Interest Rate Dynamics and Consistent Forward Rate Curves

26 Pages Posted: 3 Jun 2004

See all articles by Tomas Bjork

Tomas Bjork

Stockholm School of Economics - Swedish House of Finance

Bent Jesper Christensen

Aarhus University; Aarhus University; Aarhus University

Abstract

We consider, as given, an arbitrage-free interest rate model 'M' and a parametrized family of forward rate curves 'g'. We study the question as to when the given family 'g' is consistent with the dynamics of the interest rate model 'M', in the sense that 'M' actually will produce forward rate curves belonging to 'g'. We allow the interest rate model to be driven by a multidimensional Wiener process, as well as by a marked point process, and we give necessary and sufficient conditions for consistency. As test cases, we study some popular models, obtaining both positive and negative results about consistency. We also introduce a natural exponential-polynomial family of forward rate curves, and for this family we give necessary and sufficient conditions for the existence of consistent interest rate models with deterministic volatility functions.

Suggested Citation

Bjork, Tomas and Christensen, Bent Jesper, Interest Rate Dynamics and Consistent Forward Rate Curves. Mathematical Finance, Vol. 9, pp. 323-348, October 1999. Available at SSRN: https://ssrn.com/abstract=534152

Tomas Bjork (Contact Author)

Stockholm School of Economics - Swedish House of Finance ( email )

Drottninggatan 98
111 60 Stockholm
Sweden

Bent Jesper Christensen

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

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