The Empirical Research On Distribution Of Rate Of Returns In Chinese Stock Market

In the study of the volatility of stock price, we usually assumes thatstock returns are normally distributed, The research of financialderivatives’ volatility, which based on stock price, are usually also basedon this hypothesis. But through empirical research, many scholars foundthat normal distribution can’t describe the volatility of stock price well,and put forward some other distributions.This paper used eight kinds of distributions, which is often mentionedin corresponding article, and collected660stock price sequences indifferent categories and different time span, then estimated theirparameters and test the results. This paper try to find out whichdistribution is suitable to depict the stock market rate of returns in Chinawith the statistical results.First of all, this paper summed up mainly related distributions bystudying the previous works, they include Normal distribution, Levystable distribution, Laplace distribution, mixed Gauss distribution,Weibull distribution, asymmetric Laplace distribution, mixed Gumbeldistribution, Skewed student’s T distribution, and introduced them briefly.Then, this paper introduced the method of parameter estimation foreach distribution. Normal distribution, Laplace distribution, mixed Gaussdistribution, Weibull distribution, asymmetric Laplace distribution usedmaximum likelihood estimation, Normal distribution used partialderivative and others used Matlab to compute the max value of thelogarithmic likelihood function. Levy stable distribution and Skewedstudent’s T distribution used matlab function package, mixed Gaussdistribution used EM algorithm.At last, this paper selected different classes of shares in the stock market of our country, and estimated the eight distributions’ parametersfor all shares, each of which include five minutes, an hour, a day, a week,a month closing prices. And test the results with Kolmogorov-Smirnovtest. The results show that, whether from the factor of stock category ortime span, Levy stable distribution is appropriate.