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

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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