Stochastic Volatility Models Of Stock Market Based On T Distribution

In the securities market,the rate of return and volatility are two important basic variables in the theory and practice of financial assets research.In recent years,China's stock market volatility is relatively large,in 2016,A-shares successfully joined the MSCI,marking China's stock market to further docking the international standards.This paper analyzes the characteristics of A-shares index and Hong Kong's HangSeng Index.According to their characteristic distribution,three stochastic volatility models are used to fit them.In this process,MCMC method is used to estimate the parameters of these models,and then empirical comparison is made from different stock markets and different models.This article first introduces the development process of financial volatility model,research status quo and MCMC method and Bayesian theory of model parameter estimation,and then KS test,kurtosis test and so on to the stock market rate of return,illustrates the A share index and the Hong Kong Hang Seng Index earnings Rate has a peak thick tail.According to these characteristics,based on the standard stochastic volatility model,we extend it to make the error term of yield series follow the t distribution to get SV-T model.When risk and benefit coexist,risk compensation is considered and t distribution is based on SV-MT model;considering the "leverage effect" of the stock market and based on the t distribution,the SV-leverage-T model is obtained;secondly,the Gibbs algorithm and the MH algorithm in MCMC are used to calculate the parameters of the model in WinBUGS software;Get the DIC value of each model to choose the best model.After a comparative analysis,we can see that the fluctuation of Hong Kong stocks is generally more violent than that of A shares.These three models well depict the volatility aggregation of the two stock markets.The fluctuation of A shares is generally higher than that of Hong Kong stocks,That is,the stock market in Hong Kong is mature and the system is more perfect than the A-share market.The peak and tail-end properties of Hong Kong stocks are stronger than the A-shares.The Hong Kong's Hang Seng Index is more leveraged than the A-shares.According to DIC,SV-leverage-T model based on t distribution with "leverage effect" is the best model for A-share market and Hong Kong stock market.