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


  • 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)


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.

Suggested Citation

  • Yong Bao & Aman Ullah & Yun Wang & Jun Yu, 2013. "Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Lévy Processes," Working Papers 02-2013, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:02-2013

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    References listed on IDEAS

    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    4. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    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. 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 637-654, May-June.
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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.
    2. Bao, Yong & Ullah, Aman & Wang, Yun & Yu, Jun, 2015. "Bias in the estimation of mean reversion in continuous-time Lévy processes," Economics Letters, Elsevier, vol. 134(C), pages 16-19.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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