On the term structure of forwards, futures and interest rates

by Landén, Camilla

This thesis consists of four papers which all treat term structures, either of forwards and futures or of interest rates. In the rst paper we consider a di usion type model for the short rate, where the the drift and di usion coe cients are modulated by an underlying Markov process. The main objective ofthepaperistostudy how bond pricing can be carried out in this framework, both when the underlying Markov process is observable and when it is not. In the second paper weinvestigate when a model of the Heath-Jarrow- Morton-type (HJM) for the futures prices generically implies a Markovian spot price, that is when no matter which initial term structure is used for the futures prices, the spot price implied by the futures prices always satis es a stochastic di erential equation. In the third paper we investigate the term structure of forward and futures prices for models in which the price processes are assumed to be driven by amulti-dimensional Wiener process and a general marked point process. For an in nite dimensional model of HJM-type of the futures and forward prices we study properties of the futures and forward convenience yield. We also study a ne term structures, general pricing of futures options, and the problem of tting a nite dimensional factor model to an observed initial futures price curve. In the fourth paper we consider interest rate models of the HJM-type, where the forward rates are driven byamulti-dimensional Wiener process and the volatility is a smooth functional of the presentforwardratecurve. Building on earlier results in the eld, concerning when such a model can be realized by a nite dimensional Markovian state space model, we present a general method to actually construct such a realization.