Before revision:  We illustrate the distribution of this correlation in an example  .
After revision:  We illustrate the distribution of this correlation in an example . We then propose analytical expressions to obtain the copula and copula density directly from the joint characteristic function of a pair of futures. These expressions are convenient to analyze the term-structure of dependence between the two futures produced by the model. In an empirical application, we calibrate the proposed model to volatility surfaces of vanilla options on WTI and provide evidence that the model is able to produce the desired stylized facts in terms of volatility and dependence. In the two appendices, we give proofs of our main results and guidance for the implementation of the proposed model and the Fourier inversion results by means of one- and two-dimensional FFT methods .