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Optimal trade execution in an order book model with stochastic liquidity parameters

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  • Julia Ackermann
  • Thomas Kruse
  • Mikhail Urusov

Abstract

We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss several qualitative aspects of optimal strategies, such as existence of profitable round trips or closing the position in one go, and compare our findings with the literature.

Suggested Citation

  • Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "Optimal trade execution in an order book model with stochastic liquidity parameters," Papers 2006.05843, arXiv.org.
  • Handle: RePEc:arx:papers:2006.05843
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    2. Antje Fruth & Torsten Schöneborn & Mikhail Urusov, 2014. "Optimal Trade Execution And Price Manipulation In Order Books With Time-Varying Liquidity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 651-695, October.
    3. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    4. Alexander Schied, 2012. "A control problem with fuel constraint and Dawson-Watanabe superprocesses," Papers 1207.5809, arXiv.org, revised Dec 2013.
    5. Paulwin Graewe & Ulrich Horst, 2016. "Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience," Papers 1611.03435, arXiv.org, revised Jul 2017.
    6. Patrick Cheridito & Tardu Sepin, 2014. "Optimal Trade Execution Under Stochastic Volatility and Liquidity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 342-362, September.
    7. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    8. Aurélien Alfonsi & José Infante Acevedo, 2014. "Optimal execution and price manipulations in time-varying limit order books," Post-Print hal-00687193, HAL.
    9. 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.
    10. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    11. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    12. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    13. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Papers 1309.0461, arXiv.org, revised Jan 2015.
    14. Antje Fruth & Torsten Schöneborn & Mikhail Urusov, 2019. "Optimal trade execution in order books with stochastic liquidity," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 507-541, April.
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    Cited by:

    1. 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.

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