Jump Processes in Commodity Futures Prices and Options Pricing

Empirical evidence shows that log-return relatives on commodity futures prices are not normally distributed. This departure from normality seems to be caused by large price changes occurring in the commodity markets with the arrival of important new information. This suggests that a jump-diffusion model may be a plausible choice for modeling the stochastic process underlying commodity option prices. Merton (1976a) develops a jump-diffusion option pricing model assuming that jump risk is unsystematic. However, the jump-diffusion model developed by Bates (1991) is more appropriate for commodity option pricing since it allows jump risk to be systematic. In this article, recent transactions data on futures and futures options are used to test out-of-sample options using American versions of Black's diffusion and Bates's jump-diffusion models. The results show that Bates's model performs considerably better than Black's model. Jump-diffusion Asian option prices are also shown to differ considerably from geometric Brownian motion Asian option prices.