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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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 209.

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Length: 38 pages
Date of creation: 27 Nov 1997
Date of revision:
Publication status: Published in Mathematical Finance, 1999, pages 323-348.
Handle: RePEc:hhs:hastef:0209

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Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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Keywords: Forward rate curves; interest rate models; invariant manifolds; marked point processes;

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References

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  1. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 60(4), pages 473-89, October.
  2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 211-239.
  3. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, American Finance Association, vol. 50(2), pages 507-28, June.
  4. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 41(5), pages 1011-29, December.
  5. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 50(2), pages 125-150, November.
  6. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 1(4), pages 77-94.
  7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  8. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 4(3), pages 259-283.
  9. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, Annual Reviews, vol. 1(1), pages 69-96, November.
  10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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