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Estimating the efficient price from the order flow: A Brownian Cox process approach

Author

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  • Delattre, Sylvain
  • Robert, Christian Y.
  • Rosenbaum, Mathieu

Abstract

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price, etc.). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price from the order flow.

Suggested Citation

  • Delattre, Sylvain & Robert, Christian Y. & Rosenbaum, Mathieu, 2013. "Estimating the efficient price from the order flow: A Brownian Cox process approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2603-2619.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:7:p:2603-2619
    DOI: 10.1016/j.spa.2013.04.012
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    References listed on IDEAS

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    1. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    2. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
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    Citations

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    Cited by:

    1. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    2. N Baradel & B Bouchard & Ngoc Minh Dang, 2016. "Optimal trading with online parameters revisions," Papers 1604.06342, arXiv.org.
    3. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2019. "Optimal make-take fees for market making regulation," Working Papers hal-02379592, HAL.
    4. Pierre Perron & Eduardo Zorita & Wen Cao & Clifford Hurvich & Philippe Soulier, 2017. "Drift in Transaction-Level Asset Price Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 769-790, September.
    5. Valenzuela, Marcela & Zer, Ilknur & Fryzlewicz, Piotr & Rheinländer, Thorsten, 2015. "Relative liquidity and future volatility," Journal of Financial Markets, Elsevier, vol. 24(C), pages 25-48.
    6. Thibault Jaisson, 2015. "Liquidity and Impact in Fair Markets," Papers 1506.02507, arXiv.org.
    7. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    8. Friedrich Hubalek & Paul Kruhner & Thorsten Rheinlander, 2017. "Brownian trading excursions and avalanches," Papers 1701.00993, arXiv.org.
    9. N. Baradel & Bruno Bouchard & N. m. Dang, 2016. "Optimal Trading with Online Parameter Revisions," Post-Print hal-01590602, HAL.
    10. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2021. "Optimal make–take fees for market making regulation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 109-148, January.
    11. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.
    12. N Baradel & Bruno Bouchard & Ngoc Minh Dang, 2016. "Optimal trading with online parameters revisions," Post-Print hal-01304019, HAL.
    13. E. Löcherbach, 2019. "Large Deviations for Cascades of Diffusions Arising in Oscillating Systems of Interacting Hawkes Processes," Journal of Theoretical Probability, Springer, vol. 32(1), pages 131-162, March.
    14. N Baradel & B Bouchard & Ngoc Minh Dang, 2016. "Optimal trading with online parameters revisions," Working Papers hal-01304019, HAL.
    15. Valenzuela, Marcela & Zer, Ilknur & Fryzlewicz, Piotr & Rheinlander, Thorsten, 2015. "Relative liquidity and future volatility," LSE Research Online Documents on Economics 62181, London School of Economics and Political Science, LSE Library.
    16. Joffrey Derchu & Philippe Guillot & Thibaut Mastrolia & Mathieu Rosenbaum, 2020. "AHEAD : Ad-Hoc Electronic Auction Design," Papers 2010.02827, arXiv.org.
    17. Piotr Fryzlewicz & Thorsten Rheinlander & Marcela Valenzuela & Ilknur Zer, 2014. "Relative Liquidity and Future Volatility," Finance and Economics Discussion Series 2014-45, Board of Governors of the Federal Reserve System (U.S.).

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