This study examines the volatility dynamics of the Greater China stock markets by employing a multivariate framework that incorporates the features of asymmetries, persistence and time-varying correlations. The multivariate framework with these features will contribute to a better understanding of the interdependence and integration among the stock markets in the Greater China region. Our results confirm the existence of volatility persistence and asymmetries, and there is some evidence of a common degree of persistence (‘co-persistence’) among the markets. It is also found that the Mainland Chinese markets are actually less volatile than the Taiwan and Hong Kong stock exchanges in the late 1990s and early 2000s. The Shenzhen and Shanghai stock exchanges are positively (not perfectly) correlated with each other, but they show a weaker correlation with the Hong Kong and Taiwan markets. These findings have important implications for hedging and portfolio management.