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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,不同模型下的期权价格存在显著的差异
AEPD distribution function is a newly proposed distribution function in recent years. By setting different parameter values to control the skewness of the distribution and left and right thick-tail, so as to capture more accurately the distribution characteristics of the data. In the existing simulation Based on the levy process of stock price movement, by introducing AEPD distribution, the model can not only simulate the peak-tail-tail of stock returns, but also describe the skewness and asymmetry of stock returns more accurately. By establishing random items According to the AEPD-based Levy process, we obtain a new stock price model (AEPD stock price model, hereinafter referred to AEPD stock price model, the original model), we use the Wind industry index from 2000 to 2013, respectively, using the AEPD stock price model and the original model The results show that: First, the residuals of the AEPD stock price model are in good agreement with the real residuals, showing obvious peaked and fat tail properties. Second, the implied risk-free interest rates and volatility under the two models obvious difference. Furthermore, we use the AEPD stock price model to calculate the theoretical price of its “European options” under a risk-neutral assumption. There is a significant difference in option prices under different models