Consistent Variance Curve Models

We introduce equity forward variance term-structure models and derive the respective HJM-type arbitrage conditions. We then discuss finitedimensional Markovian representations of the infinite-dimensional fixed time-to-maturity forward variance swap curve and analyse examples of such variance curve functionals. The results are then applied to show that the speed of mean-reversion in standard stochastic volatility models must be kept constant when the model is recalibrated (a finding similar to Filipovic’s [13] observation for interest-rate models). We also show that some standard implied volatility term-structure functionals can lead to arbitrage when refitted on a regular basis.