A Simple Class Of Multivariate GARCH Models And Application

In the article,at first, we reviewed relevant documents about multivariable GARCH model, and introduced a new kind of estimator put forward by Engle recently. Then we analysised the correlation of the main stock index in Chinese market, it was found that conditional correlation can describe accurately a long time moving trend of two variables. Because of the basic homogeneity of Shenzhen and Shanghai stock market, the correlation between them is very strong at some time, but not still very steady, this demonstrated because each market had its own trusteeships and exchange system and had not formed the unified stock market yet, so the company can not issue their stocks at the same time on two market, and the trader can't trade trans-market (hardly having condition and chance of stepping marketing), this didn't control favorablely the market risk. And the correlation of the A-share B-share market of our country is small, but seldom negative relatively. though correlation got weaken in some times, in total trend, the correlation increased steadyly all the time, this is consistent with the development process of B-share market. The correlation of two markets is still unstable, proved that the indentity between them has not been produced yet, so the amalgamation of two market is still early.In financial research, by use of a market model to estimate that a constand beta coefficient has long history, but some increased newly evidences show not only the personal share but also portfolio's beta coefficient changes with time, then we can set up conditional beta series of by the conditional variance information which GARCH model generated. In the past documents, because of unmature multivariable GARCH theory, when studying the correlation between the personal share and market index, people generally adopted Bollerslev's constant correlation model, but some researchers found that the constand correlation assumption can not be supported by the real financial data, so in the article, in order to estimate time varying beta coefficient of several stocks in the Shanghai stock market, we assumed that the sport trend between each stock and market index obeyed a DCC- MVGARCH process, thus gained the comparatively accurate time varying beta coefficient. Finally, we supplied a CAPM formula based on time varying beta coefficient.