Many previous studies provide pricing models of options on futures spreads. However, none of them fully reflect the economic reality that spreads can stay near full carry for long periods of time. We suggest a new option pricing model that assumes that convenience yield follows arithmetic Brownian motion and is truncated at zero. An analytical solution of the new pricing model is obtained. We empirically test the new model by testing the truth of its assumptions. We determine the distribution of calendar spreads and convenience yield for Chicago Board of Trade corn calendar spread options. 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 is a normal distribution truncated at zero is only approximate as the volatility of convenience yield never goes to zero and spreads tend to approach full carry, but rarely reach full carry.