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On the Dybvig-Ingersoll-Ross Theorem

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  • Constantinos Kardaras
  • Eckhard Platen

Abstract

The Dybvig-Ingersoll-Ross (DIR) theorem states that, in arbitrage-free term structure models, long-term yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that long-term rates at earlier dates can dominate long-term rates at later dates. The viability assumption imposed on the market model is weaker than those appearing previously in the literature.

Suggested Citation

  • Constantinos Kardaras & Eckhard Platen, 2009. "On the Dybvig-Ingersoll-Ross Theorem," Papers 0901.2080, arXiv.org, revised Mar 2010.
    • Handle: RePEc:arx:papers:0901.2080
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    2. J. Huston McCulloch, 2000. "Long Forward and Zero-Coupon Rates Indeed Can Never Fall, but Are Indeterminate: A Comment on Dybvig, Ingersoll and Ross," Working Papers 00-12, Ohio State University, Department of Economics.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Schulze, Klaas, 2008. "Asymptotic Maturity Behavior of the Term Structure," Bonn Econ Discussion Papers 11/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    5. Friedrich Hubalek & Irene Klein & Josef Teichmayn, 2002. "A General Proof Of The Dybvig‐Ingersoll‐Ross Theorem: Long Forward Rates Can Never Fall," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 447-451, October.
    6. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
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    Cited by:

    1. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2015. "The Long-Term Swap Rate and a General Analysis of Long-Term Interest Rates," Papers 1507.00208, arXiv.org, revised Jun 2019.
    2. Francesca Biagini & Maximilian Härtel, 2014. "Behavior Of Long-Term Yields In A Lévy Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 1-24.
    3. Dorje C. Brody & Lane P. Hughston, 2018. "Social Discounting And The Long Rate Of Interest," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 306-334, January.
    4. Jan de Kort, 2018. "A note on the long rate in factor models of the term structure," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 656-667, April.
    5. Francesca Biagini & Alessandro Gnoatto & Maximilian Härtel, 2020. "General Analysis Of Long-Term Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-29, January.
    6. Dorje C. Brody & Lane P. Hughston & David M. Meier, 2018. "Lévy–Vasicek Models And The Long-Bond Return Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-26, May.
    7. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org, revised Aug 2015.
    8. Sebastián A. Rey, 2016. "Theory of long-term interest rates," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-18, September.
    9. Dorje C. Brody & Lane P. Hughston, 2013. "Social Discounting and the Long Rate of Interest," Papers 1306.5145, arXiv.org, revised Sep 2015.

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