Testing continuous-time models of the spot interest rate

Different continuous-time models for interest rates coexistin the literature. We test parametric models by comparing theirimplied parametric density to the same density estimated nonparametrically.We do not replace the continuous-time model by discrete approximations,even though the data are recorded at discrete intervals. Theprincipal source of rejection of existing models is the strongnon-linearity of the drift. Around its mean, where the driftis essentially zero, the spot rate behaves like a random walk.The drift then mean-reverts strongly when far away from themean. The volatility is higher when away from the mean.