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Term Structure Models: A Perspective from the Long Rate

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  • Yong Yao

Abstract

Term structure models based on dynamic asset-pricing theory are discussed by taking a perspective from the long rate. This paper partially answers two questions about the asymptotic behavior of yields on default-free zero-coupon bonds: in frictionless markets having no arbitrage, what should the behavior be; and, in known term structure models, what can the behavior be.In frictionless markets having no arbitrage, yields of all maturities should be positive and uniformly bounded from above. The yield curve should level out as term to maturity increases. Slopes with large absolute values occur only in the early maturities. In a continuous-time framework, the longer the maturity of the yield is, the less volatile it will be. The long rate should be a nondecreasing process. Furthermore, the long rate in continuous-time factor models with nonsingular volatility matrices should be a nondecreasing deterministic function.In the Black, Derman, and Toy model and factor models with the short rate having the mean reversion property, yields of all maturities are uniformly bounded from above. The long rate in the Duffie and Kan model with the mean reversion property is a constant. The long rate in the Heath, Jarrow, and Morton model can be infinite or a nondecreasing process. Examples with the long rate increasing are given in this paper. A model with the long rate and short rate as two state variables is then obtained.

Suggested Citation

  • Yong Yao, 1999. "Term Structure Models: A Perspective from the Long Rate," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(3), pages 122-138.
  • Handle: RePEc:taf:uaajxx:v:3:y:1999:i:3:p:122-138
    DOI: 10.1080/10920277.1999.10595839
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    Cited by:

    1. Jorge De Andrés Sánchez & Antonio Terceño Gómez, 2003. "Applications of Fuzzy Regression in Actuarial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 665-699, December.
    2. 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).
    3. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
    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. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.

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