This paper investigates optimal futures hedge ratios in stock markets. We use univariate skewed t stochastic volatility (SV) models to capture the time-varying (TV) volatility of our data and set up Markov-switching (MS) copula models to derive the dynamic dependence structure. According to the variance minimization method, we obtain optimal hedge ratios for the CSI 300 Index spot and futures in China’s stock market. We examine the hedging performance of various models and compare their effectiveness with the most common dynamic copula hedging models, including Patton’s TV copula and Engle’s dynamic conditional correlation (DCC) copula models. The empirical results show that the proposed MS dynamic copula models derive better hedging effectiveness than the corresponding dynamic copula models. The hedge ratios constructed by the MS time-varying (MSTV) Gaussian copula model demonstrate the best performance in terms of variance reduction.