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Interest Rate Dynamics and Consistent Forward Rate Curves

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  • Björk, Tomas

    (Dept. of Finance, Stockholm School of Economics)

  • Christensen, Bent Jesper

    (School of Economics and Management, University of Aarhus)

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.

Suggested Citation

  • Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," SSE/EFI Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0209
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
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    7. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
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    More about this item

    Keywords

    Forward rate curves; interest rate models; invariant manifolds; marked point processes;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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