Hedging crude oil derivatives in GARCH-type models

We investigate the empirical performance of hedging strategies based on Greeks, such as Delta and Delta-Gamma, for (European-style) crude oil options in a generalized autoregressive conditional heteroscedasticity (GARCH) model environment. Particular attention is paid to studying the impacts of the conditional heteroscedasticity and the conditional nonnormality of the GARCH innovations on the option prices and the performance of these hedging strategies. To examine the empirical performance of the hedging strategies, we evaluate the value-at-risk and the expected shortfall of the terminal values of the hedging portfolios using the New York Mercantile Exchange (West Texas Intermediate) data for the period 1991-2011. Our hedging results show that GARCH with shifted gamma innovations systematically outperforms the benchmark models, namely, GARCH with normal innovations and the Black-Scholes-Merton model, in capturing tail risk across maturities and strikes for the different hedging frequencies.