A Geometric View of Interest Rate Theory

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.

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Year of publication:	2000-12-20
Authors:	Björk, Tomas
Institutions:	Economics Institute for Research (SIR), Handelshögskolan i Stockholm
Subject:	interest rates \| Markovian realizations \| forward rates \| invariant manifold

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Extent:	application/pdf
Series:	SSE/EFI Working Paper Series in Economics and Finance.
Type of publication:	Book / Working Paper
Language:	English
Notes:	To appear in "Handbook of Mathematical Finance". Cambridge University Press Published in Option pricing, Interest Rates and Risk Management, Jouini, Elyes, Cvitanic, Jaksa, Musiela, Marek (eds.), 2001, chapter 7, pages 241-277, Cambridge University Press. The text is part of a series SSE/EFI Working Paper Series in Economics and Finance Number 419 39 pages
Classification:	E43 - Determination of Interest Rates; Term Structure Interest Rates ; G13 - Contingent Pricing; Futures Pricing
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005649234