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Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact

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  • Eyal Neuman
  • Moritz Vo{ss}

Abstract

We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk functional over a class of absolutely continuous and signal-adaptive strategies. The stochastic control problem is solved by following a probabilistic and convex analytic approach. We show that the optimal trading strategy is given by a system of four coupled forward-backward SDEs, which can be solved explicitly. Our results reveal how the induced transient price distortion provides together with the predictive signal an additional predictor about future price changes. As a consequence, the optimal signal-adaptive trading rate trades off exploiting the predictive signal against incurring the transient displacement of the execution price from its unaffected level. This answers an open question from Lehalle and Neuman [29] as we show how to derive the unique optimal signal-adaptive liquidation strategy when price impact is not only temporary but also transient.

Suggested Citation

  • Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2002.09549
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    References listed on IDEAS

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    1. Charles-Albert Lehalle & Sophie Laruelle (ed.), 2013. "Market Microstructure in Practice," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8967, January.
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    5. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    6. Ying Chen & Ulrich Horst & Hoang Hai Tran, 2019. "Portfolio liquidation under transient price impact -- theoretical solution and implementation with 100 NASDAQ stocks," Papers 1912.06426, arXiv.org.
    7. Alexander Schied, 2012. "A control problem with fuel constraint and Dawson-Watanabe superprocesses," Papers 1207.5809, arXiv.org, revised Dec 2013.
    8. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    9. Gârleanu, Nicolae & Pedersen, Lasse Heje, 2016. "Dynamic portfolio choice with frictions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 487-516.
    10. Kyle Bechler & Michael Ludkovski, 2017. "Order Flows and Limit Order Book Resiliency on the Meso-Scale," Papers 1708.02715, arXiv.org.
    11. Ulrich Horst & Jinniao Qiu & Qi Zhang, 2014. "A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition," Papers 1407.0108, arXiv.org, revised Jul 2015.
    12. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Papers 1309.0461, arXiv.org, revised Jan 2015.
    13. Ibrahim Ekren & Johannes Muhle‐Karbe, 2019. "Portfolio choice with small temporary and transient price impact," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1066-1115, October.
    14. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
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    Cited by:

    1. Eduardo Abi Jaber & Eyal Neuman & Moritz Voss, 2023. "Equilibrium in Functional Stochastic Games with Mean-Field Interaction," Working Papers hal-04119787, HAL.
    2. Rama Cont & Alessandro Micheli & Eyal Neuman, 2022. "Fast and Slow Optimal Trading with Exogenous Information," Papers 2210.01901, arXiv.org, revised Jun 2023.
    3. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Working Papers hal-03835948, HAL.
    4. Eyal Neuman & Yufei Zhang, 2023. "Statistical Learning with Sublinear Regret of Propagator Models," Papers 2301.05157, arXiv.org.
    5. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Papers 2211.00447, arXiv.org.
    6. Eduardo Abi Jaber & Eyal Neuman & Moritz Vo{ss}, 2023. "Equilibrium in Functional Stochastic Games with Mean-Field Interaction," Papers 2306.05433, arXiv.org, revised Feb 2024.
    7. Eyal Neuman & Moritz Voß, 2023. "Trading with the crowd," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 548-617, July.
    8. Philippe Bergault & Fayc{c}al Drissi & Olivier Gu'eant, 2021. "Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics," Papers 2103.13773, arXiv.org, revised Mar 2022.
    9. Ulrich Horst & Evgueni Kivman, 2021. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Papers 2103.05957, arXiv.org, revised Jul 2023.
    10. Damiano Brigo & Federico Graceffa & Eyal Neuman, 2022. "Price impact on term structure," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 171-195, January.
    11. Tao Chen & Mike Ludkovski & Moritz Vo{ss}, 2022. "On Parametric Optimal Execution and Machine Learning Surrogates," Papers 2204.08581, arXiv.org, revised Oct 2023.
    12. 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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