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An arbitrage-free generalized Nelson-Siegel term structure model

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

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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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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  1. Francis X. Diebold & Monika Piazzesi & Glenn Rudebusch, 2005. "Modeling Bond Yields in Finance and Macroeconomics," NBER Working Papers 11089, National Bureau of Economic Research, Inc.
  2. 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.
  3. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models," PIER Working Paper Archive 07-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
  5. 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.
  6. 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.
  7. Qiang Dai & Kenneth J. Singleton, 1997. "Specification Analysis of Affine Term Structure Models," NBER Working Papers 6128, National Bureau of Economic Research, Inc.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Bowsher, Clive G. & Meeks, Roland, 2008. "The dynamics of economics functions: modelling and forecasting the yield curve," Working Papers 0804, Federal Reserve Bank of Dallas.
  13. 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.
  14. 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.
  15. 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.
  16. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  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.
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