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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'

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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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  1. Gregory R. Duffee, 1994. "Idiosyncratic variation of Treasury bill yields," Finance and Economics Discussion Series 94-28, Board of Governors of the Federal Reserve System (U.S.).
  2. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA.
  3. 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.
  4. David A. Chapman & John B. Long Jr. & Neil D. Pearson, 1998. "Using Proxies for the Short Rate: When are Three Months Like an Instant?," Finance 9808004, EconWPA, revised 07 Oct 1998.
  5. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
  6. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  7. 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.
  8. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  9. 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.
  10. 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.
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  13. repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
  14. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
  15. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  16. 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.
  17. 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.
  18. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  19. 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 449-87.
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