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Taking Positive Interest Rates Seriously

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Author Info

  • Enlin Pan

    (Chicago Partners, LLC)

  • Liuren Wu

    (Zicklin School of Business, Baruch College)

Abstract

We present a dynamic term structure model in which interest rates of all maturities are bounded from below at zero. Positivity and continuity, combined with no arbitrage, result in only one functional form for the term structure with three sources of risk. One dynamic factor controls the level of the interest rate and follows a special two-parameter square-root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and act as two static factors. This model has no other parameters to estimate and hence bears no other risks.

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File URL: http://128.118.178.162/eps/fin/papers/0409/0409013.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0409013.

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Length: 41 pages
Date of creation: 07 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0409013

Note: Type of Document - pdf; pages: 41
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Web page: http://128.118.178.162

Related research

Keywords: Term structure; consistency; positivity; quadratic forms;

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References

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  1. Leippold, Markus & Wu, Liuren, 2002. "Asset Pricing under the Quadratic Class," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(02), pages 271-295, June.
  2. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  3. 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.
  4. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA.
  5. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
  6. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  7. David Backus & Silverio Foresi & Abon Mozumdar & Liuren Wu, 1998. "Predictable Changes in Yields and Forward Rates," NBER Working Papers 6379, National Bureau of Economic Research, Inc.
  8. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
  9. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. " Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-82, December.
  10. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-76, December.
  11. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  12. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  13. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc.
  14. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
  15. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
  16. Jin, Yan & Glasserman, Paul, 2001. "Equilibrium Positive Interest Rates: A Unified View," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 187-214.
  17. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78.
  18. repec:aah:aarmng:1999-4 is not listed on IDEAS
  19. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
  20. 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.
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