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Fast and Slow Optimal Trading with Exogenous Information

Author

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  • Rama Cont
  • Alessandro Micheli
  • Eyal Neuman

Abstract

We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.

Suggested Citation

  • Rama Cont & Alessandro Micheli & Eyal Neuman, 2022. "Fast and Slow Optimal Trading with Exogenous Information," Papers 2210.01901, arXiv.org, revised Jun 2023.
    • Handle: RePEc:arx:papers:2210.01901
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    References listed on IDEAS

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    1. Eyal Neuman & Alexander Schied, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    2. 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.
    3. Samuel Drapeau & Peng Luo & Alexander Schied & Dewen Xiong, 2019. "An FBSDE approach to market impact games with stochastic parameters," Papers 2001.00622, arXiv.org.
    4. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    5. Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
    6. Gârleanu, Nicolae & Pedersen, Lasse Heje, 2016. "Dynamic portfolio choice with frictions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 487-516.
    7. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
    8. Andrei Kirilenko & Albert S. Kyle & Mehrdad Samadi & Tugkan Tuzun, 2017. "The Flash Crash: High-Frequency Trading in an Electronic Market," Journal of Finance, American Finance Association, vol. 72(3), pages 967-998, June.
    9. Philippe Casgrain & Sebastian Jaimungal, 2018. "Mean Field Games with Partial Information for Algorithmic Trading," Papers 1803.04094, arXiv.org, revised Mar 2019.
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    Cited by:

    1. Yufan Chen & Lan Wu & Renyuan Xu & Ruixun Zhang, 2024. "Periodic Trading Activities in Financial Markets: Mean-field Liquidation Game with Major-Minor Players," Papers 2408.09505, arXiv.org.
    2. 'Alvaro Cartea & Sebastian Jaimungal & Leandro S'anchez-Betancourt, 2024. "Nash Equilibrium between Brokers and Traders," Papers 2407.10561, arXiv.org, revised Jul 2024.

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