A Theoretical Foundation for the Nelson and Siegel Class of Yield Curve Models

Abstract

This article establishes that most yield curve models within the popular Nelson and Siegel (1987, hereafter NS) class may be obtained as a formal Taylor approximation to the dynamic component of the generic Gaussian affine term structure model outlined in Dai and Singleton (2002). That fundamental theoretical foundation provides an assurance to users of NS models that they correspond to a well-accepted set of principles and assumptions for modeling the yield curve and its dynamics. Indeed, arbitrage-free NS models will parsimoniously and reliably represent the data generated by any Gaussian affine term structure model regardless of its true number of underlying factors and specification, and even non-arbitrage-free NS models will adequately capture the dynamics of the state variables. Combined with the well-established practical benefits of applying NS models, the theoretical foundation provides a compelling case for applying NS models as standard tools for yield curve modeling and analysis in economics and finance. As an illustration, this article develops a two-factor arbitrage-free NS model and applies it to testing for changes in United States yield curve dynamics. The results confirm those of Rudebusch and Wu (2007) based on a latent two-factor essentially affine term structure model: there was a material change in the behavior of the yield curve between the sample prior to 1988 and the sample from 1988 onwards.