Forecasting the VaR of the crude oil market: A combination of mixed data sampling and extreme value theory

When forecasting the value-at-risk (VaR) of the crude oil market, traditional models often fail to capture the information embedded in low-frequency macro-variables and tend to underestimate the high quantiles caused by adopting commonly used distributions. To address these problems, this paper proposes a new approach, which combines the generalized autoregressive condition heteroskedasticity (GARCH)-mixed data sampling (MIDAS) models with extreme value theory (EVT). Our empirical results show that first, the GARCH-MIDAS models outperform the benchmark models when they incorporate suitable low-frequency macroeconomic variables. Second, the VaR forecasting accuracy of some GARCH-MIDAS models can be further improved when combined with EVT. Third, the EVT-based GARCH-MIDAS model that contains the demand-side information of the oil market achieves the best performance among all the models. Fourth, the historical simulation (HS) method that is widely used by financial institutions is extremely inaccurate.