A Comparison of Alternative Nonparametric Estimators of the Short Rate Diffusion Coefficient

In this paper we discuss the estimation of the diffusion coefficient of one-factor models for the short rate via non-parametric methods. We test the estimators proposed by Ait Sahalia (1996a), Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulation of the Vasicek and CIR model and show that all estimators, especially that proposed by Ait-Sahalia (1996a), are problematic for values of the mean reversion coefficient typically displayed by interest rate data. Moreover all estimators depend crucially on the choice of the bandwith parameter. Data analysis shows that the estimators lead to different estimates on the data set analyzed by Ait-Sahalia (1996a) and Stanton (1997); moreover we show that the two data set are inherently different.