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The Yield Curve Under Nelson-Siegel

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  • Rodrigo Alfaro

Abstract

Nelson and Siegel (1987) propose a parametric model for the yield curve. Since it is easy to estimate, it became popular among practitioners and Central Bank’s analysts. Diebold and Li (2006) provide a dynamic version of the Nelson-Siegel (DNS) model, showing that it performs well in outof- sample forecasting exercises. However, the model was originally proposed as a curve-fitting tool as opposed to being obtained from a theoretical non-arbitrage framework. Christensen et al. (2009) show that the DNS model is arbitrage-free, giving it theoretical support. In this paper we consider a discrete version of the DNS model, and following the notation developed in Campbell et al. (1997), we show that it belongs to the class of affine-yield model. This provides an alternative proof of the one presented in Christensen et al. (2009), since we use the Euler Equation to show that the yield on a bond is linear in three factors. As in Balduzzi et al. (1998), one of these factors is unobserved, whereas the observed ones can be associated with the long term interest rate and the term spread, respectively. Finally, we discuss the implications of the DNS model for forward rate and the neutral interest rate.

Suggested Citation

  • Rodrigo Alfaro, 2009. "The Yield Curve Under Nelson-Siegel," Working Papers Central Bank of Chile 531, Central Bank of Chile.
    • Handle: RePEc:chb:bcchwp:531
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    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. J.Marcelo Ochoa, 2006. "An interpretation of an affine term structure model of Chile," Estudios de Economia, University of Chile, Department of Economics, vol. 33(2 Year 20), pages 155-184, December.
    3. Luis Oscar Herrera & Igal Magendzo, 1997. "Expectativas Financieras y la Curva de Tasas Forward de Chile," Working Papers Central Bank of Chile 23, Central Bank of Chile.
    4. Marco Morales, 2010. "The real yield curve and macroeconomic factors in the Chilean economy," Applied Economics, Taylor & Francis Journals, vol. 42(27), pages 3533-3545.
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