A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

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A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

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Leo Krippner

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Leo Krippner

Abstract

A popular class of yield curve models is based on the Nelson and Siegel approach of 'fitting’ yield curve data with simple functions of maturity. However, such models cannot be consistent across time. This article addresses that deficiency by deriving an intertemporally consistent and arbitrage-free version of the Nelson and Siegel model. Adding this theoretical consistency expands the potential applications of the Nelson and Siegel approach to exercises involving a time-series context, such as forecasting the yield curve and pricing interest rate derivatives. As a practical example, the intertemporal consistency of the model is exploited to derive a theoretical framework for forecasting the yield curve. The empirical application of that framework to United States data results in out-of-sample forecasts that outperform the random walk over the sample period of almost 50 years, for forecast horizons ranging from six months to three years.

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Publisher Info
Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 1 (March)
Pages: 39-59
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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:39-59

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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.:

Arturo Estrella & Anthony P. Rodrigues & Sebastian Schich, 2000. "How stable is the predictive power of the yield curve? evidence from Germany and the United States," Staff Reports 113, Federal Reserve Bank of New York. [Downloadable!]
Other versions:
- Arturo Estrella & Anthony P. Rodrigues & Sebastian Schich, 2003. "How Stable is the Predictive Power of the Yield Curve? Evidence from Germany and the United States," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 629-644, 07. [Downloadable!] (restricted)
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)
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)
Francis X. Diebold & Canlin Li, 2002. "Forecasting the Term Structure of Government Bond Yields," Center for Financial Institutions Working Papers 02-34, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
Other versions:
- Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
- Francis X. Diebold & Canlin Li, 2004. "Forecasting the Term Structure of Government Bond Yields," CFS Working Paper Series 2004/09, Center for Financial Studies. [Downloadable!]
- 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. [Downloadable!] (restricted)
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.
Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
Other versions:
- Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
- Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.

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.)

Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The Affine Arbitrage-Free Class of: Nelson-Siegel Term Structure Models," NBER Working Papers 13611, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Other versions:
- Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The affine arbitrage-free class of Nelson-Siegel term structure models," Working Paper Series 2007-20, Federal Reserve Bank of San Francisco. [Downloadable!]
- Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models," PIER Working Paper Archive 07-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
Leo Krippner, 2005. "A New Framework for Yield Curve, Output and Inflation Relationships," Working Papers in Economics 05/07, University of Waikato, Department of Economics. [Downloadable!]
Leo Krippner, 2009. "A theoretical foundation for the Nelson and Siegel class of yield curve models," Reserve Bank of New Zealand Discussion Paper Series DP2009/10, Reserve Bank of New Zealand. [Downloadable!]
Leo Krippner, 2006. "A Yield Curve Perspective on Uncovered Interest Parity," Working Papers in Economics 06/16, University of Waikato, Department of Economics. [Downloadable!]
Leo Krippner, 2008. "A Macroeconomic Foundation for the Nelson and Siegel Class of Yield Curve Models," Research Paper Series 226, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]

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