A comparison between several correlated stochastic volatility models

We compare the most common stochastic volatility models such as the Ornstein–Uhlenbeck (OU), the Heston and the exponential OU models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on market indices confirming the universality of the leverage and volatility correlations.