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

26 Pages Posted: 21 Mar 2007

See all articles by Roberto Renò

Roberto Renò

University of Verona - Department of Economics

Antonio Roma

Universita di Siena

Stephen M. Schaefer

London Business School - Institute of Finance and Accounting

Abstract

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.

Suggested Citation

Renò, Roberto and Roma, Antonio and Schaefer, Stephen M., A Comparison of Alternative Non-Parametric Estimators of the Short Rate Diffusion Coefficient. Economic Notes, Vol. 35, No. 3, pp. 227-252, November 2006. Available at SSRN: https://ssrn.com/abstract=975360 or http://dx.doi.org/10.1111/j.1468-0300.2006.00169.x

Roberto Renò (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Antonio Roma

Universita di Siena ( email )

Via Banchi di Sotto, 55
I-53100 Siena
Italy

Stephen M. Schaefer

London Business School - Institute of Finance and Accounting ( email )

Sussex Place
Regent's Park
London NW1 4SA
United Kingdom
+44 171 706 6887 (Phone)
+44 171 724 3317 (Fax)

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