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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.

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  • 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. 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.
    2. Ioane Muni Toke, 2010. ""Market making" behaviour in an order book model and its impact on the bid-ask spread," Papers 1003.3796, arXiv.org, revised Jun 2010.
    3. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
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    7. 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.
    8. 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.
    9. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    10. 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.
    11. 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.
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    Citations

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    Cited by:

    1. Can Yilmaz Altinigne & Harun Ozkan & Veli Can Kupeli & Zehra Cataltepe, 2019. "An Empirical Study on Arrival Rates of Limit Orders and Order Cancellation Rates in Borsa Istanbul," Papers 1909.08308, arXiv.org.
    2. Ulrich Horst & Dorte Kreher, 2017. "Second order approximations for limit order books," Papers 1708.07394, arXiv.org, revised Mar 2018.
    3. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    4. Ben Hambly & Jasdeep Kalsi & James Newbury, 2018. "Limit order books, diffusion approximations and reflected SPDEs: from microscopic to macroscopic models," Papers 1808.07107, arXiv.org, revised Jun 2019.
    5. Ulrich Horst & Dorte Kreher & Konstantins Starovoitovs, 2023. "Second-Order Approximation of Limit Order Books in a Single-Scale Regime," Papers 2308.00805, arXiv.org, revised Sep 2024.
    6. 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.
    7. Justin Sirignano, 2016. "Deep Learning for Limit Order Books," Papers 1601.01987, arXiv.org, revised Jul 2016.
    8. Scalas, Enrico & Rapallo, Fabio & Radivojević, Tijana, 2017. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 61-72.
    9. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.

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