Unifying Variance Swap Term Structures, SPX and VIX Derivatives

We propose a term structure function, a two-factor variance process and a return process to jointly price SPX and VIX derivatives. The distinctive feature of the variance model is that the factor coefficients are time-varying and they are bonded with the term structure of variance swaps. The model incorporates additional characteristics that jumps in the return process and in the variance process are more recognizable in short terms, the term structure of variance swaps is versatilely rich to be able to accommodate many desired features, and the leverage effect is stochastic. In the interest of analytical tractability, the two-factor variance process and the return process are structured by affine processes