条件下的欧式期权定价 |
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| 引用本文： | 周海林,吴鑫育,高凌云,陆凤彬. 随机利率条件下的欧式期权定价[J]. 系统工程理论与实践, 2011, 31(4): 729-734. DOI: 10.12011/1000-6788(2011)4-729 |
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| 作者姓名： | 周海林 吴鑫育 高凌云 陆凤彬 |
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| 作者单位： | 1. 安徽财经大学 金融学院, 蚌埠 233030;2. 湖南大学 工商管理学院, 长沙 410082;3. 中国社会科学院 世界经济与政治研究所, 北京 100732;4. 中国科学院 数学与系统科学研究院, 北京 100190 |
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| 基金项目： | NSFC/RGC of Hong Kong，国家自然科学基金 |
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| 摘 要： | 分别选择标的资产价格和零息债券价格为计价单位,给出了利率和标的资产价格的漂移系数和扩散系数为适应随机过程的条件下、在期权生命期内任意时刻的欧式期权价格的一般形式.当 利率和标的资产价格的波动率过程为时间 $t$的非随机函数时,欧式期权价格具有解析形式. 给出了一个标的资产价格服从几何布朗运动、利率服从HJM模型的欧式期权定价的例子,并导出期权价格的解析式.
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| 关 键 词： | 期权定价 随机利率 计价单位转换 解析解 |
| 收稿时间： | 2010-05-31 |
Pricing European options under stochastic interest rate |
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| ZHOU Hai-lin,WU Xin-yu,GAO Ling-yun,LU Feng-bin. Pricing European options under stochastic interest rate[J]. Systems Engineering —Theory & Practice, 2011, 31(4): 729-734. DOI: 10.12011/1000-6788(2011)4-729 |
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| Authors: | ZHOU Hai-lin WU Xin-yu GAO Ling-yun LU Feng-bin |
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| Affiliation: | 1. School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China;2. College of Business Administration, Hunan University, Changsha 410082, China;3. Institute of World Economics and Politics, Chinese Academy of Social Science, Beijing 100732, China;4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | With the assumption that the underlying asset price and interest rate follow diffusion process, the structure of the price of European option is obtained by choosing the underlying asset price and zero coupon price as numeraires respectively.A sufficient condition that the volatility processes of interest rate and the price of underlying asset are deterministic function of time is also derived,under which the price of European option has a close-formed structure.A case of European option pricing is presente... |
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| Keywords: | option pricing stochastic interest rate changes of numeraire closed-form solution |
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