IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v27y2023i1d10.1007_s00780-022-00491-w.html
   My bibliography  Save this article

Optimal execution with stochastic delay

Author

Listed:
  • Álvaro Cartea

    (University of Oxford
    Oxford-Man Institute of Quantitative Finance)

  • Leandro Sánchez-Betancourt

    (King’s College London)

Abstract

We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs are liquidity-taking orders that specify a price limit and are for immediate execution only; however, if the price limit of the MLO precludes it from being filled, the exchange cancels the order. We frame our model as an impulse control problem with stochastic latency where the trader controls the times and the price limits of the MLOs sent to the exchange. We show that impatient liquidity takers submit MLOs that may walk the book (capped by the limit price) to increase the probability of filling the trades. On the other hand, patient liquidity takers use speculative MLOs that are only filled if there has been an advantageous move in prices over the latency period. Patient traders who are fast do not use their speed to hit the quotes they observe, or to finish the execution programme early; they use speed to complete the execution programme with as many speculative MLOs as possible. We use foreign exchange data to implement the random-latency-optimal strategy and to compare it with four benchmarks. For patient traders, the random-latency-optimal strategy outperforms the benchmarks by an amount that is greater than the transaction costs paid by liquidity takers in foreign exchange markets. Around news announcements, the value of the outperformance is between two and ten times the value of the transaction costs. The superiority of the strategy is due to both the speculative MLOs that are filled and the price protection of the MLOs.

Suggested Citation

  • Álvaro Cartea & Leandro Sánchez-Betancourt, 2023. "Optimal execution with stochastic delay," Finance and Stochastics, Springer, vol. 27(1), pages 1-47, January.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:1:d:10.1007_s00780-022-00491-w
    DOI: 10.1007/s00780-022-00491-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-022-00491-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-022-00491-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. �lvaro Cartea & Sebastian Jaimungal, 2015. "Optimal execution with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1279-1291, August.
    3. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    4. 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.
    5. Weston Barger & Matthew Lorig, 2019. "Optimal Liquidation Under Stochastic Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-28, March.
    6. Xuefeng Gao & Yunhan Wang, 2020. "Optimal market making in the presence of latency," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1495-1512, September.
    7. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    8. Xuefeng Gao & Yunhan Wang, 2018. "Optimal Market Making in the Presence of Latency," Papers 1806.05849, arXiv.org, revised Mar 2020.
    9. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    10. Bruder, Benjamin & Pham, Huyên, 2009. "Impulse control problem on finite horizon with execution delay," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1436-1469, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 'Alvaro Cartea & Gerardo Duran-Martin & Leandro S'anchez-Betancourt, 2023. "Detecting Toxic Flow," Papers 2312.05827, arXiv.org.
    2. 'Alvaro Cartea & Sebastian Jaimungal & Leandro S'anchez-Betancourt, 2024. "Nash Equilibrium between Brokers and Traders," Papers 2407.10561, arXiv.org, revised Jul 2024.
    3. Yan Dolinsky, 2023. "Delayed Semi-static Hedging in the Continuous Time Bachelier Model," Papers 2311.17270, arXiv.org, revised Sep 2024.
    4. Yan Dolinsky & Or Zuk, 2023. "Explicit Computations for Delayed Semistatic Hedging," Papers 2308.10550, arXiv.org, revised Sep 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    2. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    3. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A Mean Field Game of Portfolio Trading and Its Consequences On Perceived Correlations," Papers 1902.09606, arXiv.org.
    4. Joseph Jerome & Leandro Sanchez-Betancourt & Rahul Savani & Martin Herdegen, 2022. "Model-based gym environments for limit order book trading," Papers 2209.07823, arXiv.org.
    5. Jiafa He & Cong Zheng & Can Yang, 2023. "Integrating Tick-level Data and Periodical Signal for High-frequency Market Making," Papers 2306.17179, arXiv.org.
    6. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    7. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    8. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454, arXiv.org, revised Nov 2016.
    9. S. C. P. Yam & W. Zhou, 2017. "Optimal Liquidation of Child Limit Orders," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 517-545, May.
    10. 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.
    11. Max O. Souza & Yuri Thamsten, 2021. "On regularized optimal execution problems and their singular limits," Papers 2101.02731, arXiv.org, revised Aug 2023.
    12. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org, revised Jan 2015.
    13. Jonathan Ch'avez-Casillas & Jos'e E. Figueroa-L'opez & Chuyi Yu & Yi Zhang, 2024. "Adaptive Optimal Market Making Strategies with Inventory Liquidation Cos," Papers 2405.11444, arXiv.org.
    14. Bastien Baldacci & Jerome Benveniste, 2020. "A note on Almgren-Chriss optimal execution problem with geometric Brownian motion," Papers 2006.11426, arXiv.org, revised Jun 2020.
    15. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    16. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.
    17. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    18. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    19. Aur'elien Alfonsi & Alexander Schied & Florian Klock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised Sep 2015.

    More about this item

    Keywords

    Algorithmic trading; High-frequency trading; Stochastic delay; Latency;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:27:y:2023:i:1:d:10.1007_s00780-022-00491-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.