Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 419: A Geometric View of Interest Rate Theory

Tomas Björk ()
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Tomas Björk: Department of Finance, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden

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

JEL-codes: E43; G13

39 pages, First version: December 20, 2000. Revised: December 21, 2000.

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

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