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Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model

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  • Ioane Muni Toke

    (FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec)

Abstract

We develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.

Suggested Citation

  • Ioane Muni Toke, 2017. "Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model," Post-Print hal-01705085, HAL.
    • Handle: RePEc:hal:journl:hal-01705085
    DOI: 10.1142/S021902491750039X
    Note: View the original document on HAL open archive server: https://centralesupelec.hal.science/hal-01705085
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    References listed on IDEAS

    as
    1. I. Muni Toke, 2015. "The order book as a queueing system: average depth and influence of the size of limit orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 795-808, May.
    2. Abergel,Frédéric & Anane,Marouane & Chakraborti,Anirban & Jedidi,Aymen & Muni Toke,Ioane, 2016. "Limit Order Books," Cambridge Books, Cambridge University Press, number 9781107163980.
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    4. Frédéric Abergel & Anirban Chakraborti & Aymen Jedidi & Ioane Muni Toke & Marouane Anane, 2016. "Limit Order Books," Post-Print hal-02177394, HAL.
    5. Harris, Lawrence & Hasbrouck, Joel, 1996. "Market vs. Limit Orders: The SuperDOT Evidence on Order Submission Strategy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(2), pages 213-231, June.
    6. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    7. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
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    9. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    10. Ioane Muni Toke, 2015. "The order book as a queueing system: average depth and influence of the size of limit orders," Post-Print hal-01006410, HAL.
    11. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    12. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Charles-Albert Lehalle & Othmane Mounjid & Mathieu Rosenbaum, 2018. "Optimal liquidity-based trading tactics," Papers 1803.05690, arXiv.org.

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    More about this item

    Keywords

    aggressive limit orders; volume of the best quote; limit order book; aggressive market orders; killing and resurrecting Markov processes;
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