Bayesian Modeling Method Research On Stochastic Volatility Model Based On Mixed Beta Distribution

It is an important part in econometric modeling to determinate the variable distribution, because from the estimation to test, it is all based on the distribution. We usually assume the return rate to a normal distribution when studying the volatility of stock market, but in fact normal distribution can not portray the characteristics of peak thick tail, negative bias, so, to find a more appropriate distribution for return rate and model volatility suitable will contribute to econometric analysis method, and help securities investors correctly measure the market risk and make right investment strategy, also help the securities industry regulatory body accurately grasp of market dynamics and scientific set regulatory measures protecting the securities of stock market.In this paper, combined with the characteristics of return on assets and China’s securities market trading system of price limits, a new point of the distribution of China’s stock market return is proposed that it should be within the limited range, at the same time learned the technology of the mixed normal distribution, we construct mixed beta distribution to fit the Shanghai A-share composite index simple rate of return. Practice has proved that the mixed beta distribution depicts the distribution characteristics of peak, fat tail, the negative bias better.In order to study the Shanghai A-share composite index fluctuations of the simple rate of return, a kind of stochastic volatility (SV) model was made based on mixed beta distribution, the Bayesian analysis method also was given in this paper. First, we discussed the model structure of the SV model, then derived the likelihood function of the model and the posterior conditional distribution of each unknown parameters, and gave the GIBBS sampling program, ultimately we estimated the S V model based on mixed beta distribution using the professional GIBBS sampling tool WINBUGS.Empirical study indicates that mixed beta distribution stochastic volatility model (SV-M), accurately fit the sample data of true generation process, and characterize the yield peak, fat tail, and negative bias better. Compared with the stochastic volatility model based on normal distribution (SV-N), we believe that the SV-N model underestimated the average level of volatility of the stock market and overestimate the persistence of fluctuations.