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An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models

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  • Leo Krippner

    ()
    (AMP Capital Investors)

Abstract

This article derives a generic, intertemporally-consistent, and arbitrage-free version of the popular class of yield curve models originally introduced by Nelson and Siegel (1987). The derived model has a theoretical foundation (conferred via the Heath, Jarrow and Morton (1992) framework) that allows it to be used in applications that involve an implicit or explicit time-series context. As an example of the potentialapplication of the model, the intertemporal consistency is exploited to derive a theoretical time-series process that may be used to forecast the yield curve. The empirical application of the forecasting framework to United States data results in out-of-sample forecasts that outperform the random walk over a sample period of almost 50 years, for forecast horizons ranging from six months to three years.

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File URL: ftp://mngt.waikato.ac.nz/RePEc/wai/econwp/0501.pdf
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Bibliographic Info

Paper provided by University of Waikato, Department of Economics in its series Working Papers in Economics with number 05/01.

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Length: 32 pages
Date of creation: 31 Jan 2005
Date of revision:
Handle: RePEc:wai:econwp:05/01

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Keywords: yield curve; term structure of interest rates; Nelson and Siegel model; Heath-Jarrow-Morton framework;

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References

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  1. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
  2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  3. David K. Backus & Silverio Foresi & Stanley E. Zin, 1994. "Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing," Working Papers 94-28, New York University, Leonard N. Stern School of Business, Department of Economics.
  4. Seppälä, Juha & Viertiö, Petri, 1996. "The Term Structure of Interest Rates: Estimation and Interpretation," Research Discussion Papers 19/1996, Bank of Finland.
  5. Ben Hunt, 1995. "Fitting Parsimonious Yield Curve Models to Australian Coupon Bond Data," Working Paper Series 51, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  6. Soderlind, P & Svensson, L-E-O, 1996. "New Techniques to Extract Market Expectations from Financial Instruments," Papers 621, Stockholm - International Economic Studies.
  7. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  8. Fang, Victor & Muljono, Ronny, 2003. "An empirical analysis of the Australian dollar swap spreads," Pacific-Basin Finance Journal, Elsevier, vol. 11(2), pages 153-173, April.
  9. Francis X. Diebold & Glenn D. Rudebusch & S. Boragan Aruoba, 2003. "The Macroeconomy and the Yield Curve: A Nonstructural Analysis," PIER Working Paper Archive 03-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  10. James Steeley, 2004. "Estimating time-varying risk premia in UK long-term government bonds," Applied Financial Economics, Taylor & Francis Journals, vol. 14(5), pages 367-373.
  11. 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.
  12. Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
  13. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonormalised Laguerre Polynomials: A Consistent Cross-Sectional and Inter-Temporal Approach," Working Papers in Economics 03/02, University of Waikato, Department of Economics.
  14. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonomalised Laguerre Polynomials: An Intertemporally Consistent Approach with an Economic Interpretation," Working Papers in Economics 03/01, University of Waikato, Department of Economics.
  15. Soto, Gloria M., 2001. "Immunization derived from a polynomial duration vector in the Spanish bond market," Journal of Banking & Finance, Elsevier, vol. 25(6), pages 1037-1057, June.
  16. Dahlquist, Magnus & Svensson, Lars E O, 1996. " Estimating the Term Structure of Interest Rates for Monetary Policy Analysis," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 163-83, June.
  17. Ioannides, Michalis, 2003. "A comparison of yield curve estimation techniques using UK data," Journal of Banking & Finance, Elsevier, vol. 27(1), pages 1-26, January.
  18. Jordan, James V. & Mansi, Sattar A., 2003. "Term structure estimation from on-the-run Treasuries," Journal of Banking & Finance, Elsevier, vol. 27(8), pages 1487-1509, August.
  19. Mansi, Sattar A & Phillips, Jeffrey H, 2001. "Modeling the Term Structure from the On-the-Run Treasury Yield Curve," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 545-64, Winter.
  20. 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.
  21. 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.
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Cited by:
  1. Leo Krippner, 2005. "Investigating the Relationships between the Yield Curve, Output and Inflation using an Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics 05/02, University of Waikato, Department of Economics.
  2. Leo Krippner, 2005. "Attributing Returns and Optimising United States Swaps Portfolios Using an Intertemporally-Consistent and Arbitrage-Free Model of the Yield Curve," Working Papers in Economics 05/03, University of Waikato, Department of Economics.
  3. De Pooter, Michiel & Ravazzolo, Francesco & van Dijk, Dick, 2006. "Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information," MPRA Paper 2512, University Library of Munich, Germany, revised 03 Mar 2007.

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