基于EM估计的正态逆高斯分布下中国股票收益率分布研究

发布时间：2018-01-16 04:22

本文关键词：基于EM估计的正态逆高斯分布下中国股票收益率分布研究　出处：《南京大学》2014年硕士论文　论文类型：学位论文

【摘要】：传统意义上,我们习惯用正态分布来描述金融资产收益率的分布,很多金融模型都是建立在收益率服从正态分布的假设基础之上。但是越来越多的学者通过经验数据发现金融数据并非服从正态分布,我国学者吴世龙在1999年以深圳股票综合指数为样本,验证了中国证券市场的投资收益率属于非正态分布。这是因为金融数据往往具有尖峰、厚尾、偏态等特征,已经无法用传统的正态分布来进行准确刻画。而国外学者研究发现国外金融资产的收益率更符合广义双曲线分布,针对本国的实际情况,本文力图通过历史数据验证我国的股票市场的收益率符合该广义双曲线分布下的一个子类——正态逆高斯分布,并通过Monte Carlo模拟法验证中国的股票收益率确实符合正态逆高斯分布,而且进一步从VaR角度对这一拟合进行了分析,从而得出这种拟合的合理性。由于正态逆高斯分布参数估计的复杂性,本文在借鉴国外学者观点的基础上,采用EM算法对正态逆高斯分布进行参数估计,并给出正态逆高斯分布参数估计的详细过程和实现步骤。
[Abstract]:In the traditional sense, we are used to describe the distribution of return on financial assets by normal distribution. Many financial models are based on the hypothesis of normal distribution of yield, but more and more scholars find that financial data is not from normal distribution through empirical data. In 1999, Wu Shilong, a Chinese scholar, took Shenzhen stock composite index as a sample to verify that the return on investment in China's securities market belongs to a non-normal distribution. This is because financial data tend to have sharp peaks and thick tails. Skewness and other characteristics can not be accurately characterized by the traditional normal distribution. Foreign scholars found that the return rate of foreign financial assets is more in line with the generalized hyperbolic distribution in accordance with the actual situation in our country. This paper tries to verify that the return rate of stock market in China accords with a subclass-normal inverse Gao Si distribution under the generalized hyperbolic distribution. And through the Monte Carlo simulation method to verify that the Chinese stock returns really accord with the normal inverse Gao Si distribution, and further from the point of view of VaR, this fitting is analyzed. Because of the complexity of parameter estimation of normal inverse Gao Si distribution, this paper uses EM algorithm to estimate the parameter of normal inverse Gao Si distribution on the basis of reference from foreign scholars. The detailed process and implementation steps of normal inverse Gao Si distribution parameter estimation are also given.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224

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