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Yield Curve Estimation by Kernel Smoothing Methods

Author

Listed:
  • Oliver Linton
  • Enno Mammen
  • Jens Perch Nielsen
  • C Tanggaard

Abstract

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not explicit and our estimation procedure is iterative, rather like the backfitting method of estimating additive nonparametric models. We establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients. The rate of convergence is standard for one dimensional nonparametric regression. We investigate the finite sample performance of our method, in comparison with other well-established methods, in a small simulation experiment.

Suggested Citation

  • Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield Curve Estimation by Kernel Smoothing Methods," STICERD - Econometrics Paper Series 385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:385
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    1. is not listed on IDEAS
    2. Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2010. "Bayesian extensions to Diebold-Li term structure model," International Review of Financial Analysis, Elsevier, vol. 19(5), pages 342-350, December.
    3. David Bolder & Scott Gusba, 2002. "Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada," Staff Working Papers 02-29, Bank of Canada.
    4. Oleksandr Castello & Marina Resta, 2025. "Optimal Time Varying Parameters in Yield Curve Modeling and Forecasting: A Simulation Study on BRICS Countries," Computational Economics, Springer;Society for Computational Economics, vol. 65(4), pages 2081-2113, April.
    5. Vadim Kaushanskiy & Victor Lapshin, 2016. "A nonparametric method for term structure fitting with automatic smoothing," Applied Economics, Taylor & Francis Journals, vol. 48(58), pages 5654-5666, December.
    6. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    7. Lorenčič Eva, 2016. "Testing the Performance of Cubic Splines and Nelson-Siegel Model for Estimating the Zero-coupon Yield Curve," Naše gospodarstvo/Our economy, Sciendo, vol. 62(2), pages 42-50, June.
    8. Liu, Yan & Wu, Jing Cynthia, 2021. "Reconstructing the yield curve," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1395-1425.
    9. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org, revised Sep 2025.
    10. Koo, B. & La Vecchia, D. & Linton, O., 2019. "Nonparametric Recovery of the Yield Curve Evolution from Cross-Section and Time Series Information," Cambridge Working Papers in Economics 1916, Faculty of Economics, University of Cambridge.
    11. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.
    12. Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(2), pages 258-278, April.
    13. Tong, Xiaojun & He, Zhuoqiong Chong & Sun, Dongchu, 2018. "Estimating Chinese Treasury yield curves with Bayesian smoothing splines," Econometrics and Statistics, Elsevier, vol. 8(C), pages 94-124.
    14. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Ivailo Arsov & Matthew Brooks & Mitch Kosev, 2013. "New Measures of Australian Corporate Credit Spreads," RBA Bulletin (Print copy discontinued), Reserve Bank of Australia, pages 15-26, December.
    16. Wali Ullah & Yasumasa Matsuda & Yoshihiko Tsukuda, 2014. "Dynamics of the term structure of interest rates and monetary policy: is monetary policy effective during zero interest rate policy?," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 546-572, March.
    17. Tatyana Krivobokova & Göran Kauermann & Theofanis Archontakis, 2006. "Estimating the term structure of interest rates using penalized splines," Statistical Papers, Springer, vol. 47(3), pages 443-459, June.
    18. Koo, Bonsoo & La Vecchia, Davide & Linton, Oliver, 2021. "Estimation of a nonparametric model for bond prices from cross-section and time series information," Journal of Econometrics, Elsevier, vol. 220(2), pages 562-588.
    19. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    20. Cai, Junyang & Zhou, Jian, 2022. "How many asymptomatic cases were unconfirmed in the US COVID-19 pandemic? The evidence from a serological survey," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    21. Andrew Jeffrey & Oliver Linton & Thong Nguyen, 2006. "Flexible Term Structure Estimation: Which Method is Preferred?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(1), pages 99-122, February.
    22. Michiel De Pooter, 2007. "Examining the Nelson-Siegel Class of Term Structure Models," Tinbergen Institute Discussion Papers 07-043/4, Tinbergen Institute.
    23. Hiroyuki Kawakatsu, 2020. "Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors," Stats, MDPI, vol. 3(3), pages 1-46, August.

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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