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Calibrating the Nelson–Siegel–Svensson model

Author

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  • Manfred Gilli
  • Stefan Große
  • Enrico Schumann

Abstract

The Nelson–Siegel–Svensson model is widely-used for modelling the yield curve, yet many authors have reported ‘numerical difficulties’ when calibrating the model. We argue that the problem is twofold: firstly, the optimisation problem is not convex and has multiple local optima. Hence standard methods that are readily available in statistical packages are not appropriate. We implement and test an optimisation heuristic, Differential Evolution, and show that it is capable of reliably solving the model. Secondly, we also stress that in certain ranges of the parameters, the model is badly conditioned, thus estimated parameters are unstable given small perturbations of the data. We discuss to what extent these difficulties affect applications of the model.

Suggested Citation

  • Manfred Gilli & Stefan Große & Enrico Schumann, 2010. "Calibrating the Nelson–Siegel–Svensson model," Working Papers 031, COMISEF.
    • Handle: RePEc:com:wpaper:031
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    References listed on IDEAS

    as
    1. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    2. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    3. 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.
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    Cited by:

    1. Groll, Andreas & López-Cabrera, Brenda & Meyer-Brandis, Thilo, 2016. "A consistent two-factor model for pricing temperature derivatives," Energy Economics, Elsevier, vol. 55(C), pages 112-126.
    2. Karahan, Cenk C. & Soykök, Emre, 2023. "On illiquidity of an emerging sovereign bond market," Economic Systems, Elsevier, vol. 47(2).
    3. 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.
    4. Virmani, Vineet, 2013. "On the Choice of Optimization Routine in Estimation of Parsimonious Term Structure Models: Results from the Svensson Model," IIMA Working Papers WP2013-01-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Molenaars, Tomas K. & Reinerink, Nick H. & Hemminga, Marcus A., 2015. "Forecasting the yield curve: art or science?," MPRA Paper 61917, University Library of Munich, Germany.
    6. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.
    7. Cousin, Areski & Maatouk, Hassan & Rullière, Didier, 2016. "Kriging of financial term-structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 631-648.
    8. Francisco Ibáñez, 2016. "Calibrating the Dynamic Nelson-Siegel Model: A Practitioner Approach," Working Papers Central Bank of Chile 774, Central Bank of Chile.
    9. Grochola, Nicolaus, 2023. "The influence of negative interest rates on life insurance companies," ICIR Working Paper Series 53/23, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    10. Luchelle Soobyah & Daan Steenkamp, 2020. "Term premium and rate expectation estimates from the South African yield curve," Working Papers 9998, South African Reserve Bank.
    11. Agnieszka Konicz & David Pisinger & Alex Weissensteiner, 2015. "Optimal annuity portfolio under inflation risk," Computational Management Science, Springer, vol. 12(3), pages 461-488, July.
    12. Eran Raviv, 2013. "Prediction Bias Correction for Dynamic Term Structure Models," Tinbergen Institute Discussion Papers 13-041/III, Tinbergen Institute.
    13. Ibanez, Francisco, 2015. "Calibrating the Dynamic Nelson-Siegel Model: A Practitioner Approach," MPRA Paper 68377, University Library of Munich, Germany.
    14. Michał Brzoza-Brzezina & Jacek Kotłowski, 2014. "Measuring the natural yield curve," Applied Economics, Taylor & Francis Journals, vol. 46(17), pages 2052-2065, June.
    15. Mantilla-Garcia, Daniel & Martellini, Lionel & Garcia-Huitrón, Manuel E. & Martinez-Carrasco, Miguel A., 2024. "Back to the funding ratio! Addressing the duration puzzle and retirement income risk of defined contribution pension plans," Journal of Banking & Finance, Elsevier, vol. 159(C).
    16. Maria Teresa Medeiros Garcia & Vítor Hugo Ferreira Carvalho, 2018. "A static approach to the Nelson-Siegel-Svensson model: an application for several negative yield cases," Working Papers REM 2018/35, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    17. Francisco Rivadeneyra, 2012. "The U.S.-Dollar Supranational Zero-Coupon Curve," Discussion Papers 12-5, Bank of Canada.
    18. repec:hum:wpaper:sfb649dp2014-006 is not listed on IDEAS
    19. Asif Lakhany & Andrej Pintar & Amber Zhang, 2021. "Calibrating the Nelson-Siegel-Svensson Model by Genetic Algorithm," Papers 2108.01760, arXiv.org.
    20. Dang-Nguyen, Stéphane & Le Caillec, Jean-Marc & Hillion, Alain, 2014. "The deterministic shift extension and the affine dynamic Nelson–Siegel model," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 402-417.

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