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Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Lévy Processes

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  • Yong Bao

    ()
    (Department of Economics, Purdue University)

  • Aman Ullah

    ()
    (Department of Economics, University of California,)

  • Yun Wang

    ()
    (School of International Trade and Economics, University of International Business and Economics)

  • Jun Yu

    ()
    (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business, Singapore Management University)

Abstract

This paper develops the approximate finite-sample bias of the ordinary least squares or quasi max- imum likelihood estimator of the mean reversion parameter in continuous-time Levy processes. For the special case of Gaussian processes, our results reduce to those of Tang and Chen (2009) (when the long-run mean is unknown) and Yu (2012) (when the long-run mean is known). Simulations show that in general the approximate bias works well in capturing the true bias of the mean reversion estimator under difference scenarios. However, when the time span is small and the mean reversion parameter is approaching its lower bound, we nd it more difficult to approximate well the finite-sample bias.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 02-2013.

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Date of creation: Mar 2013
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Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:02-2013

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  1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  2. 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.
  3. Jun Yu, 2007. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Working Papers CoFie-06-2008, Sim Kee Boon Institute for Financial Economics, revised Oct 2008.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  6. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488, September.
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Cited by:
  1. Iglesias, Emma M., 2014. "Testing of the mean reversion parameter in continuous time models," Economics Letters, Elsevier, vol. 122(2), pages 187-189.

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