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An arbitrage-free generalized Nelson-Siegel term structure model

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  • 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.

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Bibliographic Info

Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2008-07.

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Date of creation: 2008
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Handle: RePEc:fip:fedfwp:2008-07

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Keywords: Interest rates ; Econometric models;

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References

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  1. Söderlind, Paul & Svensson, Lars E.O., 1996. "New Techniques to Extract Market expectations from Financial Instruments," Working Paper Series in Economics and Finance 142, Stockholm School of Economics.
  2. 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, February.
  3. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  4. Diebold, Francis X. & Piazzesi, Monica & Rudebusch, Glenn D., 2005. "Modeling bond yields in finance and macroeconomics," CFS Working Paper Series 2005/03, Center for Financial Studies (CFS).
  5. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The Affine Arbitrage-Free Class of: Nelson-Siegel Term Structure Models," NBER Working Papers 13611, National Bureau of Economic Research, Inc.
  6. Diebold, Francis X. & Li, Canlin, 2003. "Forecasting the term structure of government bond yields," CFS Working Paper Series 2004/09, Center for Financial Studies (CFS).
  7. 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.
  8. 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.
  9. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2008. "How arbitrage-free is the Nelson-Siegel Model?," Working Paper Series 0874, European Central Bank.
  10. Michiel De Pooter, 2007. "Examining the Nelson-Siegel Class of Term Structure Models," Tinbergen Institute Discussion Papers 07-043/4, Tinbergen Institute.
  11. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
  12. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2009. "Inflation expectations and risk premiums in an arbitrage-free model of nominal and real bond yields," Proceedings, Federal Reserve Bank of San Francisco, issue Jan.
  13. Francis X. Diebold & Glenn D. Rudebusch & S. Boragan Aruoba, 2004. "The Macroeconomy and the Yield Curve: A Dynamic Latent Factor Approach," NBER Working Papers 10616, National Bureau of Economic Research, Inc.
  14. Almeida, Caio Ibsen Rodrigues de & Vicente, José Valentim M., 2007. "The Role of No-Arbitrage on Forecasting: Lessons from a Parametric Term Structure Model," Economics Working Papers (Ensaios Economicos da EPGE) 657, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  15. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
  16. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2009. "Do central bank liquidity facilities affect interbank lending rates?," Working Paper Series 2009-13, Federal Reserve Bank of San Francisco.
  17. 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.
  18. 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, 03.
  19. repec:aah:aarmng:1999-4 is not listed on IDEAS
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