股票收益率非正态性的蒙特卡罗模拟检验

The Test of non-normal Distribution of Stock Returns with Monte Carlo Simulation and The Explanation

现实金融数据的分布通常表现为厚尾性和不对称性,因此用正态分布拟合实际金融数据的分布有很大的局限性.文章利用广义双曲线分布的厚尾性和不对称性对1997年1月2日～2003年9月19日的上证综指日收益率分布分别做了正态分布、广义双曲线分布、正态逆高斯分布和双曲线分布的拟合及蒙特卡罗模拟检验,结果表明广义双曲线分布和正态逆高斯分布可以较好地拟合上证综指日收益率分布.另外,文章还建立了一个带噪声干扰的线性系统,对实际的股票收益率并不服从正态分布,而表现出尖峰厚尾的特征做出了一种可能的解释.

The distribution of financial data is usually fat-tailed and asymmetric, so it is not proper to fit the real tinanclal data by normal distribution. This paper fits the returns of Shanghai Composite using generalized hyperblic distribution and tests its goodness-of-fit. The results of test show that the daily log-return of Shanghai Composite can be well described by generalized hyperbolic distribution and normal inverse Gaussian distribution. The fact of non-normal distribution can be well explained by a simple linear system with noise.