A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression setup. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.
This paper develops a generic adjustment framework to improve in the market risk forecasts of diverse risk forecasting models, which indicates the degree to which risk is under‐ and overestimated. In the context of the energy commodity market, a market in which tail risk management is of crucial importance, the empirical analysis shows that after this adjustment framework is applied, the forecasting performance of various risk models generally improves, as verified by a battery of backtesting methods. Additionally, our method also lessens the risk model disagreement among post‐adjusted risk forecasts.
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