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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.

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File URL: http://alcor.concordia.ca/~gospodin/research/diffusion.pdf
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Bibliographic Info

Paper provided by Concordia University, Department of Economics in its series Working Papers with number 08011.

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Length: 34 pages
Date of creation: Oct 2008
Date of revision: Dec 2008
Handle: RePEc:crd:wpaper:08011

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

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References

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  1. 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.
  2. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
  3. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
  4. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
  5. J. Gustafsson & M. Hagmann & J.P. Nielsen & O. Scaillet, 2006. "Local Transformation Kernel Density Estimation of Loss Distributions," Swiss Finance Institute Research Paper Series 06-32, Swiss Finance Institute, revised Jun 2007.
  6. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
  7. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
  8. 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.
  9. 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.
  10. 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.
  11. Dennis Kristensen, 2004. "Estimation of partial differential equations with applications in finance," LSE Research Online Documents on Economics 24738, London School of Economics and Political Science, LSE Library.
  12. 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.
  13. 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.
  14. Olivier RENAULT & Olivier SCAILLET, 2003. "On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities," FAME Research Paper Series rp83, International Center for Financial Asset Management and Engineering.
  15. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
  16. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
  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.
  18. Nicolau, Jo o, 2003. "Bias Reduction In Nonparametric Diffusion Coefficient Estimation," Econometric Theory, Cambridge University Press, vol. 19(05), pages 754-777, October.
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Cited by:
  1. Debopam Bhattacharya & Shin Kanaya & Margaret Stevens, 2012. "Are University Admissions Academically Fair?," Economics Series Working Papers 608, University of Oxford, Department of Economics.

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