IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1911.10450.html
   My bibliography  Save this paper

A singular stochastic control approach for optimal pairs trading with proportional transaction costs

Author

Listed:
  • Haipeng Xing

Abstract

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and number of shares in pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem which involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.

Suggested Citation

  • Haipeng Xing, 2019. "A singular stochastic control approach for optimal pairs trading with proportional transaction costs," Papers 1911.10450, arXiv.org.
    • Handle: RePEc:arx:papers:1911.10450
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1911.10450
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lei, Yaoting & Xu, Jing, 2015. "Costly arbitrage through pairs trading," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 1-19.
    2. Tourin, Agnès & Yan, Raphael, 2013. "Dynamic pairs trading using the stochastic control approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1972-1981.
    3. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    4. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    5. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    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. Krauss, Christopher, 2015. "Statistical arbitrage pairs trading strategies: Review and outlook," FAU Discussion Papers in Economics 09/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Haipeng Xing, 2022. "A Singular Stochastic Control Approach for Optimal Pairs Trading with Proportional Transaction Costs," JRFM, MDPI, vol. 15(4), pages 1-23, March.
    3. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    4. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697, arXiv.org, revised Sep 2018.
    5. Minh Man Ngo & Huyen Pham, 2014. "Optimal switching for pairs trading rule: a viscosity solutions approach," Papers 1412.7649, arXiv.org.
    6. Thomas Nanfeng Li & Agnès Tourin, 2016. "Optimal pairs trading with time-varying volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-29, September.
    7. Fenghui Yu & Wai-Ki Ching & Chufang Wu & Jia-Wen Gu, 2023. "Optimal Pairs Trading Strategies: A Stochastic Mean–Variance Approach," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 36-55, January.
    8. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    9. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    10. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    11. Kiyoshi Suzuki, 2018. "Optimal pair-trading strategy over long/short/square positions—empirical study," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 97-119, January.
    12. Yuji Yamada & James A. Primbs, 2018. "Model Predictive Control for Optimal Pairs Trading Portfolio with Gross Exposure and Transaction Cost Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(1), pages 1-21, March.
    13. Zequn Li & Agnès Tourin, 2022. "A Finite Difference Scheme for Pairs Trading with Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 601-632, August.
    14. Álvaro Cartea & Sebastian Jaimungal, 2016. "Algorithmic Trading Of Co-Integrated Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-18, September.
    15. T. N. Li & A. Papanicolaou, 2019. "Statistical Arbitrage for Multiple Co-Integrated Stocks," Papers 1908.02164, arXiv.org, revised Feb 2022.
    16. P. S. Lintilhac & A. Tourin, 2017. "Model-based pairs trading in the bitcoin markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(5), pages 703-716, May.
    17. Boming Ning & Kiseop Lee, 2024. "Advanced Statistical Arbitrage with Reinforcement Learning," Papers 2403.12180, arXiv.org.
    18. Jorge Guijarro-Ordonez, 2019. "High-dimensional statistical arbitrage with factor models and stochastic control," Papers 1901.09309, arXiv.org, revised Jun 2021.
    19. Boming Ning & Prakash Chakraborty & Kiseop Lee, 2023. "Optimal Entry and Exit with Signature in Statistical Arbitrage," Papers 2309.16008, arXiv.org, revised Mar 2024.
    20. Sovan Mitra & Andreas Karathanasopoulos, 2019. "Firm Value and the Impact of Operational Management," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(1), pages 61-85, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1911.10450. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.