A Comparison of Alternative Non-parametric Estimators of the Short Rate Diffusion Coefficient

In this paper we discuss the estimation of the diffusion coefficient in one-factor models for the short rate via non-parametric methods. We test the estimators proposed by Ait-Sahalia (1996), Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulations of the Vasicek and CIR model. We show that the Ait-Sahalia estimator is not applicable for values of the mean reversion coefficient typically displayed by interest rate data, while the Stanton and Bandi-Phillips estimators perform better. Each of the three estimators depends crucially on the choice of the bandwidth parameter. Our analysis shows that the estimators give different results for both the data set analysed by Ait-Sahalia (1996) and by Stanton (1997). Finally we show that the data sets used by Ait-Sahalia and Stanton are inherently different and, in particular, that very short-term data exhibit characteristics which are inconsistent with a diffusion. Copyright 2006 The Authors Journal compilation 2006 Banca Monte dei Paschi di Siena SpA