Estimation of Value at Risk of Oil Prices Using Normal, Stable, and Generalized Hyperbolic Distributions

Abstract

This study applies the variance-covariance technique to estimate the Value at Risk (VaR) of OPEC crude oil prices. To capture the variability, heavy tails, and uncertainty in the dataset, three distributions were utilized within an ARIMA-GARCH framework: Normal, α -Stable, and Generalized Hyperbolic Distribution (GHD). The efficacy of the estimated VaR was evaluated using Kupiec test, Christoffersen test, and Lopez’s loss function. At 95% confidence level: ARIMA-GARCH-Normal and Monte Carlo Simulation produced more precise VaR estimates according to the Kupiec test, while only ARIMA-GARCH-Normal produced accurate estimates according to the Christoffersen test. Based on Lopez’s loss function, the ranking from best to worst is: Normal, Monte Carlo, Stable, GHD, Historical Simulation. At 99% confidence level: ARIMA-GARCH-Normal, ARIMA-GARCH-Stable, and ARIMA-GARCH-GHD are statistically accurate under both the Kupiec and Christoffersen tests. Based on Lopez’s loss function, the ranking from best to worst is: Stable, Normal, GHD, Monte Carlo, Historical Simulation. The findings indicate that ARIMA-GARCH-Normal is the most consistently accurate model across confidence levels. It is recommended that risk analysts adopt Normal and Stable distributions within an ARIMA-GARCH framework for estimating VaR of OPEC oil prices, as these distributions provide the most accurate and stable estimations across the backtesting criteria.