Identifying Jumps and Systematic Risk in Futures

A variety of multivariate jump-diffusion models have been suggested as models of asset prices. This paper extends the literature on (joint) mixed jump-diffusion processes in futures markets by using the CRB index futures to represent systematic risk in commodity prices. We derive (joint) mixed bivariate normal distributions and likelihood functions for estimating the parameters of jump-diffusion processes. Likelihood ratio tests are used to select among nested models. The empirical results show the presence of downside jumps and significant systematic risk in wheat futures returns. Amin and Ng’s (1993) model with a single counter of jumps fits better than other jump-diffusion processes considered. The jump components did not have significantly more systematic risk than the continuous component. In terms of wheat prices, one standard deviation jumps are 14 cents per bushel and two standard deviation jumps are 29 cents per bushel and are within the price limits. These jumps occur once in every six business days and are mostly crashes.