Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails∗

We propose a new model for dynamic volatilities and correlations of skewed and heavytailed data. Our model endows the Generalized Hyperbolic distribution with time-varying parameters driven by the score of the observation density function. The key novelty in our approach is the fact that the skewed and fat-tailed shape of the distribution directly affects the dynamic behavior of the time-varying parameters. This distinguishes our approach from familiar alternatives such as the generalized autoregressive conditional heteroskedasticity model and the dynamic conditional correlation model where distributional assumptions affect the likelihood but not the parameter dynamics. We present a modified expectation-maximization algorithm to estimate the model. Simulated and empirical evidence shows that the model outperforms its close competitors if skewness and kurtosis are relevant features of the data.