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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. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327, arXiv.org, revised Jan 2019.
    2. 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).
    3. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A Mean Field Game of Portfolio Trading and Its Consequences On Perceived Correlations," Papers 1902.09606, arXiv.org.
    4. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org.
    5. Jasdeep Kalsi & Terry Lyons & Imanol Perez Arribas, 2019. "Optimal execution with rough path signatures," Papers 1905.00728, arXiv.org.
    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.

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