A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity 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 generalized autoregressive conditional heteroscedasticity model, this new family of distributions is found to be more useful than its symmetric counterpart for modeling stock returns and especially for forecasting the value-at-risk of portfolios.