Specification Testing Of Univariate Continuous-Time Interest Rate Models

We propose a general framework for specification testing of univariate continuous-time stationary interest rate models, as a complement to AÐt-Sahalia (1996) and Pritsker (1998). Based on the Pearson families of distributions [Cramer (1946), Wong (1964)], we define a class of stationary distributions that encompasses many of those in the most used models of the finance literature, such as the Vasicek (1977) and Cox-Ingersoll-Ross (1985) models, among others. By rejecting a general class given by the corresponding differential equation, one can strongly reject the models which are nested within this particular class. This avoids ad hoc choices of interest rate models and the mispricing of interest rate derivative securities. The test statistic consists on a comparison between the nonparametric density estimate and a term combining estimated coefficients of the drift and volatility functions. As the Generalized Method of Moments estimator is unidentified, alternative ways of computing the statistics are developed. Finally, we provide an application of the procedure and discuss its multivariate extensions.