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Nonparametric Estimation of the Diffusion Coefficient via Fourier Analysis, with Aplication to Short Rate Modeling

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Roberto Reno' ()
Abstract

In this paper a new fully nonparametric estimator of the diffusion coefficient is introduced, based on Fourier analysis of the observed trajectory. The proposed estimator is proved to be consistent and asymptotically normally distributed. After testing the estimator on Monte Carlo simulations, we use it to estimate an univariate model of the short rate with available interest rate data. Data analysis helps shedding new light on the functional form of the diffusion coefficient.

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Paper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 440.

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Date of creation: Nov 2004
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Handle: RePEc:usi:wpaper:440

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

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  1. 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 1209-27, July. [Downloadable!] (restricted)
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  3. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 449-87.
  4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  5. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
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  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  8. repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
  9. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility and the GARCH forecasting performance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 12(3), pages 183-200, July. [Downloadable!] (restricted)
  10. 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, 02. [Downloadable!] (restricted)
  11. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July. [Downloadable!] (restricted)
  12. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  13. Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June. [Downloadable!] (restricted)
  14. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA. [Downloadable!]
  15. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61. [Downloadable!] (restricted)
  16. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  17. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 793-843, July. [Downloadable!] (restricted)
  18. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 763-806.
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  19. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
    Other versions:
  20. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility of diffusion processes with high frequency data," Economics Letters, Elsevier, vol. 74(3), pages 371-378, February. [Downloadable!] (restricted)
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