This paper by Yacine Aït-Sahalia tests the specification of parametric interest rate models by comparing their implied parametric density to the nonparametric density estimated from the data. The author focuses on the short-term spot interest rate and evaluates various models, including the Vasicek, Cox-Ingersoll-Ross, and Courtadon models. The main finding is that the drift of the spot rate process is essentially zero when the rate is between 4% and 17%, but strongly mean-reverts when far from this range. The volatility is higher when the rate is away from the mean. The paper also discusses the limitations of discrete approximations and proposes a test statistic based on the comparison of the marginal and transitional densities. The results suggest that the linearity of the drift and the constant elasticity of variance (CEV) specification of the diffusion are major sources of misspecification. The paper concludes with a discussion of the implications of these findings for the specification of interest rate models and the interpretation of market dynamics.This paper by Yacine Aït-Sahalia tests the specification of parametric interest rate models by comparing their implied parametric density to the nonparametric density estimated from the data. The author focuses on the short-term spot interest rate and evaluates various models, including the Vasicek, Cox-Ingersoll-Ross, and Courtadon models. The main finding is that the drift of the spot rate process is essentially zero when the rate is between 4% and 17%, but strongly mean-reverts when far from this range. The volatility is higher when the rate is away from the mean. The paper also discusses the limitations of discrete approximations and proposes a test statistic based on the comparison of the marginal and transitional densities. The results suggest that the linearity of the drift and the constant elasticity of variance (CEV) specification of the diffusion are major sources of misspecification. The paper concludes with a discussion of the implications of these findings for the specification of interest rate models and the interpretation of market dynamics.