Density and Risk Prediction with Non-Gaussian COMFORT Models

Abstract

The CCC-GARCH model, and its dynamic correlation extensions, form the most important model class for multivariate asset returns. For multivariate density and portfolio risk forecasting, a drawback of these models is the underlying assumption of Gaussianity. This paper considers the so-called COMFORT model class, which is the CCC-GARCH model but endowed with multivariate generalized hyperbolic innovations. The novelty of the model is that parameter estimation is conducted by joint maximum likelihood, of all model parameters, using an EM algorithm, and so is feasible for hundreds of assets. This paper demonstrates that (i) the new model is blatantly superior to its Gaussian counterpart in terms of forecasting ability, and (ii) also outperforms ad-hoc three step procedures common in the literature to augment the CCC and DCC models with a fat-tailed distribution. An extensive empirical study confirms the COMFORT model’s superiority in terms of multivariate density and Value-at-Risk forecasting.