IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2307.15300.html
   My bibliography  Save this paper

Pairs Trading: An Optimal Selling Rule with Constraints

Author

Listed:
  • Ruyi Liu
  • Jingzhi Tie
  • Zhen Wu
  • Qing Zhang

Abstract

The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the optimal time to sell the long position and repurchase the short position in order to close the pairs position. The paper presents an optimal pairs-trading selling rule with trading constraints. In particular, the underlying stock prices evolve according to a two dimensional geometric Brownian motion and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold curve which is obtained by solving the associated HJB equations (quasi-variational inequalities). A closed form solution is obtained. A verification theorem is provided. Numerical experiments are also reported to demonstrate the optimal policies and value functions.

Suggested Citation

  • Ruyi Liu & Jingzhi Tie & Zhen Wu & Qing Zhang, 2023. "Pairs Trading: An Optimal Selling Rule with Constraints," Papers 2307.15300, arXiv.org.
    • Handle: RePEc:arx:papers:2307.15300
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2307.15300
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
    2. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    3. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    4. 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.
    5. Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
    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. Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
    2. Michele Moretto & Gianpaolo Rossini, 2008. "Vertical Integration and Operational Flexibility," Working Papers 2008.37, Fondazione Eni Enrico Mattei.
    3. Vadim Arkin & Alexander Slastnikov, 2007. "The effect of depreciation allowances on the timing of investment and government tax revenue," Annals of Operations Research, Springer, vol. 151(1), pages 307-323, April.
    4. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    5. Dammann, Felix & Ferrari, Giorgio, 2021. "On an Irreversible Investment Problem with Two-Factor Uncertainty," Center for Mathematical Economics Working Papers 646, Center for Mathematical Economics, Bielefeld University.
    6. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    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. Haipeng Xing, 2019. "A singular stochastic control approach for optimal pairs trading with proportional transaction costs," Papers 1911.10450, arXiv.org.
    9. 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.
    10. Louberge, Henri & Villeneuve, Stephane & Chesney, Marc, 2002. "Long-term risk management of nuclear waste: a real options approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 157-180, November.
    11. Armerin, Fredrik, 2024. "A Comment on “The effectiveness of carbon pricing: The role of diversification in a firm’s investment decision”," Energy Economics, Elsevier, vol. 132(C).
    12. Rohlfs, Wilko & Madlener, Reinhard, 2010. "Valuation of CCS-Ready Coal-Fired Power Plants: A Multi-Dimensional Real Options Approach," FCN Working Papers 7/2010, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    13. Christensen, Sören & Irle, Albrecht, 2020. "The monotone case approach for the solution of certain multidimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1972-1993.
    14. Luis H. R. Alvarez & Erkki Koskela, 2006. "Irreversible Investment under Interest Rate Variability: Some Generalizations," The Journal of Business, University of Chicago Press, vol. 79(2), pages 623-644, March.
    15. Hampe, Jona & Madlener, Reinhard, 2012. "Economics of High-Temperature Nuclear Reactors for Industrial Cogeneration," FCN Working Papers 10/2012, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    16. 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.
    17. Tine Compernolle & Kuno J. M. Huisman & Peter M. Kort & Maria Lavrutich & Cláudia Nunes & Jacco J. J. Thijssen, 2021. "Investment Decisions with Two-Factor Uncertainty," JRFM, MDPI, vol. 14(11), pages 1-17, November.
    18. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Sufficient and necessary conditions for perpetual multi-assets exchange options," LIDAM Discussion Papers CORE 2011035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Optimal time to invest when the price processes are geometric Brownian motions. A tentative based on smooth fit," LIDAM Discussion Papers CORE 2011034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. 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.

    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:2307.15300. 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.