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Long Forward and Zero-Coupon Rates Can Never Fall

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Author Info
Jonathan E. Ingersoll Jr. () (School of Management)
Philip H. Dybvig () (John M. Olin School of Business)
Stephen A. Ross () (Sloan School of Management)

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Abstract

In frictionless markets having no arbitrage, the asymptotic zero-coupon rate never falls. The same is true of the long forward rate. The long par-coupon rate can rise and fall due to forward rate movements at short maturities. This paper relates the three types of interest rate and formalizes and proves the impossibility results for falling asymptotic rates. These results can be tested in a parametric term structure specification that is rich enough to identify a time series of long rates. The results show that it is not possible to specify arbitrarily the long forward or zero-coupon rate process.

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Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm45.

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Date of creation: 22 Aug 1998
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Handle: RePEc:ysm:somwrk:ysm45

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G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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  1. 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. [Downloadable!]
  2. Frank Riedel, 1999. "Heterogeneous Time Preferences and Interest Rates - The Preferred Habitat Theory Revisited," Finance 9903001, EconWPA. [Downloadable!]
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  3. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Research series 200402, National Bank of Belgium. [Downloadable!]
    Other versions:
  4. Christiansen, Charlotte, 2001. "Long Maturity Forward Rates," Finance Working Papers 01-12, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  5. Klaas Schulze, 2008. "Asymptotic Maturity Behavior of the Term Structure," Bonn Econ Discussion Papers bgse11_2008, University of Bonn, Germany. [Downloadable!]
  6. P. Santa-Clara & D. Sornette, 1998. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Quantitative Finance Papers cond-mat/9801321, arXiv.org. [Downloadable!]
  7. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA. [Downloadable!]
  8. Juha Ilmari Seppala, 2000. "The Term Structure of Real Interest Rates: Theory and Evidence from the U.K. Index-Linked Bonds," Econometric Society World Congress 2000 Contributed Papers 0245, Econometric Society. [Downloadable!]
  9. Ekaterini Panopoulou & B. Groom & P. Koundouri & Theologos Pantelidis, 2005. "Discounting the distant future: How much does model selection affect the certainty equivalent rate?," Economics, Finance and Accounting Department Working Paper Series n1480105, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth. [Downloadable!]
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  10. J. Huston McCulloch, 2001. "The Inflation Premium implicit in the US Real and Nominal," Computing in Economics and Finance 2001 210, Society for Computational Economics. [Downloadable!]
  11. Tomoki Fujii & Larry Karp, 2006. "Numerical Analysis of Non-Constant Discounting with an Application to Renewable Resource Management," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series 1019, Department of Agricultural & Resource Economics, UC Berkeley. [Downloadable!]
  12. Xavier Gabaix, 2008. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," NBER Working Papers 13724, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  13. Rama Cont, 1999. "Modeling interest rate dynamics: an infinite-dimensional approach," Quantitative Finance Papers cond-mat/9902018, arXiv.org. [Downloadable!]
  14. Balázs Romhányi, 2005. "A learning hypothesis of the term structure of interest rates," Macroeconomics 0503001, EconWPA. [Downloadable!]
  15. Yvan Lengwiler, 2005. "Heterogeneous Patience and the Term Structure of Real Interest Rates," American Economic Review, American Economic Association, vol. 95(3), pages 890-896, June. [Downloadable!]
  16. Clive G. Bowsher & Roland Meeks, 2008. "Stationarity and the term structure of interest rates: a characterisation of stationary and unit root yield curves," Working Papers 0811, Federal Reserve Bank of Dallas. [Downloadable!]
  17. Mark Fisher, 2001. "Forces that shape the yield curve: Parts 1 and 2," Working Paper 2001-3, Federal Reserve Bank of Atlanta. [Downloadable!]
  18. Elyès Jouini & Jean-Michel Marin & Clotilde Napp, 2008. "Discounting and Divergence of Opinion," Working Papers halshs-00176636_v2, HAL. [Downloadable!]
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