Multivariate volatility models are widely used in Finance to capture both volatility
clustering and contemporaneous correlation of asset return vectors. Here we focus on
multivariate GARCH models. In this common model class it is assumed that the covariance
of the error distribution follows a time dependent process conditional on information
which is generated by the history of the process. To provide a particular example, we
consider a system of exchange rates of two currencies measured against the US Dollar
(USD), namely the Deutsche Mark (DEM) and the British Pound Sterling (GBP). For this
process we compare the dynamic properties of the bivariate model with univariate GARCH
specifications where cross sectional dependencies are ignored. Moreover, we illustrate
the scope of the bivariate model by ex-ante forecasts of bivariate exchange rate
densities.