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Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach

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  • Alexandre Roch

    (University of Quebec at Montreal)

Abstract

We present a learning algorithm based on simulation and neural networks to solve a stochastic optimal control problem with a large state space using dynamic programming. The problem consists in liquidating a given number of shares of a stock through a limit order book (LOB). The state space includes prices and quantities at each level in the LOB. The objective is to maximize the expected liquidation proceeds. Shares are sold by market orders matching the current limit orders in the LOB and have an impact on the future evolution of the LOB. The optimal strategy is obtained using a hybrid form of performance and value iteration procedures based on neural networks. The probability distribution of the LOB is estimated by a deep learning classification task. The model is tested on 12 stocks traded through the NYSE Arcabook, and a numerical implementation shows that the model outperforms the most common optimal liquidation models in the literature by a significant amount.

Suggested Citation

  • Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09996-z
    DOI: 10.1007/s11009-023-09996-z
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    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    3. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    4. �lvaro Cartea & Sebastian Jaimungal, 2015. "Optimal execution with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1279-1291, August.
    5. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    6. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2018. "Optimal liquidation under stochastic liquidity," Finance and Stochastics, Springer, vol. 22(1), pages 39-68, January.
    7. Lokka, A. & Xu, Junwei, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model," LSE Research Online Documents on Economics 106977, London School of Economics and Political Science, LSE Library.
    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. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    10. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    11. Arne Lokka & Junwei Xu, 2020. "Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes," Papers 2002.03376, arXiv.org, revised Sep 2020.
    12. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    13. repec:dau:papers:123456789/12195 is not listed on IDEAS
    14. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Working Papers hal-03115503, HAL.
    15. Arne Løkka & Junwei Xu, 2020. "Optimal Liquidation Trajectories For The Almgren–Chriss Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-35, November.
    16. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    17. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    18. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    19. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    20. Justin A. Sirignano, 2019. "Deep learning for limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 549-570, April.
    21. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    22. repec:dau:papers:123456789/7391 is not listed on IDEAS
    23. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    24. Alexandre Carbonneau & Frédéric Godin, 2021. "Equal risk pricing of derivatives with deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 593-608, April.
    25. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    26. Maximilien Germain & Huy^en Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance," Papers 2101.08068, arXiv.org, revised Apr 2021.
    27. Achref Bachouch & Côme Huré & Nicolas Langrené & Huyên Pham, 2022. "Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Numerical Applications," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 143-178, March.
    28. Denis Belomestny & Stefan Hafner & Mikhail Urusov, 2016. "Regression-based complexity reduction of the nested Monte Carlo methods," Papers 1611.06344, arXiv.org, revised Jun 2018.
    29. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    30. Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    31. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    32. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.
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    Cited by:

    1. Yang, Qing-Qing & Ching, Wai-Ki & Gu, Jia-wen & Wong, Tak Kwong & Zhu, Dong-Mei, 2024. "Viscosity solution for optimal liquidation problems with randomly-terminated horizon," Finance Research Letters, Elsevier, vol. 61(C).

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