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

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  • Roberto Renò
  • Antonio Roma
  • Stephen Schaefer

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

  • Roberto Renò & Antonio Roma & Stephen Schaefer, 2006. "A Comparison of Alternative Non‐parametric Estimators of the Short Rate Diffusion Coefficient," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 35(3), pages 227-252, November.
    • Handle: RePEc:bla:ecnote:v:35:y:2006:i:3:p:227-252
    DOI: 10.1111/j.1468-0300.2006.00169.x
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    References listed on IDEAS

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    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    5. Hamilton, James D, 1996. "The Daily Market for Federal Funds," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 26-56, February.
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    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    8. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
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    Cited by:

    1. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.

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