Risk management application of the recurrent mixture density network models

Abstract

We consider the generalization of the classical GARCH model in two directions: the first is to allow for non-linear dependencies in the conditional mean and in the conditional variance and the second concerns specification of the conditional density. As a tool for non-linear ' regression we use neural network-based modeling, so called recurrent mixture density networks, describing conditional mean and variance by multi-layer perceptrons. All of the models are compared for their out-of-sample predictive ability in terms of Value-at-Risk forecast evaluation. The empirical analysis is based on return series of stock indices from different financial markets. The results indicate that for all markets the improvement in the forecast by non-linear models over linear ones is negligible, while non-gaussian models significantly dominate the gaussian models with respect to most evaluation tests. © Springer-Verlag Berlin Heidelberg 2003.