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An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model

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  • Jens H. E. Christensen

    () (Economic Research Department, Federal Reserve Bank of San Francisco)

  • Francis X. Diebold

    () (Department of Economics, University of Pennsylvania and NBER)

  • Glenn D. Rudebusch

    () (Economic Research Department, Federal Reserve Bank of San Francisco)

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 Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 08-030.

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Length: 29 pages
Date of creation: 27 May 2008
Date of revision:
Handle: RePEc:pen:papers:08-030

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Keywords: Yield Curve; Interest Rate; Bond Market; Svensson Model;

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References

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  1. Francis X. Diebold & Monika Piazzesi & Glenn D. Rudebusch, 2005. "Modeling bond yields in finance and macroeconomics," Working Paper Series 2005-04, Federal Reserve Bank of San Francisco.
  2. 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, Graduate School of Economics, Getulio Vargas Foundation (Brazil).
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Clive Bowsher & Roland Meeks, 2008. "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," OFRC Working Papers Series 2008fe24, Oxford Financial Research Centre.
  8. 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.
  9. Laura Coroneo & Ken Nyholm & Rositsa Vidova-Koleva, 2008. "How Arbitrage-free is the Nelson-Siegel Model?," Working Paper Series 874, European Central Bank.
  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. Michiel De Pooter, 2007. "Examining the Nelson-Siegel Class of Term Structure Models," Tinbergen Institute Discussion Papers 07-043/4, Tinbergen Institute.
  12. 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.
  13. 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.
  14. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2008. "Inflation expectations and risk premiums in an arbitrage-free model of nominal and real bond yields," Working Paper Series 2008-34, Federal Reserve Bank of San Francisco.
  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. 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. 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.
  18. Damir Filipović, 1999. "A Note on the Nelson-Siegel Family," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 349-359.
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Citations

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Cited by:
  1. Glenn D. Rudebusch, 2010. "Macro-Finance Models Of Interest Rates And The Economy," Manchester School, University of Manchester, vol. 78(s1), pages 25-52, 09.
  2. Craig Blackburn & Michael Sherris, 2011. "Consistent Dynamic Affine Mortality Model for Longevity Risk Applications," Working Papers 201107, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
  3. Di Maggio, Marco, 2010. "The Political Economy of the Yield Curve," MPRA Paper 20697, University Library of Munich, Germany.
  4. Michał Brzoza-Brzezina & Jacek Kotłowski, 2012. "Measuring the natural yield curve," National Bank of Poland Working Papers 108, National Bank of Poland, Economic Institute.
  5. Dauwe, Alexander & Moura, Marcelo L., 2011. "Forecasting the term structure of the Euro Market using Principal Component Analysis," Ibmec Working Papers wpe_233, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  6. Márcio Laurini, 2011. "Bayesian Factor Selection in Dynamic Term Structure Models," IBMEC RJ Economics Discussion Papers 2011-02, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  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. Márcio Laurini & João Frois Caldeira, 2012. "Some Comments on a Macro-Finance Model with Stochastic Volatility," IBMEC RJ Economics Discussion Papers 2012-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  9. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  10. Wolfgang Karl Härdle,Piotr Majer & Melanie Schienle, 2012. "Yield Curve Modeling and Forecasting using Semiparametric Factor Dynamics," SFB 649 Discussion Papers SFB649DP2012-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Leo Krippner, 2012. "Modifying Gaussian term structure models when interest rates are near the zero lower bound (this is a revised version of CAMA working paper 36/2011)," CAMA Working Papers 2012-05, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  12. Michael D. Bauer & Glenn D. Rudebusch & Jing (Cynthia) Wu, 2011. "Unbiased estimate of dynamic term structure models," Working Paper Series 2011-12, Federal Reserve Bank of San Francisco.
  13. Rafael Barros de Rezende, 2008. "Giving flexibility to the Nelso-Siegel class of term structure models," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807211322560, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  14. Leo Krippner, 2012. "Modifying Gaussian term structure models when interest rates are near the zero lower bound," Reserve Bank of New Zealand Discussion Paper Series DP2012/02, Reserve Bank of New Zealand.
  15. Caio Almeida & Axel Simonsen & José Vicente, 2012. "Forecasting Bond Yields with Segmented Term Structure Models," Working Papers Series 288, Central Bank of Brazil, Research Department.
  16. António Afonso & Manuel M. F. Martins, 2010. "Level, Slope, Curvature of Sovereign Yield Curve and Fiscal Behaviour," Working Papers 2010/23, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon..
  17. ZHU Xiaoneng & Shahidur RAHMAN, 2009. "A Regime Switching Macro-finance Model of the Term Structure," Economic Growth centre Working Paper Series 0901, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.

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