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.
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Fengler, M.R., Herwartz, H. (2009). Multivariate Volatility Models. In: Härdle, W.K., Hautsch, N., Overbeck, L. (eds) Applied Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69179-2_15
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