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Mean Field Game of High-Frequency Anticipatory Trading

Author

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  • Xue Cheng
  • Meng Wang
  • Ziyi Xu

Abstract

The interactions between a large population of high-frequency traders (HFTs) and a large trader (LT) who executes a certain amount of assets at discrete time points are studied. HFTs are faster in the sense that they trade continuously and predict the transactions of LT. A jump process is applied to model the transition of HFTs' attitudes towards inventories and the equilibrium is solved through the mean field game approach. When the crowd of HFTs is averse to running (ending) inventories, they first take then supply liquidity at each transaction of LT (throughout the whole execution period). Inventory-averse HFTs lower LT's costs if the market temporary impact is relatively large to the permanent one. What's more, the repeated liquidity consuming-supplying behavior of HFTs makes LT's optimal strategy close to uniform trading.

Suggested Citation

  • Xue Cheng & Meng Wang & Ziyi Xu, 2024. "Mean Field Game of High-Frequency Anticipatory Trading," Papers 2404.18200, arXiv.org.
    • Handle: RePEc:arx:papers:2404.18200
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    References listed on IDEAS

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    1. Liyan Yang & Haoxiang Zhu, 2020. "Back-Running: Seeking and Hiding Fundamental Information in Order Flows," Review of Finance, European Finance Association, vol. 33(4), pages 1484-1533.
    2. Vincent Van Kervel & Albert J. Menkveld, 2019. "High‐Frequency Trading around Large Institutional Orders," Journal of Finance, American Finance Association, vol. 74(3), pages 1091-1137, June.
    3. Ziyi Xu & Xue Cheng, 2023. "The Effects of High-frequency Anticipatory Trading: Small Informed Trader vs. Round-Tripper," Papers 2304.13985, arXiv.org, revised Feb 2024.
    4. Nicholas Hirschey, 2021. "Do High-Frequency Traders Anticipate Buying and Selling Pressure?," Management Science, INFORMS, vol. 67(6), pages 3321-3345, June.
    5. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    6. Liyan Yang & Haoxiang Zhu, 2020. "Back-Running: Seeking and Hiding Fundamental Information in Order Flows," The Review of Financial Studies, Society for Financial Studies, vol. 33(4), pages 1484-1533.
    7. Robert A Korajczyk & Dermot Murphy, 2019. "High-Frequency Market Making to Large Institutional Trades," The Review of Financial Studies, Society for Financial Studies, vol. 32(3), pages 1034-1067.
    8. Xuancheng Huang & Sebastian Jaimungal & Mojtaba Nourian, 2019. "Mean-Field Game Strategies for Optimal Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(2), pages 153-185, March.
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