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Linearized Nelson–Siegel and Svensson models for the estimation of spot interest rates

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  • Gauthier, Geneviève
  • Simonato, Jean-Guy

Abstract

Linearized versions of the Nelson–Siegel (1987) and Svensson (1994) models for the cross-sectional estimation of spot yield curves from samples of coupon bonds are developed and analyzed. It is shown how these models can be made linear in the level, slope and curvature parameters and how prior information about these parameters can be incorporated in the estimation procedure. The performance of the linearized models are assessed in a Monte Carlo setting and with a sample of US government bonds. The results reveal that the linearized models compare favorably to the original models in terms of parameter estimates stability, computing effort and prevalence of local optima.

Suggested Citation

  • Gauthier, Geneviève & Simonato, Jean-Guy, 2012. "Linearized Nelson–Siegel and Svensson models for the estimation of spot interest rates," European Journal of Operational Research, Elsevier, vol. 219(2), pages 442-451.
  • Handle: RePEc:eee:ejores:v:219:y:2012:i:2:p:442-451
    DOI: 10.1016/j.ejor.2012.01.004
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    References listed on IDEAS

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    1. 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.
    2. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    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. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    5. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
    6. Edwin J. Elton, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, February.
    7. Bank for International Settlements, 2005. "Zero-coupon yield curves: technical documentation," BIS Papers, Bank for International Settlements, number 25, November.
    8. Gurkaynak, Refet S. & Sack, Brian & Wright, Jonathan H., 2007. "The U.S. Treasury yield curve: 1961 to the present," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2291-2304, November.
    9. 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.
    10. Bolder, David & Streliski, David, 1999. "Yield Curve Modelling at the Bank of Canada," Technical Reports 84, Bank of Canada.
    11. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
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    Cited by:

    1. Hana Hladíková & Jarmila Radová, 2012. "Term Structure Modelling by Using Nelson-Siegel Model," European Financial and Accounting Journal, University of Economics, Prague, vol. 2012(2), pages 36-55.
    2. Lorenčič Eva, 2016. "Testing the Performance of Cubic Splines and Nelson-Siegel Model for Estimating the Zero-coupon Yield Curve," Naše gospodarstvo/Our economy, De Gruyter Open, vol. 62(2), pages 42-50, June.
    3. Blomvall, Jörgen, 2017. "Measurement of interest rates using a convex optimization model," European Journal of Operational Research, Elsevier, vol. 256(1), pages 308-316.
    4. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    5. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.

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