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Term Structure Models with Parallel and Proportional Shifts

Author

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  • Armerin, Frederik

    (Department of Mathematics)

  • Björk, Tomas

    (Department of Finance,)

  • Jensen, Bjarne Astrup

    (Department of Finance, Copenhagen Business School)

Abstract

We investigate the possibility of an arbitrage free model for the term structure of interest rates where the yield curve only changes through a parallel shift. We consider HJM type forward rate models driven by a multidimensionalWiener process as well as by a general marked point process. Within this general framework we show that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. We also show that there exists no nontrivial flat term structure model. The same analysis is repeated for the similar case, where the yield curve only changes through proportional shifts.

Suggested Citation

  • Armerin, Frederik & Björk, Tomas & Jensen, Bjarne Astrup, 2005. "Term Structure Models with Parallel and Proportional Shifts," Working Papers 2005-5, Copenhagen Business School, Department of Finance.
    • Handle: RePEc:hhs:cbsfin:2005_005
    Note: Forthcoming in Applied Mathematical Finance
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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7137
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    References listed on IDEAS

    as
    1. 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.
    2. Ingersoll, Jonathan E. & Skelton, Jeffrey & Weil, Roman L., 1978. "Duration Forty Years Later," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(4), pages 627-650, November.
    3. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    4. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    5. Bierwag, G. O., 1977. "Immunization, Duration, and the Term Structure of Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(5), pages 725-742, December.
    6. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    7. Montrucchio, Luigi & Peccati, Lorenzo, 1991. "A note on Shiu--Fisher--Weil immunization theorem," Insurance: Mathematics and Economics, Elsevier, vol. 10(2), pages 125-131, July.
    8. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
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    Cited by:

    1. Raquel M. Gaspar & Mariana Khapko, 2023. "In memoriam: Tomas Björk (1947–2021)," Finance and Stochastics, Springer, vol. 27(4), pages 867-885, October.

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    More about this item

    Keywords

    bond market; term structure of interest rates; flat term structures;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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