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Microstructure noise, realized volatility, and optimal sampling

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  • Jeffrey R. Russell
  • Federico M. Bandi

Abstract

Recorded prices are known to diverge from their "efficient" values due to the presence of market microstructure contaminations. The microstructure noise creates a dichotomy in the model-free estimation of integrated volatility. While it is theoretically necessary to sum squared returns that are computed over very small intervals to better identify the underlying quadratic variation over a period, the summing of numerous contaminated return data entails substantial accumulation of noise. Using asymptotic arguments as in the extant theoretical literature on the subject, we argue that the realized volatility estimator diverges to infinity almost surely when noise plays a role. While realized volatility cannot be a consistent estimate of the quadratic variation of the log price process, we show that a standardized version of the realized volatility estimator can be employed to uncover the second moment of the (unobserved) noise process. More generally, we show that straightforward sample moments of the noisy return data provide consistent estimates of the moments of the noise process. Finally, we quantify the finite sample bias/variance trade-off that is induced by the accumulation of noisy observations and provide clear and easily implementable directions for optimally sampling contaminated high frequency return data for the purpose of volatility estimation

Suggested Citation

  • Jeffrey R. Russell & Federico M. Bandi, 2004. "Microstructure noise, realized volatility, and optimal sampling," Econometric Society 2004 Latin American Meetings 220, Econometric Society.
  • Handle: RePEc:ecm:latm04:220
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    File URL: http://repec.org/esLATM04/up.3725.1082044351.pdf
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    References listed on IDEAS

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    1. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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    4. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
    5. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    6. Roel C.A. Oomen, 2004. "Statistical Models for High Frequency Security Prices," Econometric Society 2004 North American Winter Meetings 77, Econometric Society.
    7. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    8. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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    11. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    12. S. Baranzoni & P. Bianchi & L. Lambertini, 2000. "Multiproduct Firms, Product Differentiation, and Market Structure," Working Papers 368, Dipartimento Scienze Economiche, Universita' di Bologna.
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    Cited by:

    1. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
    3. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2007. "Real-time price discovery in global stock, bond and foreign exchange markets," Journal of International Economics, Elsevier, vol. 73(2), pages 251-277, November.
    4. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
    5. B. Jungbacker & S.J. Koopman, 2005. "Model-based Measurement of Actual Volatility in High-Frequency Data," Tinbergen Institute Discussion Papers 05-002/4, Tinbergen Institute.

    More about this item

    Keywords

    Microstructure noise; realized volatility;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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