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A Markov model of a limit order book: thresholds, recurrence, and trading strategies

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  • Frank Kelly
  • Elena Yudovina

Abstract

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds. We make extensive use of fluid limits in order to establish recurrence properties of the model. We use the model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.

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  • Frank Kelly & Elena Yudovina, 2015. "A Markov model of a limit order book: thresholds, recurrence, and trading strategies," Papers 1504.00579, arXiv.org, revised Mar 2017.
    • Handle: RePEc:arx:papers:1504.00579
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    References listed on IDEAS

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    1. Ivo Adan & Gideon Weiss, 2012. "Exact FCFS Matching Rates for Two Infinite Multitype Sequences," Operations Research, INFORMS, vol. 60(2), pages 475-489, April.
    2. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    3. Stefanos A. Zenios & Glenn M. Chertow & Lawrence M. Wein, 2000. "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," Operations Research, INFORMS, vol. 48(4), pages 549-569, August.
    4. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    5. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    6. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    7. Aim'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323, arXiv.org, revised Aug 2015.
    8. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    9. Eric Budish & Peter Cramton & John Shim, 2014. "Implementation Details for Frequent Batch Auctions: Slowing Down Markets to the Blink of an Eye," American Economic Review, American Economic Association, vol. 104(5), pages 418-424, May.
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    Cited by:

    1. Fan Fang & Waichung Chung & Carmine Ventre & Michail Basios & Leslie Kanthan & Lingbo Li & Fan Wu, 2020. "Ascertaining price formation in cryptocurrency markets with DeepLearning," Papers 2003.00803, arXiv.org.
    2. Eduard Silantyev, 2019. "Order flow analysis of cryptocurrency markets," Digital Finance, Springer, vol. 1(1), pages 191-218, November.
    3. Hainaut, Donatien & Goutte, Stephane, 2018. "A switching microstructure model for stock prices," LIDAM Discussion Papers ISBA 2018014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.

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