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Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels

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Abstract

This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed estimators are evaluated in the context of bond and option pricing. We also present estimation results from empirical analysis of the term structure of U.S. interest rates.

Suggested Citation

  • Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.
  • Handle: RePEc:crd:wpaper:08011
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    File URL: http://alcor.concordia.ca/~gospodin/research/diffusion.pdf
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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(05), pages 615-645, October.
    2. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, pages 199-223.
    3. 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.
    4. Jiang, George J., 1998. "Nonparametric Modeling of U.S. Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(04), pages 465-497, December.
    5. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, pages 213-249.
    6. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
    7. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    8. Gustafsson, J. & Hagmann, M. & Nielsen, J. P. & Scaillet, O., 2009. "Local Transformation Kernel Density Estimation of Loss Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 161-175.
    9. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    10. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    11. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 310-345.
    12. Renault, Olivier & Scaillet, Olivier, 2004. "On the way to recovery: A nonparametric bias free estimation of recovery rate densities," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2915-2931, December.
    13. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
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    16. 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.
    17. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(02), pages 390-412, April.
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    1. Debopam Bhattacharya & Shin Kanaya & Margaret Stevens, 2017. "Are University Admissions Academically Fair?," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 449-464, July.

    More about this item

    Keywords

    Nonparametric regression; Gamma kernel; diffusion estimation; spot interest rate; derivative pricing;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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