Wolfgang Scherrer: Modelling Conditional Variances and Covariances; An Introduction to MGARCH Models

Abstract 

Understanding and predicting the temporal and cross-sectional dependence of variances and covariances is an important issue in financial econometrics. Important areas of application include asset pricing, portfolio selection, hedging, risk management and option pricing. Scalar ARCH-type models are commonly used to model conditional variances. However the generalization of such models to the multivariate case is by no means trivial. In particular many models suffer from the curse of dimensionality, ie. the number of parameters grows very fast with the cross sectional dimension. In this talk we will give a survey on some of the most commonly used model specifications, like the VECH, BEKK, DVECH, FGARCH, CCC and DCC models. Furthermore some structural problems like the relation of VECH and BEKK models and parametrization issues for BEKK models are discussed.