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A simple microstructure return model explaining microstructure noise and Epps effects

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  • A. Saichev
  • D. Sornette
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    Abstract

    We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time scale used to estimate it. Paradoxically, the Epps effect states that cross correlations between asset returns are increasing functions of the time scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time scale in the presence of the long memory process (i).

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    File URL: http://arxiv.org/pdf/1202.3915
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    Paper provided by arXiv.org in its series Papers with number 1202.3915.

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    Date of creation: Feb 2012
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    Publication status: Published in International Journal of Modern Physics C 25 (6),1450012 (36 pages) (2014)
    Handle: RePEc:arx:papers:1202.3915

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    1. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 79(3), pages 655-692, March.
    2. Yacine A\"it-Sahalia & Jialin Yu, 2009. "High frequency market microstructure noise estimates and liquidity measures," Papers 0906.1444, arXiv.org.
    3. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
    4. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 387(8), pages 2025-2034.
    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
    6. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 68-104.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    8. Enrico Scalas, 2006. "Mixtures of compound Poisson processes as models of tick-by-tick financial data," Papers physics/0608217, arXiv.org.
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