IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1701.00875.html
   My bibliography  Save this paper

Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach

Author

Listed:
  • Tim Leung
  • Yerkin Kitapbayev

Abstract

We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short strategy; (ii) the short-long strategy, and (iii) the chooser strategy, i.e. the trader can enter into the spread by taking either long or short position. In each of these cases, we solve an optimal double stopping problem to determine the optimal timing for starting and subsequently closing the position. We utilize the local time-space calculus of Peskir (2005a) and derive the nonlinear integral equations of Volterra-type that uniquely char- acterize the boundaries associated with the optimal timing decisions in all three problems. These integral equations are used to numerically compute the optimal boundaries.

Suggested Citation

  • Tim Leung & Yerkin Kitapbayev, 2017. "Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach," Papers 1701.00875, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1701.00875
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1701.00875
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    2. Robert Elliott & John Van Der Hoek & William Malcolm, 2005. "Pairs trading," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 271-276.
    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. Tim Leung & Xin Li, 2016. "Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9839.
    5. Marco Avellaneda & Jeong-Hyun Lee, 2010. "Statistical arbitrage in the US equities market," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 761-782.
    6. Min Dai & Yifei Zhong & Yue Kuen Kwok, 2011. "Optimal arbitrage strategies on stock index futures under position limits," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(4), pages 394-406, April.
    7. 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.
    8. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    9. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    10. Tim Leung & Xin Li, 2016. "Futures Trading Under Mean Reversion," World Scientific Book Chapters, in: Optimal Mean Reversion Trading Mathematical Analysis and Practical Applications, chapter 5, pages 105-127, World Scientific Publishing Co. Pte. Ltd..
    11. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    12. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    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. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    2. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    3. D'Auria, Bernardo & García Portugués, Eduardo & Guada Azze, Abel, 2021. "Optimal stopping of an Ornstein-Uhlenbeck bridge," DES - Working Papers. Statistics and Econometrics. WS 33508, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Jize Zhang & Tim Leung & Aleksandr Y. Aravkin, 2018. "Mean Reverting Portfolios via Penalized OU-Likelihood Estimation," Papers 1803.06460, arXiv.org.
    5. 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.

    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. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    2. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    3. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    4. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
    5. 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.
    6. Endres, Sylvia & Stübinger, Johannes, 2017. "Optimal trading strategies for Lévy-driven Ornstein-Uhlenbeck processes," FAU Discussion Papers in Economics 17/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. Stübinger, Johannes & Endres, Sylvia, 2017. "Pairs trading with a mean-reverting jump-diffusion model on high-frequency data," FAU Discussion Papers in Economics 10/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    8. Boming Ning & Prakash Chakraborty & Kiseop Lee, 2023. "Optimal Entry and Exit with Signature in Statistical Arbitrage," Papers 2309.16008, arXiv.org, revised Mar 2024.
    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. Tim Leung & Kevin W. Lu, 2023. "Monte Carlo Simulation for Trading Under a L\'evy-Driven Mean-Reverting Framework," Papers 2309.05512, arXiv.org, revised Jan 2024.
    11. Peng Huang & Tianxiang Wang, 2016. "On the Profitability of Optimal Mean Reversion Trading Strategies," Papers 1602.05858, arXiv.org.
    12. Bahman Angoshtari & Tim Leung, 2020. "Optimal trading of a basket of futures contracts," Annals of Finance, Springer, vol. 16(2), pages 253-280, June.
    13. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    14. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078.
    15. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    16. Johannes Stübinger & Lucas Schneider, 2019. "Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500," JRFM, MDPI, vol. 12(2), pages 1-19, April.
    17. Ahmet Göncü & Erdinc Akyildirim, 2017. "Statistical Arbitrage In The Multi-Asset Black–Scholes Economy," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-18, March.
    18. Boming Ning & Kiseop Lee, 2024. "Advanced Statistical Arbitrage with Reinforcement Learning," Papers 2403.12180, arXiv.org.
    19. Haipeng Xing, 2019. "A singular stochastic control approach for optimal pairs trading with proportional transaction costs," Papers 1911.10450, arXiv.org.
    20. Tim Leung & Brian Ward, 2020. "Tracking VIX with VIX Futures: Portfolio Construction and Performance," World Scientific Book Chapters, in: John B Guerard & William T Ziemba (ed.), HANDBOOK OF APPLIED INVESTMENT RESEARCH, chapter 21, pages 557-596, World Scientific Publishing Co. Pte. Ltd..

    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:1701.00875. 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.