YIELD CURVE ESTIMATION BY KERNEL SMOOTHING METHODS by O Linton1, E Mammen2, J Nielsen3, and C Tanggaard4
Contents: Abstract 1. Introduction 2. Smoothing of Pure Discount Bond Yields 3. Smoothing of Coupon Bonds 4. Asymptotic Properties 5. Simulation Study 6. Concluding Comment Appendix: Proof of Theorems References Tables 1 – 4
The Suntory Centre Suntory and Toyota International Centres for Economics and Related Disciplines London School of Economics and Political Science Houghton Street London WC2A 2AE Tel.: 020 7405 7686
Discussion Paper No. EM/00/385 April 2000
Affiliations and acknowledgements: 1
London School of Economics and Yale University. E-mail:
[email protected] Research was supported by the National Science Foundation, the Danish Social Research Council, and the North Atlantic Treaty Organization. Thanks go to Frank Diebold and two referees, to Olaf Bunke, Greg Connor, Stewart Hodges, Andrew Jeffrey, Thong Nguyen, and Peter Phillips for helpful comments. 2
Institut für Angewandte Mathematik, Ruprechts-Karls-Universität Heidelberg, Germany. Supported by the Deutsche Forschungsgemeinschaft, Sonderforschungs-bereich 373 “Quantifikation und Simulation Ökonomischer Prozesse”, Humboldt-Universität zu Berlin und
Project MA1026/6-1. E-mail:
[email protected] 3
Codan,
60
Gammel
Kongevej,
DK-1790
Copenhagen
V,
Denmark.
E-mail:
npj@codan,dk Research is supported by Bergiafonden and the Danish Social Science Research Council. 4
Department of Finance, The Aarhus School of Business, Denmark. E-mail:
[email protected] Research is supported by the Danish Social Science Research Council.
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.
Keywords: Coupon bonds; kernel estimation; Hilbert space; nonparametric regression; term structure estimation; yield curve; zero coupon. JEL Nos.: C14, G12.
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