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Parametric Estimation Of Diffusion Processes Sampled At First Exit Time

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Author Info
Jaime A. Londoño (Universidad EAFIT)

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Abstract

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross' model and the constant elasticity of variance (CEV) process illustrate the use of the technique proposed herein.

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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 0305002.

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Length: 31 pages
Date of creation: 06 May 2003
Date of revision: 16 Feb 2004
Handle: RePEc:wpa:wuwpem:0305002

Note: Type of Document - Acrobat PDF; prepared on IBM PC - PC- TEX/UNIX Sparc TeX; to print on PostScript; pages: 31 . Paper published in International Journal of Pure and Applied Mathematics 7, No. 4 (2003), 449-486. MR1994830 (2004c:62175).
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Related research
Keywords: Continuous time Markov processes discrete time sampling diffusions interest rate models stochastic algorithms.

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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  1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  4. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August. [Downloadable!] (restricted)
    Other versions:
  5. Gourieroux, C. & Monfort, A & Renault, E., 1992. "Indirect Inference," Papers 9215, Institut National de la Statistique et des Etudes Economiques-.
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  6. 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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  7. 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)
  8. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May. [Downloadable!] (restricted)
  9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  10. Hua He., 1990. "Moment Approximation and Estimation of Diffusion Models of Asset Prices," Research Program in Finance Working Papers RPF-193, University of California at Berkeley.
  11. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Marsh, Terry A & Rosenfeld, Eric R, 1983. " Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, vol. 38(2), pages 635-46, May. [Downloadable!] (restricted)
  13. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January. [Downloadable!] (restricted)
  14. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292. [Downloadable!] (restricted)
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