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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 AFGNS model and demonstrate its tractability and good in-sample fit. Copyright The Author(s). Journal compilation Royal Economic Society 2009

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 12 (2009)
Issue (Month): 3 (November)
Pages: C33-C64

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Handle: RePEc:ect:emjrnl:v:12:y:2009:i:3:p:c33-c64

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References

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  1. 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.
  2. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2008. "How arbitrage-free is the Nelson-Siegel Model?," Working Paper Series 0874, European Central Bank.
  3. Francis X. Diebold & Monika Piazzesi & Glenn D. Rudebusch, 2005. "Modeling Bond Yields in Finance and Macroeconomics," PIER Working Paper Archive 05-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. Kim, Don H. & Orphanides, Athanasios, 2005. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," CEPR Discussion Papers 5341, C.E.P.R. Discussion Papers.
  5. 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.
  6. 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).
  7. 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.
  8. repec:aah:aarmng:1999-4 is not listed on IDEAS
  9. Francis X. Diebold & Canlin Li, 2002. "Forecasting the Term Structure of Government Bond Yields," Center for Financial Institutions Working Papers 02-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
  10. Paul Soderlind & Lars E. O. Svensson, 1997. "New Techniques to Extract Market Expectations from Financial Instruments," NBER Working Papers 5877, National Bureau of Economic Research, Inc.
  11. 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.
  12. 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.
  13. 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.
  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, 02.
  15. Clive G. Bowsher & Roland Meeks, 2008. "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," Economics Series Working Papers 2008-WO5, University of Oxford, Department of Economics.
  16. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
  17. Michiel De Pooter, 2007. "Examining the Nelson-Siegel Class of Term Structure Models," Tinbergen Institute Discussion Papers 07-043/4, Tinbergen Institute.
  18. 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.
  19. 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.
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