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Estimating Yield Curves by Kernel Smoothing Methods

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Author Info
Oliver Linton (Cowles Foundation, Yale University)
E. Mammen (Ruprecht-Karls-Universitat Heidelberg)
J. Nielsen
C. Tanggaard (The Aarhus School of Business)

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Abstract

We introduce a new method for the estimation of discount functions, yield curves and forward curves for 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 important 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.

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1205.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1205.

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Length: 50 pages
Date of creation: Dec 1998
Date of revision:
Handle: RePEc:cwl:cwldpp:1205

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Coupon bonds; forward curve; Hilbert space; local linear; nonparametric regression; yield curve;

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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. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January. [Downloadable!] (restricted)
  2. Linton, Oliver B., 2000. "Efficient Estimation Of Generalized Additive Nonparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 16(04), pages 502-523, August. [Downloadable!]
  3. Marti G. Subrahmanyam & Young Ho Eom & Jun Uno, 1998. "Coupon Effects and the Pricing of Japanese Government Bonds: An Empirical Analysis," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-078, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  4. Mark Fisher & Douglas Nychka & David Zervos, 1995. "Fitting the term structure of interest rates with smoothing splines," Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (U.S.).
  5. J. P. Nielsen & O. B. Linton, . "An Optimization Interpretation of Integration and Backfitting Estimators for Separable Nonparametric Models," Sonderforschungsbereich 373 1996-88, Humboldt Universitaet Berlin.
  6. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  7. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
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  8. Engsted, Tom & Tanggaard, Carsten, 1995. " The Predictive Power of Yield Spreads for Future Interest Rates: Evidence from the Danish Term Structure," Scandinavian Journal of Economics, Blackwell Publishing, vol. 97(1), pages 145-59, March.
  9. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation, Yale University. [Downloadable!]
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  10. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  12. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-76, November. [Downloadable!] (restricted)
  13. Jordan, James V, 1984. " Tax Effects in Term Structure Estimation," Journal of Finance, American Finance Association, vol. 39(2), pages 393-406, June. [Downloadable!] (restricted)
  14. Frankel, Jeffrey A & Lown, Cara S, 1994. "An Indicator of Future Inflation Extracted from the Steepness of the Interest Rate Yield Curve along Its Entire Length," The Quarterly Journal of Economics, MIT Press, vol. 109(2), pages 517-30, May. [Downloadable!] (restricted)
    Other versions:
  15. Campbell, John Y & Shiller, Robert J, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 495-514, May. [Downloadable!] (restricted)
    Other versions:
  16. Arturo Estrella & Frederic S. Mishkin, 1996. "Predicting U.S. recessions: financial variables as leading indicators," Research Paper 9609, Federal Reserve Bank of New York. [Downloadable!]
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  17. Tanggaard, Carsten, 1997. " Nonparametric Smoothing of Yield Curves," Review of Quantitative Finance and Accounting, Springer, vol. 9(3), pages 251-67, October. [Downloadable!] (restricted)
  18. Dahlquist, Magnus & Svensson, Lars E O, 1996. " Estimating the Term Structure of Interest Rates for Monetary Policy Analysis," Scandinavian Journal of Economics, Blackwell Publishing, vol. 98(2), pages 163-83, June.
  19. Andrew Chesher, 1997. "Diet Revealed?: Semiparametric Estimation of Nutrient Intake-Age Relationships," Journal Of The Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 389-428. [Downloadable!] (restricted)
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. Andrew Jeffrey & Oliver Linton & Thong Nguyen, 2006. "Flexible Term Structure Estimation: Which Method is Preferred?," Metrika, Springer, vol. 63(1), pages 99-122, February. [Downloadable!] (restricted)
    Other versions:
  2. Laurini, Márcio P. & Hotta, Luiz K., 2008. "Bayesian extensions to diebold-li term structure model," Ibmec Working Papers wpe_120, Ibmec Working Paper, Ibmec São Paulo. [Downloadable!]
  3. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  4. Michael Wegener & Göran Kauermann, 2008. "Examining heterogeneity in implied equity risk premium using penalized splines," AStA Advances in Statistical Analysis, Springer, vol. 92(1), pages 35-56, February. [Downloadable!] (restricted)
  5. Oliver Linton & Yoon-Jae Whang, 2000. "Nonparametric Estimation with Aggregated Data," STICERD - Econometrics Paper Series /2000/397, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  6. Laurini, Márcio P. & Moura, Marcelo, 2007. "Constrained Smoothing Splines for the Term Structure of Interest Rates," Ibmec Working Papers wpe_98, Ibmec Working Paper, Ibmec São Paulo. [Downloadable!]
  7. Andrew Jeffrey & Linton, Oliver Linton & Thong Nguyen & Peter C.B. Phillips, 2001. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Cowles Foundation Discussion Papers 1311, Cowles Foundation, Yale University. [Downloadable!]
  8. David Jamieson Bolder & Scott Gusba, 2002. "Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada," Working Papers 02-29, Bank of Canada. [Downloadable!]
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