A New Class of Multivariate Skew Densities, with Application to GARCH Models

We propose a practical and flexible method to introduce skewness in multivariate symmetric distributions. Applying this procedure to the multivariate Student density leads to a multivariate skew-Student density, in which each marginal has a specific asymmetry coefficient. Combined with a multivariate GARCH model, this new family of distributions is found to be more useful than its symmetric counterpart for modelling stock returns and especially forecasting the Value-at-Risk of portfolios