Testing Continuous-Time Models of the Spot Interest Rate
通过比较参数模型隐含密度与非参数估计密度来检验连续时间利率模型，发现漂移项的非线性是模型被拒绝的主要原因，利率在均值附近呈随机游走，远离均值时则强均值回归。
Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied 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. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean. The continuous-time financial theory has developed extensive tools to price derivative securities when the underlying traded asset(s) or nontraded factor(s) follow stochastic differential equations [see Merton (1990) for examples]. However, as a practical matter, how to specify an appropriate stochastic differential equation is for the most part an unanswered question. For example, many different continuous-time The comments and suggestions of Kerry Back (the editor) and an anonymous referee were very helpful. I am also grateful to George Constantinides,