Semi-parametric financial risk forecasting incorporating multiple realized measures

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the quantile regression using multiple realized measures as exogenous variables to model the VaR. Then, the information from realized measures is used to model the time-varying relationship between VaR and ES. Finally, a measurement equation that models the contemporaneous dependence between the quantile and realized measures is used to complete the model. A quasi-likelihood, built on the asymmetric Laplace distribution, enables the Bayesian inference for the proposed model. An adaptive Markov Chain Monte Carlo method is used for the model estimation. The empirical section evaluates the performance of the proposed framework with six stock markets from January 2000 to June 2022, covering the period of COVID-19. Three realized measures, including 5-minute realized variance, bi-power variation, and realized kernel, are incorporated and evaluated in the proposed framework. One-step ahead VaR and ES forecasting results of the proposed model are compared to a range of parametric and semi-parametric models, lending support to the effectiveness of the proposed framework.