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Optimal Trade Execution Under Stochastic Volatility and Liquidity

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  • Patrick Cheridito
  • Tardu Sepin

Abstract

We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential or a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases, we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases, we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo (1998; Optimal control of execution costs. Journal of Financial Markets , 1 , 1-50) and Almgren and Chriss (2001; Optimal execution of portfolio transactions. Journal of Risk , 3 , 5-33).

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:342-362
    DOI: 10.1080/1350486X.2014.881005
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    Citations

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    Cited by:

    1. Ivan Cherednik, 2019. "Artificial intelligence approach to momentum risk-taking," Papers 1911.08448, arXiv.org, revised Mar 2020.
    2. Jean-Pierre Fouque & Sebastian Jaimungal & Yuri F. Saporito, 2021. "Optimal Trading with Signals and Stochastic Price Impact," Papers 2101.10053, arXiv.org, revised Aug 2023.
    3. 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.
    4. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org, revised Aug 2023.
    5. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    6. 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.
    7. Chiara Benazzoli & Luca Di Persio, 2017. "Optimal execution strategy in liquidity framework," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1364902-136, January.
    8. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Execution and Speculation," Papers 2307.03499, arXiv.org.
    9. David Evangelista & Yuri Thamsten, 2023. "Approximately optimal trade execution strategies under fast mean-reversion," Papers 2307.07024, arXiv.org, revised Aug 2023.
    10. 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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