Pricing Crude Oil Options Using Lévy Processes

Crude oil prices exhibit significant volatility over time. The distribution of returns on crude oil prices shows fat tails and skewness that barely follow a normal distribution. For this reason, we use the normal Gaussian process, jump diffusion process and variance gamma process as three Levy processes that do not have these drawbacks. Their tails also carry a heavier mass than in a normal distribution. We employ the fractional fast Fourier transform to calibrate parameters in an optimization setup, using data about European-style options on crude oil futures in the New York Mercantile Exchange for a settlement date of April 24, 2015. Our results indicate that these three Levy processes have very good out-of-sample results for near at-the-money options compared with others.