Reducing the Risk in Tail Risk Forecasting Models

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, a new additive-type model is developed for the ES component that is robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.