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Interest Rate Dynamics and Consistent Forward Rate Curves

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  • Tomas Björk
  • Bent Jesper Christensen

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. Copyright Blackwell Publishers Inc 1999.

Suggested Citation

  • Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  • Handle: RePEc:bla:mathfi:v:9:y:1999:i:4:p:323-348
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    References listed on IDEAS

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    1. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
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    5. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
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    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    8. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94.
    9. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
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    More about this item

    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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