This paper first briefly reviews the evolvement of univariate ARCH class models , and introduces several multivariate GARCH class models. Considering the shortage of traditional estimation methods for multivariate GARCH based on gradient information , we give out the likelihood estimating method based on genetic algorithm. Fi2 nally , the paper presents the demonstration of Chinese stock markets : Both Shanghai and Shenzhen stock markets show volatility persistence in variance. When combined together , the two markets show obvious bivariate GARCH effect , and there is no common persistence in Shanghai and Shenzhen stock markets.