A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework

Abstract: A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES. The measurement equation models the contemporaneous dependence between the realized measure (i.e., Realized Variance and Realized Range) and the latent conditional ES. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, the properties of which are assessed and compared with maximum likelihood through a simulation study. In a comprehensive forecasting study on 1% and 2.5 % quantile levels, the proposed models are compared to a range of parametric, non-parametric and semi-parametric models, based on 7 market indices and 7 individual assets. One-day-ahead VaR and ES forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.