IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v13y2006i1p39-59.html
   My bibliography  Save this article

A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

Author

Listed:
  • Leo Krippner

Abstract

A popular class of yield curve models is based on the Nelson and Siegel approach of 'fitting' yield curve data with simple functions of maturity. However, such models cannot be consistent across time. This article addresses that deficiency by deriving an intertemporally consistent and arbitrage-free version of the Nelson and Siegel model. Adding this theoretical consistency expands the potential applications of the Nelson and Siegel approach to exercises involving a time-series context, such as forecasting the yield curve and pricing interest rate derivatives. As a practical example, the intertemporal consistency of the model is exploited to derive a theoretical framework for forecasting the yield curve. The empirical application of that framework to United States data results in out-of-sample forecasts that outperform the random walk over the sample period of almost 50 years, for forecast horizons ranging from six months to three years.

Suggested Citation

  • Leo Krippner, 2006. "A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 39-59.
    • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:39-59
    DOI: 10.1080/13504860500394367
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394367
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13504860500394367?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonomalised Laguerre Polynomials: An Intertemporally Consistent Approach with an Economic Interpretation," Working Papers in Economics 03/01, University of Waikato.
    2. Jardet, Caroline, 2004. "Why did the term structure of interest rates lose its predictive power?," Economic Modelling, Elsevier, vol. 21(3), pages 509-524, May.
    3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    4. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    5. Bank for International Settlements, 2005. "Zero-coupon yield curves: technical documentation," BIS Papers, Bank for International Settlements, number 25.
    6. Ben Hunt, 1995. "Fitting Parsimonious Yield Curve Models to Australian Coupon Bond Data," Working Paper Series 51, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    8. Arturo Estrella & Anthony P. Rodrigues & Sebastian Schich, 2003. "How Stable is the Predictive Power of the Yield Curve? Evidence from Germany and the United States," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 629-644, August.
    9. Sattar A. Mansi & Jeffery H. Phillips, 2001. "Modeling The Term Structure From The On-The-Run Treasury Yield Curve," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 545-564, December.
    10. Bernadell, Carlos & Coche, Joachim & Nyholm, Ken, 2005. "Yield curve prediction for the strategic investor," Working Paper Series 472, European Central Bank.
    11. Fang, Victor & Muljono, Ronny, 2003. "An empirical analysis of the Australian dollar swap spreads," Pacific-Basin Finance Journal, Elsevier, vol. 11(2), pages 153-173, April.
    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, February.
    13. Mansi, Sattar A & Phillips, Jeffrey H, 2001. "Modeling the Term Structure from the On-the-Run Treasury Yield Curve," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 545-564, Winter.
    14. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    15. Stoyan Valchev, 2004. "Stochastic volatility Gaussian Heath-Jarrow-Morton models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 347-368.
    16. repec:bla:scandj:v:98:y:1996:i:2:p:163-83 is not listed on IDEAS
    17. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    18. Leo Krippner, 2005. "An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics 05/01, University of Waikato.
    19. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leo Krippner, 2014. "Measuring the stance of monetary policy in conventional and unconventional environments," CAMA Working Papers 2014-06, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. Jing Yuan & Yan Peng & Zongwu Cai & Zhengyi Zhang, 2021. "A Quantitative Evaluation to Interest Rate Marketization Reform in China," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202122, University of Kansas, Department of Economics.
    3. Leo Krippner, 2009. "A theoretical foundation for the Nelson and Siegel class of yield curve models," Reserve Bank of New Zealand Discussion Paper Series DP2009/10, Reserve Bank of New Zealand.
    4. 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.
    5. Leo Krippner, 2005. "A New Framework for Yield Curve, Output and Inflation Relationships," Working Papers in Economics 05/07, University of Waikato.
