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An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model

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Listed:
  • Jens H.E. Christensen
  • Francis X. Diebold
  • Glenn D. Rudebusch

Abstract

The Svensson generalization of the popular Nelson-Siegel term structure model is widely used by practitioners and central banks. Unfortunately, like the original Nelson-Siegel specification, this generalization, in its dynamic form, does not enforce arbitrage-free consistency over time. Indeed, we show that the factor loadings of the Svensson generalization cannot be obtained in a standard finance arbitrage-free affine term structure representation. Therefore, we introduce a closely related generalized Nelson-Siegel model on which the no-arbitrage condition can be imposed. We estimate this new arbitrage-free generalized Nelson-Siegel model and demonstrate its tractability and good in-sample fit.

Suggested Citation

  • Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008. "An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model," NBER Working Papers 14463, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14463
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    References listed on IDEAS

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    1. Francis X. Diebold & Monika Piazzesi & Glenn D. Rudebusch, 2005. "Modeling Bond Yields in Finance and Macroeconomics," American Economic Review, American Economic Association, vol. 95(2), pages 415-420, May.
    2. Almeida, Caio & Vicente, José, 2008. "The role of no-arbitrage on forecasting: Lessons from a parametric term structure model," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2695-2705, December.
    3. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2014. "Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 136-151, January.
    4. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    5. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
    6. 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.
    7. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    8. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2011. "How arbitrage-free is the Nelson-Siegel model?," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 393-407, June.
    9. Kim, Don H. & Orphanides, Athanasios, 2012. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(01), pages 241-272, April.
    10. Bowsher, Clive G. & Meeks, Roland, 2008. "The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1419-1437.
    11. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2010. "Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 143-178, September.
    12. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
    13. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    14. 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, February.
    15. Glenn D. Rudebusch & Tao Wu, 2007. "Accounting for a Shift in Term Structure Behavior with No-Arbitrage and Macro-Finance Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 395-422, March.
    16. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    17. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
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    More about this item

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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