Scaling the Tails: Intraday Quantiles for Forecasting Value-at-Risk and Expected Shortfall

Incorporating realized volatility measures into risk forecasting models can lead to more accurate forecasts. This paper introduces innovative risk forecasting models that replace realized volatility measures with observable risk proxies derived from high-frequency data through the scaling of intraday quantiles. Specifically, we present a flexible approach for Value-at-Risk and Expected Shortfall forecasting by proposing novel scaling factor estimation methods based on consistent loss functions combined with Multiplicative Error Models using the Generalized F distribution. The empirical analysis across 27 Dow Jones Industrial Average stocks reveals that our proposed approach can achieve significant accuracy improvements in tail risk forecasting.