A semi-parametric dynamic conditional correlation framework for risk forecasting

Résumé : We develop a novel multivariate semi-parametric framework for joint portfolio Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting. Unlike existing univariate semi-parametric approaches, the proposed framework explicitly models the dependence structure among portfolio asset returns through a dynamic conditional correlation (DCC) parameterization. To estimate the model, a two-step procedure based on the minimization of a strictly consistent VaR and ES joint loss function is employed. This procedure allows to simultaneously estimate the DCC parameters and the portfolio risk factors. The performance of the proposed model in risk forecasting on various probability levels is evaluated by means of a forecasting study on the components of the Dow Jones index for an out-of-sample period from December 2016 to September 2021. The empirical results support effectiveness of the proposed framework compared to a variety of existing approaches.