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. <p> 1. When is a...</p>

We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures privce curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a...

Within the framework of transitive sufficient processes we investigate identifiability properties of unknown parameters. In particular we consider unbiased parameter estimators, which are shown to be closely connected to time reversal and to reverse martingales. One of the main results is that,...

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...

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. <p> In a recent paper (to appear in "Mathematical Finance"...</p>

In this paper we discuss the significant computational simplification that occurs when option pricing is approached through the change of numeraire technique. The original impetus was a recently published paper (Hoang, Powell, Shi 1999) on endowment options; in the present paper we extend these...

The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are...

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. <p> <p> 1. When is a given forward rate model consistent with a given...</p></p>

We derive general necessary and sufficient conditions for the mutual consistency of a given parametrized family of forward rate curves and the dynamics of a given interest rate model. Consistency in this context means that the interest rate model will produce forward rate curves belonging to the...