收益率基于AEPD分布的股票价格模型及其欧式期权定价  

The Pricing Model of Stock and Its European Option Based on the AEPD Distribution

作　　者：武康平[1] 田昕明 李柳玲[2] 

机构地区：[1]清华大学经济管理学院经济系,北京100084 [2]南开大学经济学院经济系,天津300071

出　　处：《数理统计与管理》2016年第3期560-570,共11页Journal of Applied Statistics and Management

摘　　要：AEPD分布函数是最近几年新提出的一种分布函数,通过设定不同的参数值来控制分布的偏度和左右厚尾性,进而更精准的捕捉数据的分布特征,本文在已有的模拟股票价格运动的levy过程的基础上,通过引入AEPD分布,使模型不仅可以模拟股票收益率的尖峰厚尾性,同时可以更精确的描述股票收益率的偏度和不对称性,通过建立随机项符合AEPD分布的Levy过程,我们得出新的股票价格模型(AEPD股价模型,以下简称AEPD股价模型,原模型),我们使用2000-2013年的Wind行业指数,分别利用AEPD股价模型与原模型进行了参数估计,结果表明:第一:AEPD股价模型的残差结果与真实残差更吻合,显示出明显的尖锋肥尾性质,第二,两种模型下隐含的无风险利率与波动率显著不同。进而,我们利用AEPD股价模型在风险中性假设下计算其"欧式期权"的理论价格。The derivatives pricing has been a hot frontier of contemporary financial research, AEPD is a new distribution that publiced two years ago. The researchers who adapt the distribution in practice can alter the value of its parameters and in this way they can control the skewness and heavy tail character of the distribution. On basis of the levy process proposed early, this paper adapt the AEPD distribution in derivatives pricing. Then the model can perform the skewness of the stocks＇ return rate more exactly besides the kurtosis and heavy tails characters of that. By constructing the levy process on AEPD, we get a new pricing model and calculate the theoretical solution with monte carlo method, while we comparing the solution with the Black-Scholes fornmla results. We find that the results under different parameters value vary quite a lot and show out the characters of skewness and heavy tails.

关 键 词：AEPD分布 LEVY过程 Black—Scholes模型 蒙特卡洛方法 

分 类 号：F830.91[经济管理—金融学] O212[理学—概率论与数理统计]