On the Term Structure of Futures and Forward Prices

We investigate the term structure of forward and futures prices for models where the price processes are allowed to be driven by a general marked point process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is shown to include almost all previously known models. We also derive two general pricing formulas for futures options. Finally we present an easily applicable sufficient condition for the possibility of fitting a finite dimensional futures price model to an arbitrary initial futures price curve, by introducing a time dependent function in the drift term.term structure; futures price; forward price; options; jump-diffusion model; affine term structure

On the construction of finite dimensional realizations for nonlinear forward rate models

We consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve. In a recent paper (to appear in "Mathematical Finance" ) Björk and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR. The method works as follows: From the results of Björk and Svensson we know that there exists an FDR if and only if a certain Lie algebra is finite dimensional. Given a set of generators for this Lie algebra we show how to construct an FDR by solving a finite number of ordinary differential equations in Hilbert space. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore, the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations. We also show how to obtain realizations in terms of benchmarforward rates from the realizations obtained using our method, and finally we present a bond pricing formula for the realizations we have obtained.forward rate; HJM models; term structure; factor models; state space models; Markovian realizations