Calendar spread options for storable commodities

Abstract

Previous studies provide pricing models of options on futures spreads. However, none fully reflect the economic reality that spreads can stay near full carry for long periods of time. A new option pricing model is derived that assumes convenience yield follows arithmetic Brownian motion that is truncated at zero. The new models as well as alternative models are tested by testing the truth of their distributional assumptions for calendar spreads and convenience yield with Chicago Board of Trade corn calendar spreads. Panel unit root tests fail to reject the null hypothesis of a unit root and thus support our assumption of arithmetic Brownian motion as opposed to a mean-reverting process as is assumed in much past research. The assumption that convenience yield follows a normal distribution truncated at zero is only approximate as the volatility of convenience yield never goes to zero. Estimated convenience yields can be negative, which is presumably due to measurement error. Option payoffs are estimated with the four different models and the relative performance of models is determined using bias and root mean squared error (RMSE). The new model outperforms three other models and that the other models overestimate actual payoffs. There is no significant difference in error variance for Hinz and Fehr, Poitras, and the new model, and the error variance of the new model is smaller than that of Gibson and Schwartz.