Scandinavian Working Papers in Economics

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

No 209: Interest Rate Dynamics and Consistent Forward Rate Curves

Tomas Björk () and Bent Jesper Christensen
Additional contact information
Tomas Björk: Dept. of Finance, Stockholm School of Economics, Postal: P.O. Box 6501, S-113 83 Stockholm, Sweden
Bent Jesper Christensen: School of Economics and Management, University of Aarhus, Postal: Bldg.350, University Park, DK-8000 Aarhus C, Denmark

Abstract: We derive general necessary and sufficient conditions for the mutual consistency of a given parametrized family of forward rate curves and the dynamics of a given interest rate model. Consistency in this context means that the interest rate model will produce forward rate curves belonging to the parameterized family. The interest rate model may be driven by a multidimensional Wiener process as well as by a market point process. As an application, the Nelson-Siegel family of forward curves is shown to be inconsistent with the Ho-Lee interest rate model, and with the Hull-White extension of the Vasicec model, but it may be adjusted to achieve consistency with these models and with extensions that allow for jumps in interest rates. For a natural exponential-polynomial generalization of the Nelson-Siegel family, we give necessary and sufficient conditions for the existence of a consistent interest rate model with deterministic volatility.

Keywords: Forward rate curves; interest rate models; invariant manifolds; marked point processes

JEL-codes: E43; G10

38 pages, November 27, 1997

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Published as
Tomas Björk and Bent Jesper Christensen, (1999), 'Interest Rate Dynamics and Consistent Forward Rate Curves', Mathematical Finance, vol 9, no 4, pages 323-348

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