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

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  • Jose Blanchet
  • Xinyun Chen

Abstract

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, arXiv.org.
  • Handle: RePEc:arx:papers:1310.1103
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    References listed on IDEAS

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    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, arXiv.org, 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, arXiv.org, revised Oct 2015.
    4. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    5. Justin Sirignano, 2016. "Deep Learning for Limit Order Books," Papers 1601.01987, arXiv.org, 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, arXiv.org.

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