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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 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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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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  1. Don H. Kim & Athanasios Orphanides, 2005. "Term structure estimation with survey data on interest rate forecasts," Finance and Economics Discussion Series 2005-48, Board of Governors of the Federal Reserve System (U.S.).
  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. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
  4. Soderlind, P & Svensson, L-E-O, 1996. "New Techniques to Extract Market Expectations from Financial Instruments," Papers 621, Stockholm - International Economic Studies.
  5. 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.
  6. 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.
  7. Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The affine arbitrage-free class of Nelson-Siegel term structure models," Working Paper Series 2007-20, Federal Reserve Bank of San Francisco.
  8. Clive G. Bowsher & Roland Meeks, 2008. "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," Economics Papers 2008-W05, Economics Group, Nuffield College, University of Oxford.
  9. 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.
  10. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
  11. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2008. "How arbitrage-free is the Nelson-Siegel Model?," Working Paper Series 0874, European Central Bank.
  12. 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).
  13. Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
  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. 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.
  16. 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.
  17. 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.
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