We investigate the empirical performance of hedging strategies basedon Greeks, such as Delta and Delta-Gamma, for (European-style)crude oil options in a GARCH model environment. Particular atten-tion is paid to studying the impacts of the conditional heteroscedas-ticity and the conditional non-normality of the GARCH innovationson the option prices and the performance of these hedging strategies.To examine the empirical performance of the hedging strategies, weevaluate the Value at Risk (VaR) and the Expected Shortfall (ES)of the terminal values of the hedging portfolios using the NYMEX(WTI) data for the 1991 - 2011 period. Our hedging results show thatGARCH with shifted gamma innovations systematically outperforms the benchmark models, namely, GARCH with normal innovations andthe Black-Scholes-Merton model, in capturing tail risk across maturi-ties and strikes for the different hedging frequencies.