Forecasting Conditional VaR of the Crude Oil Market Using GARCH-Type Models with Time-Varying High-Order Moments

Accurately modeling the distribution of the crude oil market is crucial in forecasting downside risk. In this paper, the flexible skewed generalized t (SGT) distribution is used to model the distribution of WTI and Brent crude oil market returns. The estimates of the unconditional SGT indicate that the empirical distributions of both WTI and Brent crude oil returns can be well fitted by the skewed t (ST) distribution. Furthermore, we relax the conventional GARCH-type models and allow the high-order conditional moments, such as the third and fourth moments, which are related to skewness and kurtosis, to be time-varying. The results show that all the conditional moments in the ST density function are statistically significant. Lastly, the efficiency of ST-GARCH-type models with time-varying high-order moments is evaluated based on the results from both in-sample and out-of-sample conditional value at risk (VaR) forecasting. We find that the proposed model generates superior estimates compared with the real VaR thresholds. These results have both theoretical and practical implications for financial institutions in formulating crude oil market risk management strategies and avoiding potential losses due to extreme risks in the crude oil market.