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Optimal execution and speculation with trade signals

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  • Peter Bank
  • 'Alvaro Cartea
  • Laura Korber

Abstract

We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$\sigma$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. Her trades impact the market through the same mechanism as other orders. With a novel version of Marcus-type SDEs we efficiently describe the intricate timing of market dynamics at moments when her orders concur with that of others. In this setting, we examine an optimal execution problem and derive the Hamilton--Jacobi--Bellman (HJB) equation for the value function of the trader. The HJB equation is solved numerically and we illustrate how the trader uses the signals to enhance the performance of execution problems and to execute speculative strategies.

Suggested Citation

  • Peter Bank & 'Alvaro Cartea & Laura Korber, 2023. "Optimal execution and speculation with trade signals," Papers 2306.00621, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2306.00621
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    References listed on IDEAS

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    1. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
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    4. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    5. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    6. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    7. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    8. Peter Bank & David Besslich, 2018. "Modelling information flows by Meyer-$\sigma$-fields in the singular stochastic control problem of irreversible investment," Papers 1810.08495, arXiv.org, revised Mar 2020.
    9. Thomas Cayé & Johannes Muhle-Karbe, 2014. "Liquidation with Self-Exciting Price Impact," Swiss Finance Institute Research Paper Series 14-74, Swiss Finance Institute.
    10. Álvaro Cartea & Yixuan Wang, 2020. "Market Making With Alpha Signals," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-26, May.
    11. Christoph Belak & Johannes Muhle-Karbe & Kevin Ou, 2018. "Optimal Trading with General Signals and Liquidation in Target Zone Models," Papers 1808.00515, arXiv.org.
    12. Philippe Casgrain & Sebastian Jaimungal, 2019. "Trading algorithms with learning in latent alpha models," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 735-772, July.
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    Cited by:

    1. Xuchen Wu & Sebastian Jaimungal, 2024. "Broker-Trader Partial Information Nash-Equilibria," Papers 2412.17712, arXiv.org, revised Apr 2025.
    2. Emilio Barucci & Adrien Mathieu & Leandro S'anchez-Betancourt, 2025. "Market Making with Fads, Informed, and Uninformed Traders," Papers 2501.03658, arXiv.org, revised Feb 2025.

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