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Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books


  • Jose Blanchet
  • Xinyun Chen


We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in the asymptotic regime supported by empirical observations the mid price and bid-ask-spread can be described using only certain parameters of the book (not the whole book itself). Our limit process is characterized by reflecting behavior and state-dependent jumps. Our analysis allows to explain certain characteristics observed in practice such as: the connection between power-law decaying tails in the volumes of the order book and the returns, as well as statistical properties of the long-run spread distribution.

Suggested Citation

  • Jose Blanchet & Xinyun Chen, 2013. "Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books," Papers 1310.1103,
  • Handle: RePEc:arx:papers:1310.1103

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    References listed on IDEAS

    1. Hautsch, Nikolaus & Huang, Ruihong, 2012. "The market impact of a limit order," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 501-522.
    2. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    3. Kirilenko, Andrei & Sowers, Richard B. & Meng, Xiangqian, 2013. "A multiscale model of high-frequency trading," Algorithmic Finance, IOS Press, vol. 2(1), pages 59-98.
    4. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    5. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    6. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    7. Rama Cont & Adrien De Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    8. Ilija Zovko & J Doyne Farmer, 2002. "The power of patience: a behavioural regularity in limit-order placement," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 387-392.
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    Cited by:

    1. repec:eee:phsmap:v:485:y:2017:i:c:p:61-72 is not listed on IDEAS
    2. Ulrich Horst & Dorte Kreher, 2017. "Second order approximations for limit order books," Papers 1708.07394,, revised Mar 2018.
    3. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810,, revised Oct 2015.
    4. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502,, revised Feb 2016.
    5. Justin Sirignano, 2016. "Deep Learning for Limit Order Books," Papers 1601.01987,, revised Jul 2016.
    6. Enrico Scalas & Fabio Rapallo & Tijana Radivojevi'c, 2016. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Papers 1603.09666,

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