GARCH Model And Its Application On Stock Market

With the rapidly development of the financial market,the domestic financial products have been introduced rapidly,the volume of business about exist products also increased significantly.Regardless of the market index to study,or on a single product,especially derivatives research,accurate analysis of its price fluctuations,is the key to identify risks and promote the healthy operation.Because China financial market started late,and the ratio of foreign mature financial markets,the impact of market volatility in many places have different factors,and thus China domestic stock market volatility's study is particularly important.This article studied the volatility of Shanghai composite index and Shenzhen composite index.Firstly,the two time series that was checked are smooth.The date will skewe left when the coefficient of skewness was negative,Kurtosis coefficient was large that showed the property of the top peak thick tail of the data,so the GARCH model was fitted to the above two sequences.The traditional GARCH model parameter estimation uses the maximum likelihood method,due to the parameters have certain constraints,the model parameters are difficult to be precised,it is difficult to achieve the purpose of optimization.Thus,this paper use the MCMC algorithm to fit ARMA(1,1)-GARCH(1,1)model.The MCMC method is used to avoid the limitation of GARCH model on parameter constraint.And then test the relations of overflow between the Shanghai composite index and the Shenzhen composite index.In order to measure the leverage effect of positive and negative yield,used the Shenzhen composite index as exogenous variables,the Shanghai composite index was fitted the double threshold ARMA-GJR-GARCH Model.Through the analysis found that when the Shenzhen composite index showed the profit is greater than the average,the Shanghai composite index was relativily and strongly influenced the spillover effect of the Shenzhen composite index,and appeared the phenomenon low mean regression.Finally,the low-frequency date of daily profit on the Shanghai Composite Index and the high-frequency data of the 5 minutes simple yield were fitted the Stochastic volatility model,Used the Winbugs software to get the Bayesian estimation parameters,by comparing the low-frequency data and high-frequency data fitting parameters can be found,the high-frequency data of Shanghai composite index obtained more volatility;The sustainability of Shanghai composite index daily return gained volatility impact was strong.