The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models

Abstract

We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.

Keywords: arbitrage, Nelson-Siegel, term structure, factor models, forecast accuracy

JEL Classification: C5, G1, E4