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The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models

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Author Info
Jens H. E. Christensen () (Financial Research, Federal Reserve Bank of San Francisco)
Francis X. Diebold () (Department of Economics, University of Pennsylvania)
Glenn D. Rudebusch () (Economic Research Department, Federal Reserve Bank of San Francisco)

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Abstract

We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.

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Publisher Info
Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 07-029.

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Length: 38 pages
Date of creation: 11 Sep 2007
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Handle: RePEc:pen:papers:07-029

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Related research
Keywords: arbitrage; Nelson-Siegel; term structure; factor models; forecast accuracy;

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Find related papers by JEL classification:
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
G1 - Financial Economics - - General Financial Markets
E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!]
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  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  3. Peter Hordahl & Oreste Tristani & David Vestin, 2003. "A joint econometric model of macroeconomic and term structure," Proceedings, Federal Reserve Bank of San Francisco, issue Mar. [Downloadable!]
  4. Peter Hordahl & Oreste Tristani & David Vestin, 2004. "A joint econometric model of macroeconomic and term structure dynamics," Money Macro and Finance (MMF) Research Group Conference 2003 48, Money Macro and Finance Research Group. [Downloadable!]
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  5. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May. [Downloadable!] (restricted)
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  6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  7. 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. [Downloadable!] (restricted)
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  8. Glenn D. Rudebusch & Eric T. Swanson & Tao Wu, 2006. "The bond yield "conundrum" from a macro-finance perspective," Working Paper Series 2006-16, Federal Reserve Bank of San Francisco. [Downloadable!]
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  9. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October. [Downloadable!] (restricted)
  10. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
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  11. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-92, September. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  13. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February. [Downloadable!] (restricted)
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  14. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  15. Andrew Ang & Monika Piazzesi & Min Wei, 2003. "What does the yield curve tell us about GDP growth?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar. [Downloadable!]
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  16. 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. [Downloadable!] (restricted)
    Other versions:
  17. Bank for International Settlements, 2005. "Zero-coupon yield curves: technical documentation," BIS Papers, Bank for International Settlements, number 25, 11. [Downloadable!]
  18. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March. [Downloadable!] (restricted)
  19. Leo Krippner, 2006. "A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(1), pages 39-59, March. [Downloadable!] (restricted)
  20. Duffee, Gregory R, 1996. " Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-51, June. [Downloadable!] (restricted)
  21. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(1), pages 243-288, March.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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). [Downloadable!]
    Other versions:
  2. Jens Christensen, 2008. "Treasury bond yields and long-run inflation expectations," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue Aug 15. [Downloadable!]
  3. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008. "An arbitrage-free generalized Nelson-Siegel term structure model," Working Paper Series 2008-07, Federal Reserve Bank of San Francisco. [Downloadable!]
    Other versions:
  4. Borus Jungbacker & Siem Jan Koopman & Michel van der Wel, 2009. "Dynamic Factor Models with Smooth Loadings for Analyzing the Term Structure of Interest Rates," CREATES Research Papers 2009-39, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  5. 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. [Downloadable!]
  6. Paola Donati & Francesco Donati, 2008. "Modelling and forecasting the yield curve under model uncertainty," Working Paper Series 917, European Central Bank. [Downloadable!]
  7. ZHU Xiaoneng & Shahidur RAHMAN, 2009. "Global Yield Curves and Sovereign Bond Market Integration," Economic Growth centre Working Paper Series 0902, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre. [Downloadable!]
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