Modeling the crude oil volatility : Garch & EVT

Abstract

Purpose: This study has two main purposes. First, Assess and compare the predictive ability of the Exponentially Weighted Moving Average EWMA, the Generalized Autoregressive Conditional Heteroscedasticity EGARCH (1, 1), the Exponential Generalized Autoregressive Conditional Heteroscedasticity EGARCH (1, 1), and the Glosten, Jagannathan, and Runkle Generalized Autoregressive Conditional heteroscedasticity GJR-GARCH. Second, Value at Risk is calculated using the Historical Simulation approach and the Extreme Value Theory. Methodology, Design and Approach: The models’ parameters are estimated from the in sample Crude Oil futures returns by maximizing the likelihood function. In sample volatilities are updated using the estimated parameters and the realized returns. Out of sample volatilities are forecasted using the same parameters. Both in and out of sample volatilities are compared to the realized volatilities and the models are ranked in both contexts separately. The winning model is then used to update the volatilities used in the Historical Simulation approach to calculate Value at Risk for the whole out of sample period. The Extreme Value Theory approach is performed to calculate Value at Risk at a very high confidence level. Findings: Error statistics shows the superiority of the symmetrical GARCH (1, 1) model. Value at Risk calculated using the Historical Simulation approach results in accepted number of exceptions according to the Kupiec test. The Value at Risk calculated using the Extreme Value Theory is relatively high. Research limitations: The sample used in this paper is very large and it could be divided into many subsamples to increase the accuracy of the parameters. The Extreme Value Theory could be performed for the whole out of sample period. Practical Implications: An exact calculation of VaR for Crude Oil Futures allow taking advantage of assessing the risk of this important commodity as a trading tool for hedging and for speculation. Value: This paper is the first that attempts to calculate Value at risk for Crude Oil Futures using the Extreme Value Theory.