Forecasting Risk Measures Using Intraday Data in a Generalized Autoregressive Score (GAS) Framework

A new framework for the joint estimation and forecasting of dynamic Value-at-Risk (VaR) and Expected Shortfall (ES) is proposed by incorporating intraday information into a generalized autoregressive score (GAS) model, introduced by Patton, Ziegel, and Chen (2019) to estimate risk measures in a quantile regression setup. We consider four intraday measures: the realized variance at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized variances. In a forecasting study, the set of newly proposed semiparametric models is applied to 4 international stock market indices: the S&P 500, the Dow Jones Industrial Average, the NIKKEI 225 and the FTSE 100, and is compared with a range of parametric, nonparametric and semiparametric models including historical simulations, GARCH 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 variance measures (especially at 5 minutes frequency), outperform the benchmark models consistently across all indices and various probability levels