| 摘要: |
| 依据投资者购买一家上市公司的股票，对公司进行投资，同时享受公司分红的权利，基于这样的实际情况，考虑在买卖最值期权支付红利的定价问题；假定股票的价格服从分数布朗运动驱动的随机微分方程，采用拉东-尼柯迪姆导数定理和多维哥萨诺夫定理，定义风险中性概率测度，同时建立风险中性概率测度下多维分数布朗运动每个股价的随机微分方程，在此基础上利用Wick积原理，求得每个股价的价格公式；运用风险中性定价的方法得到分数布朗运动下带有红利的最大值和最小值的看涨、看跌的期权定价公式以及平价公式;结果可在考虑股票支付红利的实际情况下，为研究最值期权定价问题提供理论参考。 |
| 关键词: 分数布朗运动 支付红利 最值期权 风险中性定价 |
| DOI： |
| 分类号: |
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| The Minimum or Maximum Option Pricing with Dividend under Fractional Brownian Motion |
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SHA Qing-bao
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School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
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| Abstract: |
| According to the investor’s purchase of a listed company’s stock and the investment in this company while enjoying the company’s right for dividends, based on this actual situation, this paper considers the pricing of the dividends on the sale of the most valued options. First, it is assumed that the price of the stock obeys the stochastic differential equation driven by fractional Brownian motion. The Radon Nikodim derivative theorem and the multidimensional Girsanov’s theorem are used to define the risk neutral probability measure. At the same time, the stochastic differential equation for each stock price of the multidimensional fractional Brown motion under the risk neutral probability measure is established. Based on the Wick product principle, the price formula of each stock price is obtained. Finally, the risk neutral pricing method is used to obtain call and put option pricing formulas and parity formulas with maximum and minimum dividends under fractional Brownian motion. The obtained results can provide a theoretical reference for studying the issue of valuation of options under consideration of the actual situation of stock dividends payment. |
| Key words: fractional Brownian motion payment of dividend the minimum or maximum option risk neutral pricing |
