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Optimal liquidity-based trading tactics

Author

Listed:
  • Charles-Albert Lehalle
  • Othmane Mounjid
  • Mathieu Rosenbaum

Abstract

We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders and cancellations. To solve the agent's control problem, we build an order book model and optimize an expected utility function based on our price impact. We derive the equations satisfied by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution strategies.

Suggested Citation

  • Charles-Albert Lehalle & Othmane Mounjid & Mathieu Rosenbaum, 2018. "Optimal liquidity-based trading tactics," Papers 1803.05690, arXiv.org.
    • Handle: RePEc:arx:papers:1803.05690
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    References listed on IDEAS

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    3. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    4. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    5. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    6. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    7. Foucault, Thierry, 1999. "Order flow composition and trading costs in a dynamic limit order market1," Journal of Financial Markets, Elsevier, vol. 2(2), pages 99-134, May.
    8. Ioane Muni Toke, 2017. "Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-22, September.
    9. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    10. Ioane Muni Toke, 2017. "Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model," Post-Print hal-01705085, HAL.
    11. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    12. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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    Citations

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    Cited by:

    1. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    2. Peng Wu & Marcello Rambaldi & Jean-François Muzy & Emmanuel Bacry, 2023. "A single queue-reactive Hawkes model for the order flow," Post-Print hal-02409073, HAL.
    3. Felix Lokin & Fenghui Yu, 2024. "Fill Probabilities in a Limit Order Book with State-Dependent Stochastic Order Flows," Papers 2403.02572, arXiv.org.
    4. Peng Wu & Marcello Rambaldi & Jean-François Muzy & Emmanuel Bacry, 2021. "Queue-reactive Hawkes models for the order flow," Working Papers hal-02409073, HAL.
    5. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    6. Peng Wu & Marcello Rambaldi & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2019. "Queue-reactive Hawkes models for the order flow," Papers 1901.08938, arXiv.org.
    7. Colaneri, Katia & Eksi, Zehra & Frey, Rüdiger & Szölgyenyi, Michaela, 2020. "Optimal liquidation under partial information with price impact," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1913-1946.
    8. Frédéric Abergel & Côme Huré & Huyên Pham, 2020. "Algorithmic trading in a microstructural limit order book model," Post-Print hal-01514987, HAL.

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