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The Yield Curve Under Nelson-Siegel

Rodrigo Alfaro ()

Working Papers Central Bank of Chile from Central Bank of Chile

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.

Date: 2009-10
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