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| 延期算术平均亚式期权价格的一个近似封闭公式 | |
| 引用本文： | 张东,鹿长余,安玉娥. 延期算术平均亚式期权价格的一个近似封闭公式[J]. 吉林大学学报(理学版), 2008, 46(3): 443-447 |
| 作者姓名： | 张东 鹿长余 安玉娥 |
| 作者单位： | 1. 上海理工大学 理学院, 上海 200093; 2. 上海金融学院 金融研究中心, 上海 201209;3. 上海大学 理学院, 上海 200466 |
| 基金项目： | 国家自然科学基金 , 上海市高校优秀青年教师后备人选科研项目 |
| 摘 要： | 在标的价格服从几何布朗运动、 收益服从对数正态分布的前提下, 通过风险中性定价原理, 对到期损益中的随机积分进行任意次Taylor近似, 并由级数定义将此连续问题离散化, 给出了延期算术平均亚式期权封闭形式的解析定价公式, 并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验, 结果表明, 所得公式可以应用到金融实务中对此类衍生品定价中. |
| 关 键 词： | 期权定价 亚式期权 延期 风险中性 Black Scholes模型 |
| 文章编号： | 1671-5489(2008)03-0443-05 |
| 收稿时间： | 2007-09-24 |
| 修稿时间： | 2007-09-24 |
An Approximate Close-form Formula of Deferred Arithmetic Average Asian Options |
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| ZHANG Dong,LU Chang-yu,AN Yue. An Approximate Close-form Formula of Deferred Arithmetic Average Asian Options[J]. Journal of Jilin University: Sci Ed, 2008, 46(3): 443-447 | |
| Authors: | ZHANG Dong LU Chang-yu AN Yue |
| Affiliation: | 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Financial Research Center, Shanghai Finance University, Shanghai 201209, China;3. College of Sciences, Shanghai University, Shanghai 200466, China |
| Abstract: | It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Takinginto account the risk neutral environment, we got a closed form analytical formula for deferred arithmetic asian optionsby the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simpleenough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives. |
| Keywords: | option pricing asian options deferred risk neutral Black Scholes model |
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