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Optimal Liquidation Under Stochastic Price Impact

Author

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  • WESTON BARGER

    (Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA)

  • MATTHEW LORIG

    (Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA)

Abstract

We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

Suggested Citation

  • Weston Barger & Matthew Lorig, 2019. "Optimal Liquidation Under Stochastic Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-28, March.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:02:n:s0219024918500590
    DOI: 10.1142/S0219024918500590
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    References listed on IDEAS

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    Cited by:

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    2. Jean-Pierre Fouque & Sebastian Jaimungal & Yuri F. Saporito, 2021. "Optimal Trading with Signals and Stochastic Price Impact," Papers 2101.10053, arXiv.org, revised Aug 2023.
    3. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org, revised Aug 2023.
    4. Ivan Guo & Shijia Jin & Kihun Nam, 2023. "Macroscopic Market Making," Papers 2307.14129, arXiv.org.
    5. Álvaro Cartea & Leandro Sánchez-Betancourt, 2023. "Optimal execution with stochastic delay," Finance and Stochastics, Springer, vol. 27(1), pages 1-47, January.
    6. Qixuan Luo & Shijia Song & Handong Li, 2023. "Research on the Effects of Liquidation Strategies in the Multi-asset Artificial Market," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1721-1750, December.
    7. Michael Karpe, 2020. "An overall view of key problems in algorithmic trading and recent progress," Papers 2006.05515, arXiv.org.
    8. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Execution and Speculation," Papers 2307.03499, arXiv.org.
    9. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org.
    10. Joseph Jerome & Leandro Sanchez-Betancourt & Rahul Savani & Martin Herdegen, 2022. "Model-based gym environments for limit order book trading," Papers 2209.07823, arXiv.org.

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