This paper studies the association and the model construction of the U.S., the Japan, and Hong Kong stock markets. In this paper we will use the heavy-tailed Student’s t distribution to analyze the proposed model, then construct a trivariate asymmetric GARCH (1, 2) model to evaluate the association and there exists an asymmetrical effect among the three stock markets. The result of empirical analyses also shows that U.S. stock market returns positively affect the Japan and Hong Kong stock market returns, and the volatility of the three stock market returns interact with one another. Furthermore, U.S stock market returns of one day before affect the stock markets of the Japan and Hong Kong. The empirical result also discovers that the U.S., Japan, and Hong Kong stock price market return volatilities have an asymmetrical phenomenon in the sample period.