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

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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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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394367
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 1 ()
Pages: 39-59

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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:39-59

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Related research

Keywords: Yield curve; term structure of interest rates; Nelson and Siegel model; Heath-Jarrow-Morton framework;

References

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  1. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
  2. Dahlquist, Magnus & Svensson, Lars E O, 1996. " Estimating the Term Structure of Interest Rates for Monetary Policy Analysis," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 163-83, June.
  3. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
  4. 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.
  5. 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.
  6. 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.
  7. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  8. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Leo Krippner, 2014. "Measuring the stance of monetary policy in conventional and unconventional environments," CAMA Working Papers 2014-06, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  4. Leo Krippner, 2006. "A Yield Curve Perspective on Uncovered Interest Parity," Working Papers in Economics 06/16, University of Waikato, Department of Economics.
  5. 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.
  6. Leo Krippner, 2010. "Connecting the dots: a yield curve perspective on New Zealand’s interest rates," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 73, September.
  7. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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