Quadratic, Affine and Hybrid Gaussian Term Structure Models in Discrete Time: Theory and Evidence

Abstract

This paper explores Affine, Quadratic and Hybrid Term Structure Models in discrete time. Hybrid specification joints ATSM and QTSM with correlated Gaussian state variables. We provide new formulae and a new estimation strategy that make these models implementable. We estimate and extract latent factors of nine specifications (Affine, Quadratic and Hybrid Gaussian types). We analyze the behavior of each model, their capacity to fit moments of data and to reproduce the yield curves shapes. Our empirical results suggest first that Hybrid models with less than two quadratic factors are not worth considering. Second, three-factor Hybrid models have to be favored over ATSMs or QTSMs. Third, all models tend to have similar performance as the number of state factors increases. Fourth, given a number of state factors, Affine, Quadratic or Hybrid models have state factors that vehicle similar information about the level, the slope and the curvature of the yield curve. As an exception, three-factor model Hybrid specifications do not exhibit curvature effect. Finally, only three-factor models have their dynamic performance structurally uncorrelated to the level, the slope and the curvature. However, no model can absorb corresponding huge squared first-order variations.

JEL Classification: G10, G11