IDEAS home Printed from
   My bibliography  Save this article

Optimal high-frequency trading with limit and market orders


  • Fabien Guilbaud
  • Huyên Pham


We propose a framework for studying optimal market-making policies in a limit order book (LOB). The bid--ask spread of the LOB is modeled by a tick-valued continuous-time Markov chain. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at best bid (resp. ask) plus (resp. minus) a tick for obtaining execution order priority, which is a crucial issue in high-frequency trading. The agent faces an execution risk since her limit orders are executed only when they meet counterpart market orders. She is also subject to inventory risk due to price volatility when holding the risky asset. The agent can then also choose to trade with market orders, and therefore obtain immediate execution, but at a less favorable price. The objective of the market maker is to maximize her expected utility from revenue over a short-term horizon by a trade-off between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/impulse control problem that we characterize in terms of a quasi-variational system by dynamic programming methods. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. We provide an explicit backward splitting scheme for solving the problem and show how it can be reduced to a system of simple equations involving only the inventory and spread variables. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:13:y:2013:i:1:p:79-94 DOI: 10.1080/14697688.2012.708779

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Francis X. Diebold & Georg H. Strasser, 2008. "On the Correlation Structure of Microstructure Noise in Theory and Practice," PIER Working Paper Archive 08-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    4. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, Department of Economics and Business Economics, Aarhus University.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Antoine Jacquier & Hao Liu, 2017. "Optimal liquidation in a Level-I limit order book for large tick stocks," Papers 1701.01327,, revised Nov 2017.
    2. M. Alessandra Crisafi & Andrea Macrina, 2015. "Dark-Pool Perspective of Optimal Market Making," Papers 1502.02863,
    3. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    4. Filippo Passerini & Samuel E. Vazquez, 2015. "Optimal Trading with Alpha Predictors," Papers 1501.03756,, revised Jan 2015.
    5. Frédéric Abergel & Côme Huré & Huyên Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    6. 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.
    7. Roman Gayduk & Sergey Nadtochiy, 2015. "Liquidity Effects of Trading Frequency," Papers 1508.07914,, revised May 2017.
    8. Christoph Kuhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision," Papers 1309.5235,, revised Feb 2015.
    9. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2016. "Optimal Execution of Limit and Market Orders with Trade Director, Speed Limiter, and Fill Uncertainty," Papers 1604.04963,, revised Apr 2017.
    10. Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
    11. Kühn, Christoph & Muhle-Karbe, Johannes, 2015. "Optimal liquidity provision," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2493-2515.
    12. Jos'e E. Figueroa-L'opez & Hyoeun Lee & Raghu Pasupathy, 2017. "Optimal placement of a small order in a diffusive limit order book," Papers 1708.04337,
    13. Qing-Qing Yang & Wai-Ki Ching & Jia-Wen Gu & Tak-Kuen Siu, 2016. "Generalized Optimal Liquidation Problems Across Multiple Trading Venues," Papers 1607.04553,, revised Aug 2017.
    14. 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.
    15. Bandini, Elena & Fuhrman, Marco, 2017. "Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1441-1474.
    16. Kyle Bechler & Mike Ludkovski, 2014. "Optimal Execution with Dynamic Order Flow Imbalance," Papers 1409.2618,, revised Oct 2014.
    17. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320,, revised Jan 2015.
    18. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454,, revised Nov 2016.
    19. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720,, revised Jun 2017.
    20. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810,, revised Oct 2015.
    21. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500054 is not listed on IDEAS
    22. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446,
    23. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862,, revised May 2017.

    More about this item


    Access and download statistics


    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:taf:quantf:v:13:y:2013:i:1:p:79-94. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.