分数布朗运动下B-S权证定价模型的修正  

Modification on Models of the B-S Pricing of Warrants under Fractional Brownian Motion

作　　者：赵旭[1] 

机构地区：[1]上海对外贸易学院金融管理学院,上海201620

出　　处：《统计与信息论坛》2011年第2期12-19,共8页Journal of Statistics and Information

基　　金：上海市教委重点学科金融学建设项目<衍生品使用与企业价值>(J512-01)

摘　　要：分析证券市场的有效性,指出其线性范式与现实市场状况并不符合。传统的金融学认为证券收益率服从对数正态分布,而大量的实证表明收益率分布与正态分布相比有"尖峰胖尾"特征,具有分形结构。在此基础上剖析了传统B-S权证定价模型的不足,结合分形市场中的分数布朗运动,提出了基于分形理论的B-S股本权证定价模型,考虑了股本稀释效应。由于股本权证定价模型需要已知企业股权价值及其波动率,但企业价值是权证价格的函数。基于此,运用数值方法以股票价格和波动率来估计企业价值波动率,并给出了在实际运用中的案例。First,the paper analyses the efficiency of the security market,points out that the linear paradigm of EMH is not an appropriated description of the true market.Traditional finance always thinks that the securities return rate follows normal distribution.However,lots of empirical research indicates that it has a fat tail compared with normal distribution and obeys fractal distribution.On the basis of these,the paper analyses the defect of the traditional B-S pricing model on warrants.And,the paper presents a fractal B-S pricing model on equity warrants by using the fractal theory.The model considers the equity warrants′ dilution effect on the stock price.The equity warrant pricing formula requires knowledge of the firm value and of the firm-value variance.However,the firm value itself is a function of the warrant price.Therefore,the paper develops a numerical method for pricing equity warrants using stock prices and stock return variance.The method enables estimation of firm-value variance.On the basis of these,the equity warrants pricing model based on the fractal theory are proposed.In the end,the paper also gives an example in which the model is used.

关 键 词：股本权证 稀释效应 B-S定价模型 分数布朗运动 

分 类 号：F830[经济管理—金融学]