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Asymptotic Maturity Behavior of the Term Structure

  • Klaas Schulze

    ()

Pricing and hedging of long-term interest rate sensitive products require to extrapolate the term structure beyond observable maturities. For the resulting limiting term structure we show two results by postulating no arbitrage in a bond market with infinitely increasing maturities: long zero-bond yields and long forward rates (i) are monotonically increasing and (ii) equal their minimal future value. Both results constrain the asymptotic maturity behavior of stochastic yield curves. They are fairly general and extend beyond semimartingale modeling. Hence our framework embeds arbitrage-free term structure models and imposes restrictions on their specification.

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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse11_2008.pdf
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Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse11_2008.

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Length: 14
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:bon:bonedp:bgse11_2008
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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  1. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
  2. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
  3. 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.
  4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
  5. 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.
  6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  7. 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.
  8. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
  9. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  12. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
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