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Optimal order execution under price impact: a hybrid model

Author

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  • Marina Giacinto

    (Università degli studi di Cassino e del Lazio Meridionale)

  • Claudio Tebaldi

    (Università Commerciale Luigi Bocconi and IGIER and Baffi-Carefin)

  • Tai-Ho Wang

    (Baruch College, The City University of New York
    China Center for Economics Research (CCER), Peking University)

Abstract

In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamics of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem. The value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk.

Suggested Citation

  • Marina Giacinto & Claudio Tebaldi & Tai-Ho Wang, 2024. "Optimal order execution under price impact: a hybrid model," Annals of Operations Research, Springer, vol. 336(1), pages 605-636, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-05082-8
    DOI: 10.1007/s10479-022-05082-8
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    1. Yadh Hafsi & Edoardo Vittori, 2024. "Optimal Execution with Reinforcement Learning," Papers 2411.06389, arXiv.org.
    2. Meng Wang & Tai-Ho Wang, 2023. "Relative entropy-regularized robust optimal order execution," Papers 2311.06476, arXiv.org, revised Sep 2024.

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