Tests of Non Linear Gaussian Term Structure Models

After the 2007-2009 financial crisis Government bond yields in US, Germany, UK and elsewhere have approached Japan-type Government bond yields, thus challenging known dynamic term structure models that cannot constrain yields to be always positive. Therefore this paper tests term structure models whereby the instantaneous short interest rate is a non-negative, non-linear function of latent factors that follow independent Ornstein-Uhlenbeck processes. These models, which we refer to as non-affine Gaussian term structure models (NAGTSM) encompass the quadratic, Black and Black-Karasinski models. The empirical evidence reveals that three factor NAGTSM and Vasicek models fi t US and German yields to a similar degree, except for the very low short maturity US yields after 2007, which the Vasicek model cannot fit very well. Three factor quadratic models generally display the worst fit to US and German yields