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...

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 is allowed to be an arbitrary smooth functional of the present forward rate curve. Using ideas from differential geometry as well as...

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing 2 asymptotic assets" which correspond to certain infinitely well diversified portfolios we study absence of...

In this paper we discuss the pricing of commercial real estate index linked swaps (CREILS). This particular pricing problem has been studied by Buttimer et al. (1997) in a previous paper. <p> We show that their results are only approximately correct and that the true theoretical price of the swap...</p>

The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. <p> In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the...</p>

We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the input-output map...

In some recent papers, such as Elliott & van der Hoek, Hu & Öksendal, a fractional Black-Scholes model have been proposed as an improvement of the classical Black-Scholes model. Common to these fractional Black-Scholes models, is that the driving Brownian motion is replaced by a fractional...

This set of lecture notes constitutes a self contained overview of the martingale based theory of interest rates. The lectures were given by the author at the 1996 CIME Summer School on Mathematical Finance, in Bressanone, Italy. The topics covered include: Bond markets, interest rates,...