This paper examines the volatility dynamics of the greater China stock markets (Shanghai A- and B-shares, Shenzhen A- and B-shares, Taiwan, and Hong Kong) by employing a multivariate (tetravariate) framework that incorporates the features of asymmetries, persistence, and time-varying correlations, which are typically observed in stock markets of developed economies. Our results indicate that, unlike the Shenzhen and Shanghai Ashares, Hong Kong and Taiwan markets, the B-share markets do not exhibit significant asymmetric volatility (“leverage effect”), and return volatility in the A-share market is substantially higher than the B-share market before April 1997, but this result is reversed after that. Also, contrary to the stylized fact that ...