中国股票市场收益率分布实证研究

发布时间：2018-01-03 11:21

本文关键词：中国股票市场收益率分布实证研究　出处：《兰州商学院》2013年硕士论文　论文类型：学位论文

【摘要】：在研究股票价格的波动性时，通常假设股票收益率服从正态分布，基于股票价格的金融衍生工具的价格波动研究通常也以这一假设为基础。但是许多学者通过实证研究发现，正态分布并不能很好地描述股票价格的波动性，进而提出了一些其它分布。本文利用在相关文献中经常使用的八种分布，搜集了660个不同类别、不同时间跨度的股票收盘价，对收益率序列进行拟合并检验，用统计结果比较出何种分布适合用来刻画我国股票市场的收益率。首先，本文参考了前人的研究工作，总结出了研究股票收益率主要涉及的分布，它们包括正态分布、稳定分布、拉普拉斯分布、混合高斯分布、韦伯分布、非对称拉普拉斯分布、混合Gumbel分布、偏t分布，并对一些分布作简要介绍。接着，介绍了一些分布的参数估计方法。正态分布、拉普拉斯分布、韦伯分布和非对称拉普拉斯分布的参数估计使用了极大似然估计，在使用极大似然估计方法时，除了正态分布可以通过求一阶偏导数直接求解外，其它四种分布都是利用Matlab程序求对数似然函数的最值来求解；稳定分布和偏t分布的参数估计使用了matlab程序的函数包；混合高斯分布和混合Gumbel分布的参数估计则使用了EM算法。最后，，选取我国股票市场不同类别的股票，并对它们的五分钟、一小时、一天、一周、一月的收益率数据作这八种分布的参数估计，再用Kolmogorov-Smirnov检验对八种分布函数的估计结果进行检验。结果表明，无论从股票类别还是时间跨度方面考查，稳定分布都是合适的。
[Abstract]:In the study of the volatility of stock price, stock returns are usually assumed to obey normal distribution, based on the price fluctuation of stock price of financial derivative instruments are also in this hypothesis. But many scholars through empirical study found that the normal distribution can not describe the volatility of stock price, and then put forward some other distributions.
Based on the eight distributions which are often used in related literature, we collect 660 stock prices with different categories and time span, and test the yield series. We use the statistical results to compare which distribution is suitable for charactering the yield of China's stock market.
First of all, this article made reference to previous research work, summed up the distribution of stock returns mainly involved, they include normal distribution, stable distribution, Laplasse distribution, mixed Gauss distribution, Webb distribution, non symmetric Laplasse distribution, mixed Gumbel distribution, skewed t distribution, and gives a brief introduction to some distribution.
Then, this paper introduced the method of parameter estimation of some distribution. The normal distribution, Laplasse distribution, Webb distribution and non symmetric Laplasse distribution parameters are estimated using the maximum likelihood estimation, using maximum likelihood estimation method, in addition to the normal distribution can be obtained by directly solving the first-order partial derivative, the other four kinds of distribution are the most the value for the log likelihood function using the Matlab procedure to solve the partial; stable distribution and parameter estimation of t distribution function using the matlab program package; parameters of mixed Gauss distribution and mixed Gumbel distribution is estimated using the EM algorithm.
Finally, from China stock market in different categories of stocks, and their five minutes, an hour, a day, a week, a month yield data for the eight kinds of distribution parameter estimation and Kolmogorov-Smirnov test to estimate the distributions of eight kinds of test results. The results show that in terms of stock or category the time span test, stable distribution is appropriate.

【学位授予单位】：兰州商学院
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

【参考文献】