General Quadratic Term Structures for Bond, Futures, and Forward Prices

Abstract

For finite dimensional factor models, the paper studies general quadratic term structures. These term structures include as special cases the ane term structures and the Gaussian quadratic term structures, previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sucient conditions for the existence of these general quadratic term structures for bond, futures and forward prices. As forward prices are martingales under the T-forward measure, their term structure equation depends on properties of bond prices’ term structure. We exploit the connection with the bond prices term structure and show that even in quadratic short rate settings we can have ane term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in a study of forward prices and show that the dierence between the two prices have to do with the correlation between bond prices and the price process of the underlying to the forward contract and this dierence may be deterministic in some (non-trivial) stochastic interest rate settings.