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


  • Roberto Reno'


  • Antonio Roma


  • Stephen Schaefer



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.

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  • Roberto Reno' & Antonio Roma & Stephen Schaefer, 2004. "A Comparison of Alternative Nonparametric Estimators of the Short Rate Diffusion Coefficient," Department of Economics University of Siena 445, Department of Economics, University of Siena.
  • Handle: RePEc:usi:wpaper:445

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    References listed on IDEAS

    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    3. Duffee, Gregory R, 1996. " Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-551, June.
    4. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    5. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    8. 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.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    10. Bianchi, C. & Cesari, R. & Panattoni, L., 1994. "Alternative Estimators of the Cox, ingersoll and Ross Model of the Term Structure of Interest Rates: A Monte Carlo Comparison," Papers 236, Banca Italia - Servizio di Studi.
    11. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    12. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    13. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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