    6. Leo Krippner, 2008. "A Macroeconomic Foundation for the Nelson and Siegel Class of Yield Curve Models," Research Paper Series 226, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Leo Krippner & Michelle Lewis, 2018. "Real-time forecasting with macro-finance models in the presence of a zero lower bound," Reserve Bank of New Zealand Discussion Paper Series DP2018/04, Reserve Bank of New Zealand.
    8. McNeil, James, 2023. "Monetary policy and the term structure of inflation expectations with information frictions," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    9. Leo Krippner, 2010. "Connecting the dots: a yield curve perspective on New Zealand’s interest rates," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 73, September.
    10. Leo Krippner, 2006. "A Yield Curve Perspective on Uncovered Interest Parity," Working Papers in Economics 06/16, University of Waikato.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leo Krippner, 2003. "Modelling the Yield Curve with Orthonomalised Laguerre Polynomials: An Intertemporally Consistent Approach with an Economic Interpretation," Working Papers in Economics 03/01, University of Waikato.
    2. Leo Krippner, 2005. "An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics 05/01, University of Waikato.
    3. 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.
    4. Francis X. Diebold, 2004. "The Nobel Memorial Prize for Robert F. Engle," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(2), pages 165-185, June.
    5. Wali Ullah & Yasumasa Matsuda, 2014. "Generalized Nelson-Siegel Term Structure Model : Do the second slope and curvature factors improve the in-sample fit and out-of-sample forecast?," TERG Discussion Papers 312, Graduate School of Economics and Management, Tohoku University.
    6. Emma Berenguer-Carceles & Ricardo Gimeno & Juan M. Nave, 2012. "Estimation of the Term Structure of Interest Rates: Methodology and Applications," Working Papers 12.06, Universidad Pablo de Olavide, Department of Financial Economics and Accounting (former Department of Business Administration).
    7. Leo Krippner, 2008. "A Macroeconomic Foundation for the Nelson and Siegel Class of Yield Curve Models," Research Paper Series 226, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Rui Chen & Jiri Svec & Maurice Peat, 2016. "Forecasting the Government Bond Term Structure in Australia," Australian Economic Papers, Wiley Blackwell, vol. 55(2), pages 99-111, June.
    9. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    10. S. Boragan Aruoba & Francis X. Diebold & Glenn D. Rudebusch, 2003. "The macroeconomy and the yield curve: a nonstructural analysis," Working Paper Series 2003-18, Federal Reserve Bank of San Francisco.
    11. Caldeira, João F. & Laurini, Márcio P. & Portugal, Marcelo S., 2010. "Bayesian Inference Applied to Dynamic Nelson-Siegel Model with Stochastic Volatility," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(1), October.
    12. Leo Krippner, 2009. "A theoretical foundation for the Nelson and Siegel class of yield curve models," Reserve Bank of New Zealand Discussion Paper Series DP2009/10, Reserve Bank of New Zealand.
    13. Molenaars, Tomas K. & Reinerink, Nick H. & Hemminga, Marcus A., 2013. "Forecasting the yield curve - Forecast performance of the dynamic Nelson-Siegel model from 1971 to 2008," MPRA Paper 61862, University Library of Munich, Germany.
    14. Choong Tze Chua & Dean Foster & Krishna Ramaswamy & Robert Stine, 2008. "A Dynamic Model for the Forward Curve," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 265-310, January.
    15. Eduardo Mineo & Airlane Pereira Alencar & Marcelo Moura & Antonio Elias Fabris, 2020. "Forecasting the Term Structure of Interest Rates with Dynamic Constrained Smoothing B-Splines," JRFM, MDPI, vol. 13(4), pages 1-14, April.
    16. Christensen, Bent Jesper & van der Wel, Michel, 2019. "An asset pricing approach to testing general term structure models," Journal of Financial Economics, Elsevier, vol. 134(1), pages 165-191.
    17. Anders B. Trolle & Eduardo S. Schwartz, 2006. "A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives," NBER Working Papers 12337, National Bureau of Economic Research, Inc.
    18. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    19. Ranik Raaen Wahlstrøm & Florentina Paraschiv & Michael Schürle, 2022. "A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Versions," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 967-1004, March.
    20. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Effects on the Riskless Yield Curve with Regime Switching Nelson†Siegel Models," Working Papers 639, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:39-59. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.