Scandinavian Working Papers in Economics
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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 419:
A Geometric View of Interest Rate Theory

Tomas Björk ()

Abstract: 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 of forward rate curves?

2. When can the inherently infinite dimensional forward rate process be realized by means of a finite dimensional state space model.

We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multi- dimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framwork we give necessary and sufficient conditions for consistency, as well as for the existence of a finite dimensional realization, in terms of the forward rate volatilities.

Keywords: interest rates; Markovian realizations; forward rates; invariant manifold; (follow links to similar papers)

JEL-Codes: E43; G13; (follow links to similar papers)

39 pages, December 20, 2000, Revised December 21, 2000

To appear in "Handbook of Mathematical Finance". Cambridge University Press

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This paper is published as:
Björk, Tomas, (2001), 'A Geometric View of Interest Rate Theory' in Jouini, Elyes, Jaksa Cvitanic and Marek Musiela (eds.) Option pricing, Interest Rates and Risk Management, Handbooks in Mathematical Finance, chapter 7, pages 241-277, Cambridge University Press, ISBN 0 521 79237 1.

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