IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v62y2023i1d10.1007_s10614-022-10272-4.html
   My bibliography  Save this article

Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset

Author

Listed:
  • Burcu Aydoğan

    (Middle East Technical University
    Atılım University
    RWTH Aachen University)

  • Ömür Uğur

    (Middle East Technical University)

  • Ümit Aksoy

    (Atılım University)

Abstract

In quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of the trader by controlling the inventories. Two types of utility functions are considered: quadratic and exponential. In both cases, the remaining inventories of the market maker are charged with a liquidation cost. In order to achieve the optimal quotes, we control the inventory risk and follow the influence of each parameter in the model to the best bid and ask prices. We show that the risk metrics including profit and loss distribution (PnL), standard deviation and Sharpe ratio play important roles for the trader to make decisions on the strategies. We apply finite differences and linear interpolation as well as extrapolation techniques to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we consider different cases on the modeling to carry out the numerical simulations.

Suggested Citation

  • Burcu Aydoğan & Ömür Uğur & Ümit Aksoy, 2023. "Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 289-324, June.
    • Handle: RePEc:kap:compec:v:62:y:2023:i:1:d:10.1007_s10614-022-10272-4
    DOI: 10.1007/s10614-022-10272-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-022-10272-4
    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/s10614-022-10272-4?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. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    2. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    3. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    4. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Post-Print hal-03885125, HAL.
    5. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    6. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    7. repec:bla:jfinan:v:43:y:1988:i:3:p:617-37 is not listed on IDEAS
    8. Bastien Baldacci & Iuliia Manziuk & Thibaut Mastrolia & Mathieu Rosenbaum, 2019. "Market making and incentives design in the presence of a dark pool: a deep reinforcement learning approach," Papers 1912.01129, arXiv.org.
    9. 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.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 85-97, January.
    12. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    13. Grossman, S.J. & Miller, M.H., 1988. "Liquidity And Market Structure," Papers 88, Princeton, Department of Economics - Financial Research Center.
    14. Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Working Papers hal-00675925, HAL.
    15. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    16. 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.
    17. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    18. Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Papers 1206.4810, arXiv.org.
    19. Kaj Nyström & Sidi Mohamed Ould Aly & Changyong Zhang, 2014. "Market Making And Portfolio Liquidation Under Uncertainty," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-33.
    20. Álvaro Cartea & Sebastian Jaimungal, 2015. "Risk Metrics And Fine Tuning Of High-Frequency Trading Strategies," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 576-611, July.
    21. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    22. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    Full references (including those not matched with items on IDEAS)

    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. Philippe Bergault & David Evangelista & Olivier Gu'eant & Douglas Vieira, 2018. "Closed-form approximations in multi-asset market making," Papers 1810.04383, arXiv.org, revised Sep 2022.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    4. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.
    5. Bastien Baldacci & Philippe Bergault & Olivier Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    6. Diego Zabaljauregui & Luciano Campi, 2019. "Optimal market making under partial information with general intensities," Papers 1902.01157, arXiv.org, revised Apr 2020.
    7. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    8. Sofiene El Aoud & Frédéric Abergel, 2015. "A stochastic control approach for options market making," Post-Print hal-01061852, HAL.
    9. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 279-322, January.
    10. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    11. 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.
    12. Xiaofei Lu & Fr'ed'eric Abergel, 2018. "Order-book modelling and market making strategies," Papers 1806.05101, arXiv.org.
    13. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    14. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    15. Olivier Gu'eant & Jiang Pu, 2018. "Mid-price estimation for European corporate bonds: a particle filtering approach," Papers 1810.05884, arXiv.org, revised Mar 2019.
    16. 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.
    17. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    18. Baron Law & Frederi Viens, 2019. "Market Making under a Weakly Consistent Limit Order Book Model," Papers 1903.07222, arXiv.org, revised Jan 2020.
    19. Thomas Spooner & Rahul Savani, 2020. "Robust Market Making via Adversarial Reinforcement Learning," Papers 2003.01820, arXiv.org, revised Jul 2020.

    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:kap:compec:v:62:y:2023:i:1:d:10.1007_s10614-022-10272-4. 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.