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Optimal Execution and Price Manipulations in Time-varying Limit Order Books

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  • Aurélien Alfonsi
  • José Infante Acevedo

Abstract

This paper focuses on an extension of the limit order book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied ((2010). Optimal execution strategies in limit order books with general shape functions. Quantitative Finance , 10 (2), 143-157). Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude price manipulations in the sense of Huberman and Stanzl ((2004). Price manipulation and quasi-arbitrage. Econometrica , 72 (4), 1247-1275) or transaction-triggered price manipulations (see Alfonsi, A., Schied, A., & Slynko, A. (2012). Order book resilience, prince manipulation, and the positive portfolio problem. SIAM Journal of Financial Mathematics, 3, 511-533.). These conditions give interesting qualitative insights on how market makers may create or not price manipulations.

Suggested Citation

  • Aurélien Alfonsi & José Infante Acevedo, 2014. "Optimal Execution and Price Manipulations in Time-varying Limit Order Books," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(3), pages 201-237, July.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:3:p:201-237
    DOI: 10.1080/1350486X.2013.845471
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    Citations

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    Cited by:

    1. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Self-exciting price impact via negative resilience in stochastic order books," Papers 2112.03789, arXiv.org, revised Jul 2022.
    2. Shanshan Wang, 2017. "Trading strategies for stock pairs regarding to the cross-impact cost," Papers 1701.03098, arXiv.org, revised Jul 2017.
    3. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2022. "Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems," Papers 2206.03772, arXiv.org, revised Sep 2023.
    4. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    5. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "Optimal trade execution in an order book model with stochastic liquidity parameters," Papers 2006.05843, arXiv.org, revised Apr 2021.
    6. Tao Chen & Mike Ludkovski & Moritz Vo{ss}, 2022. "On Parametric Optimal Execution and Machine Learning Surrogates," Papers 2204.08581, arXiv.org, revised Oct 2023.
    7. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "C\`adl\`ag semimartingale strategies for optimal trade execution in stochastic order book models," Papers 2006.05863, arXiv.org, revised Jul 2021.

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