Before revision:  We calculate the joint characteristic function of two futures contracts in the model  and use the two-dimensional FFT method of Hurd and Zhou (SIFIN 2010 ) to price calendar spread options.
After revision:  We calculate the joint characteristic function of two futures contracts in the model and use the one-dimensional Fourier inversion method of Caldana and Fusai (JBF 2013 ) to price calendar spread options.