The affine arbitrage-free class of Nelson–Siegel term structure models

We derive the class of affine arbitrage-free dynamic term structure models that approximate the widely used Nelson–Siegel yield curve specification. These arbitrage-free Nelson–Siegel (AFNS) models can be expressed as slightly restricted versions of the canonical representation of the three-factor affine arbitrage-free model. Imposing the Nelson–Siegel structure on the canonical model greatly facilitates estimation and can improve predictive performance. In the future, AFNS models appear likely to be a useful workhorse representation for term structure research.