This paper examines the ability of twelve different continuous-time two-factor models with mean-reverting stochastic volatility to capture the dynamics of the S&P 500 and three European equity indices. The stochastic volatility models are the square root variance, GARCH, and log volatility diffusions, and each is augmented with price and volatility jump extensions. Parameter estimation is by Markov Chain Monte Carlo using daily spot index returns from 1987 to 2010. For each index we find that GARCH diffusions augmented with correlated price and volatility jumps outperform other specifications with respect to all the tests we perform. The European indices have similar dynamics, which are relatively easy to capture using several of our specifications, but the S&P 500 index has different dynamics and here the GARCH-jump specification is very clearly superior.