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Optimal execution with non-linear transient market impact

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  • Gianbiagio Curato
  • Jim Gatheral
  • Fabrizio Lillo

Abstract

We study the problem of the optimal execution of a large trade in the propagator model with non-linear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy programme typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases, we find negative expected cost. We show that this undesirable characteristic of the non-linear transient impact model may be mitigated either by introducing a bid–ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates; the objective in each case is to robustify the solution in a parsimonious and natural way.

Suggested Citation

  • Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2017. "Optimal execution with non-linear transient market impact," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 41-54, January.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:1:p:41-54
    DOI: 10.1080/14697688.2016.1181274
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    2. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327, arXiv.org, revised Jan 2019.
    3. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Hugo E. Ramirez & Juli'an Fernando Sanchez, 2023. "Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies," Papers 2303.10043, arXiv.org.
    5. Fengpei Li & Vitalii Ihnatiuk & Ryan Kinnear & Anderson Schneider & Yuriy Nevmyvaka, 2022. "Do price trajectory data increase the efficiency of market impact estimation?," Papers 2205.13423, arXiv.org, revised Mar 2023.
    6. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    7. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    8. Junjie Li & Yang Liu & Weiqing Liu & Shikai Fang & Lewen Wang & Chang Xu & Jiang Bian, 2024. "MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model," Papers 2409.07486, arXiv.org.
    9. Johannes Bleher & Michael Bleher, 2024. "An Algebraic Framework for the Modeling of Limit Order Books," Papers 2406.04969, arXiv.org.
    10. Behzad Alimoradian & Karim Barigou & Anne Eyraud-Loisel, 2022. "Derivatives under market impact: Disentangling cost and information," Working Papers hal-03668432, HAL.
    11. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org, revised Aug 2023.
    12. Jasdeep Kalsi & Terry Lyons & Imanol Perez Arribas, 2019. "Optimal execution with rough path signatures," Papers 1905.00728, arXiv.org.
    13. Zequn Li & Agnès Tourin, 2022. "A Finite Difference Scheme for Pairs Trading with Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 601-632, August.
    14. Thibault Jaisson, 2021. "Deep differentiable reinforcement learning and optimal trading," Papers 2112.02944, arXiv.org, revised Apr 2022.
    15. Ramirez, H & Sanchez, J. F, 2023. "Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies," Documentos de Trabajo 20669, Universidad del Rosario.

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