Pricing with finite dimensional dependence

We consider derivative pricing in factor models, where the factor is Markov with Finite Dimensional Dependence (FDD). The FDD condition allows for explicit formulas for derivative prices and their term structure and in this respect is a serious competitor of models with affine dynamic factors. The approach is illustrated by a comparison of the prices of realized and integrated volatility swaps. We show that the usual practice of replacing a payoff written on the realized volatility by the payoff written on the integrated volatility can imply pricing errors which are not negligible when the volatility of the volatility is large.