A semi-parametric conditional autoregressive joint value-at-risk and expected shortfall modeling framework incorporating realized measures

A class of realized semi-parametric conditional autoregressive joint Value-at-Risk (VaR) and Expected Shortfall (ES) models is proposed. This class includes novel specifications that allow separate dynamics for VaR and ES, driven by realized measures of volatility. A measurement equation is included in the model class for risk modeling, meaning it generalizes the parametric Realized-GARCH model into the semi-parametric realm. The proposed models implicitly allow the conditional return distribution to change over time via the relationship between VaR and ES. Employing a quasi-likelihood built on the asymmetric Laplace distribution, a Bayesian Markov Chain Monte Carlo method is used for model estimation, whose finite sample properties are assessed via simulation. In a forecasting study applied to 7 indices and 7 assets, one-day-ahead 1% and 2.5% VaR and ES forecasting results support the proposed model class.