The opening of capital markets, foreign market information is actively using in the internationalization of stock trading, so that movement of a national in the stock market is no longer done independently and in conjunction with the movement of the external market. If the volatility of asset prices has been expanded in the world, expansion of stock market volatility in a country to be transferred to other countries or other regions, and not only rate of return, but also correlation of volatility between the stock market have increased. This study is to determine the existence of the correlation of volatility between stock markets of US, China and UK, and how to change the correlation between three stock markets before and after the subprime mortgage crisis and to determine the difference of the correlation between the Financial markets. For empirical analysis, we employ Diagonal-VECH model, which would react correlation of several financial time series. The results show that by the appearance of the volatility correlation between US, China and UK's stock market, we can know that there is a high correlation in the developed stock markets than in emerging stock markets.