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Optimal Execution Cost For Liquidation Through A Limit Order Market

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  • ETIENNE CHEVALIER

    (Laboratoire de Mathématiques et Modélisation d’Evry, Université d’Evry, Bâtiment I.B.G.B.I., 3e étage, 23 Bd. de France, 91037 Evry Cedex, France)

  • VATHANA LY VATH

    (#x2020;Ecole Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise, 1, Square de la Résistance, 91025 Evry Cedex, France)

  • SIMONE SCOTTI

    (#x2021;Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, 4, Place Jussieu, Avenue de France, 75205 Paris Cedex 13, France)

  • ALEXANDRE ROCH

    (#xA7;Finance Department, University of Quebec in Montreal, 315, Sainte-Catherine Street East, Montreal, Quebec, Canada, H2X 3X2, Canada)

Abstract

We study the problem of optimally liquidating a large portfolio position in a limit-order market. We allow for both limit and market orders and the optimal solution is a combination of both types of orders. Market orders deplete the order book, making future trades more expensive, whereas limit orders can be entered at more favorable prices but are not guaranteed to be filled. We model the bid-ask spread with resilience by a jump process, and the market-order arrival process as a controlled Poisson process. The objective is to minimize the execution cost of the strategy. We formulate the problem as a mixed stochastic continuous control and impulse problem for which the value function is shown to be the unique viscosity solution of the associated variational inequalities. We conclude with a calibration of the model on recent market data and a numerical implementation.

Suggested Citation

  • Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:01:n:s0219024916500047
    DOI: 10.1142/S0219024916500047
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    References listed on IDEAS

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    Cited by:

    1. M. Alessandra Crisafi & Andrea Macrina, 2016. "Simultaneous Trading In ‘Lit’ And Dark Pools," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-33, December.
    2. Luciano Campi & Davide Santis, 2020. "Nonzero-Sum Stochastic Differential Games Between an Impulse Controller and a Stopper," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 688-724, August.
    3. Francesco Cordoni & Luca Di Persio & Yilun Jiang, 2019. "A bank salvage model by impulse stochastic controls," Papers 1910.03056, arXiv.org.
    4. Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.

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