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Term Structure Models with Parallel and Proportional Shifts

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Author Info

  • Armerin, Frederik

    () (Department of Mathematics)

  • Björk, Tomas

    () (Department of Finance,)

  • Jensen, Bjarne Astrup

    () (Department of Finance, Copenhagen Business School)

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    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.

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    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7137
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    Bibliographic Info

    Paper provided by Copenhagen Business School, Department of Finance in its series Working Papers with number 2005-5.

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    Length: 23 pages
    Date of creation: 26 Oct 2005
    Date of revision:
    Publication status: Published in Applied Mathematical Finance , 2007, pages 243-260.
    Handle: RePEc:hhs:cbsfin:2005_005

    Note: Forthcoming in Applied Mathematical Finance
    Contact details of provider:
    Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark
    Phone: +45 3815 3815
    Email:
    Web page: http://www.cbs.dk/departments/finance/
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    Related research

    Keywords: bond market; term structure of interest rates; flat term structures;

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    1. Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
    2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    3. 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.
    4. 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.
    5. 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 408-31, October.
    6. Ingersoll, Jonathan E. & Skelton, Jeffrey & Weil, Roman L., 1978. "Duration Forty Years Later," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(04), pages 627-650, November.
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