A theoretical foundation for the Nelson and Siegel class of yield curve models, and an empirical application to U.S. yield curve dynamics

Release date
01/11/2010
Reference
DP2010/11
Author
Leo Krippner
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 a¢ ne 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 a¢ ne 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.