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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.

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File URL: http://arxiv.org/pdf/0901.2080
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0901.2080.

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Date of creation: Jan 2009
Date of revision: Mar 2010
Handle: RePEc:arx:papers:0901.2080

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Web page: http://arxiv.org/

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  1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Klaas Schulze, 2008. "Asymptotic Maturity Behavior of the Term Structure," Bonn Econ Discussion Papers bgse11_2008, University of Bonn, Germany.
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Cited by:
  1. Francesca Biagini & Alessandro Gnoatto & Maximilian H\"artel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org.

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