S-WoPEc
 
Scandinavian Working Papers in Economics
HomeAboutSeriesSubject/JEL codesAdvanced Search
The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 545:
On the Geometry of Interest Rate Models

Tomas Björk ()

Abstract: 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.

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 Markovian finite dimensional state space model.

We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framework 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. We also study stochastic volatility HJM models, and we provide a systematic method for the construction of concrete realizations.

Keywords: Forward rate curves; interest rate models; factor models; state space models; Markovian realizations; (follow links to similar papers)

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

87 pages, November 24, 2003

To apppear in "Springer Lecture Notes in Mathematics"

Before downloading any of the electronic versions below you should read our statement on copyright.
Download GhostScript for viewing Postscript files and the Acrobat Reader for viewing and printing pdf files.

Full text versions of the paper:

hastef0545.pdf    PDF-file (498kB) 
Download Statistics

Questions (including download problems) about the papers in this series should be directed to Helena Lundin ()
Report other problems with accessing this service to Sune Karlsson () or Helena Lundin ().

Programing by
Design by Joachim Ekebom

Handle: RePEc:hhs:hastef:0545 This page was generated on 2014-12-14 19:23:05