Consistent Variance Curve Models

We introduce equity forward variance term-structure market models and derive HJM-type arbitrage conditions. We then discuss finite-dimensional Markovian representations of the infinite-dimensional fixed time-to-maturity forward variance swap curve and analyse examples of such Variance Curve Functionals. We extend these results to newly introduced "Entropy Swaps", which can be used to aid the calibration of such models. As an application, the results are then applied to show that if Heston's model is recalibrated on a daily basis, mean-reversion and the product correlation and volofvol must be kept constant to avoid dynamic arbitrage.