A theoretical foundation for the Nelson-Siegel class of yield curve models

Yield curve models within the popular Nelson–Siegel class are shown to arise from formal low-order Taylor approximations of the generic Gaussian affine term structure model. Extensive empirical testing on government and bank-risk yield curve datasets for the five largest industrial economies shows that the arbitrage-free three-factor (Level, Slope, Curvature) Nelson–Siegel model generally provides an acceptable representation of the data relative to the three-factor Gaussian affine term structure model. The combined theoretical foundation and empirical evidence means that Nelson–Siegel models may be applied and interpreted from the perspective of Gaussian affine term structure models that already have firm statistical and theoretical foundations in the literature.