Measuring Risk for WTI Crude Oil - An application of Value-at-Risk

Abstract: Crude oil is the most traded energy commodity in the world, and its price has a large impact on the everyday life of billions. Given the volatility of crude oil prices and its enormous effects on economies worldwide, there has been a growing demand for risk quantification and risk management for the market participants. The measurement known as Value-at-Risk (VaR) has become the industry standard for internal risk control among firms, financial institutions and regulators. This study will assess which VaR method is most effective to quantify the risk of price changes embedded in the West Texas Intermediate (WTI); used as a benchmark for oil prices in the USA. VaR will be estimated by using both parametric and non-parametric methods that will be backtested with the Christoffersen test. The parametric methods considered in this paper are the GARCH, EGARCH, and TGARCH models, estimated by considering the effects of using normal distribution versus student’s t-distribution or the Generalized Error Distribution (GED). The non-parametric methods used in this paper are Basic Historical Simulation (BHS), Volatility-Weighted Historical Simulation (VWHS), and Age Weighted Historical Simulation (AWHS). This study also tries to answer if the optimal choice of VaR estimation method differs when evaluating WTI Crude Oil prices as opposed to the S&P 500 index. The parametric models had an in-sample of 1000 observations and estimated a one day-ahead VaR estimate over the period 2007-01-01 to 2013-12-31.The model was re-estimated every day in the period to a total of 1826 estimations. The non-parametric models had an in-sample of 1000, and the volatility calculated for VWHS used the RiskMetric approach. For both S&P 500 and WTI the non-parametric methods provided poor VaR estimates. The parametric models provided better results, the GARCH models with leptokurtic distribution was the most effective in capturing price volatility. GARCH(1,1) with GED provided the best result for WTI, while GARCH(2,1) with t-distribution was the more optimal model to capture volatility in the S&P 500 index. Thus, we conclude that different models are needed to accurately capture the risk depending on which benchmark is used.