A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain...

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...

In this paper we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, Q, consists of two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest...

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...

For finite dimensional factor models, the paper studies general quadratic term structures. These term structures include as special cases the affine term structures and the Gaussian quadratic term structures, previously studied in the literature. We show, however, that there are other,...

In this paper, which is a substantial extension of the earlier essay Björk (2001), we give an overview of some recent work on the geometric properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a...

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 )...

We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization...

The purpose of this essay is to give an overview of some recent workconcerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a given forward rate model consistent with a given family...

We will investigate valuation of derivatives with payoff defined as a nonlinear though close to linear function of tradable underlying assets. Derivatives involving Libor or swap rates in arrears, i.e. rates paid in a wrong time, are a typical example. It is generally tempting to replace the...