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Optimal order placement in limit order markets

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  • Rama Cont
  • Arseniy Kukanov

Abstract

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.

Suggested Citation

  • Rama Cont & Arseniy Kukanov, 2017. "Optimal order placement in limit order markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 21-39, January.
  • Handle: RePEc:taf:quantf:v:17:y:2017:i:1:p:21-39
    DOI: 10.1080/14697688.2016.1190030
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    References listed on IDEAS

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    1. Baron, Matthew & Brogaard, Jonathan & Hagströmer, Björn & Kirilenko, Andrei, 2019. "Risk and Return in High-Frequency Trading," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 54(3), pages 993-1024, June.
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    Cited by:

    1. Mohammad Zare & Omid Naghshineh Arjmand & Erfan Salavati & Adel Mohammadpour, 2021. "An Agent‐Based model for Limit Order Book: Estimation and simulation," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1112-1121, January.
    2. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Papers 1803.06917, arXiv.org.
    3. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    4. Johannes Muhle‐Karbe & Zexin Wang & Kevin Webster, 2023. "A Leland model for delta hedging in central risk books," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 504-547, July.
    5. Timoth'ee Fabre & Vincent Ragel, 2023. "Interpretable ML for High-Frequency Execution," Papers 2307.04863, arXiv.org, revised Sep 2024.
    6. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Wu, Liang & Yan, Xin & Fu, Zhiming & Zhang, Rui, 2019. "Do investors choose trade-size according to liquidity, empirical evidence from the S&P 500 index future market," Finance Research Letters, Elsevier, vol. 28(C), pages 275-280.
    8. Nils Bundi & Ching-Lin Wei & Khaldoun Khashanah, 2024. "Optimal trade execution in cryptocurrency markets," Digital Finance, Springer, vol. 6(2), pages 283-318, June.
    9. Schnaubelt, Matthias, 2022. "Deep reinforcement learning for the optimal placement of cryptocurrency limit orders," European Journal of Operational Research, Elsevier, vol. 296(3), pages 993-1006.
    10. Schnaubelt, Matthias, 2020. "Deep reinforcement learning for the optimal placement of cryptocurrency limit orders," FAU Discussion Papers in Economics 05/2020, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    11. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Working Papers hal-01754054, HAL.
    12. Ben Hambly & Renyuan Xu & Huining Yang, 2023. "Recent advances in reinforcement learning in finance," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 437-503, July.
    13. Johannes Muhle-Karbe & Eyal Neuman & Yonatan Shadmi, 2024. "Fluid-Limits of Fragmented Limit-Order Markets," Papers 2407.04354, arXiv.org.
    14. Bastien Baldacci & Iuliia Manziuk, 2020. "Adaptive trading strategies across liquidity pools," Papers 2008.07807, arXiv.org.
    15. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    16. Anh Tu Le & Thai-Ha Le & Wai-Man Liu & Kingsley Y. Fong, 2023. "Dynamic limit order placement activities and their effects on stock market quality," Annals of Operations Research, Springer, vol. 330(1), pages 155-175, November.
    17. Bastien Baldacci & Jerome Benveniste & Gordon Ritter, 2020. "Optimal trading without optimal control," Papers 2012.12945, arXiv.org.
    18. Andrew Y. Chen & Mihail Velikov, 2020. "Zeroing in on the Expected Returns of Anomalies," Finance and Economics Discussion Series 2020-039, Board of Governors of the Federal Reserve System (U.S.).

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