Estimating multi-period Value at Risk of oil futures prices

In this study, we estimate the multi-period Value at Risk (VaR) of oil future prices under a generalized autoregressive conditional heteroscedasticity with a skewed-t residuals (GARCH-ST) model, which is developed to account for the stylized facts of oil futures returns, such as serial correlation, volatility clustering, asymmetry and heavy tails. An efficient approximation algorithm based on the moment calibration method is developed to compute the multi-period VaR, and the numerical experiments show that the algorithm can yield good approximation quality. In the empirical analysis, we find that the GARCH-ST model can yield superior out-of-sample performance to a GARCH-normal model or a GARCH-t model, especially when measuring the extreme tail risk. Meanwhile, the square root of time rule (SRTR) tends to underestimate the multi-period tail risk, and cannot produce a better performance than the GARCH family models.