IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1706.07021.html
   My bibliography  Save this paper

Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market

Author

Listed:
  • Roberto Baviera
  • Tommaso Santagostino Baldi

Abstract

In this paper we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market entry/exit levels. First we show that the optimal strategy a' la Bertram depends on the probabilities to reach entry/exit levels, on expected First-Passage-Times and on expected First-Exit-Times from an interval. Then, when the underlying log-price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for expected First-Exit-Times and we derive the long-run return of the strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pair in the energy futures' market, reporting in detail the analysis for a spread on Heating-Oil and Gas-Oil futures in one year sample of half-an-hour market prices.

Suggested Citation

  • Roberto Baviera & Tommaso Santagostino Baldi, 2017. "Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market," Papers 1706.07021, arXiv.org.
  • Handle: RePEc:arx:papers:1706.07021
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1706.07021
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert Elliott & John Van Der Hoek & William Malcolm, 2005. "Pairs trading," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 271-276.
    2. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    3. Mark Cummins & Andrea Bucca, 2012. "Quantitative spread trading on crude oil and refined products markets," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1857-1875, December.
    4. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    5. Jun Yu & Peter C.B. Phillips, 2001. "Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate," Cowles Foundation Discussion Papers 1309, Cowles Foundation for Research in Economics, Yale University.
    6. 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.
    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.
    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. 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.
    2. Alexander Lipton & Marcos Lopez de Prado, 2020. "A closed-form solution for optimal mean-reverting trading strategies," Papers 2003.10502, arXiv.org.

    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. Baviera, Roberto & Santagostino Baldi, Tommaso, 2019. "Stop-loss and leverage in optimal statistical arbitrage with an application to energy market," Energy Economics, Elsevier, vol. 79(C), pages 130-143.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Alexander Lipton & Marcos Lopez de Prado, 2020. "A closed-form solution for optimal mean-reverting trading strategies," Papers 2003.10502, arXiv.org.
    7. 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.
    8. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697, arXiv.org, revised Sep 2018.
    9. Khizar Qureshi & Tauhid Zaman, 2024. "Pairs Trading Using a Novel Graphical Matching Approach," Papers 2403.07998, arXiv.org.
    10. Bo Liu & Lo-Bin Chang & Hélyette Geman, 2017. "Intraday pairs trading strategies on high frequency data: the case of oil companies," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 87-100, January.
    11. 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.
    12. Hsu, Chih-Hsiang, 2021. "The predictability of the return correlation of futures with different expirations in the Chinese futures market," Resources Policy, Elsevier, vol. 74(C).
    13. Peter C. B. Phillips & Jun Yu, 2023. "Information loss in volatility measurement with flat price trading," Empirical Economics, Springer, vol. 64(6), pages 2957-2999, June.
    14. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
    15. Boming Ning & Kiseop Lee, 2024. "Advanced Statistical Arbitrage with Reinforcement Learning," Papers 2403.12180, arXiv.org.
    16. Ahmet G�nc�, 2015. "Statistical arbitrage in the Black-Scholes framework," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1489-1499, September.
    17. Haipeng Xing, 2019. "A singular stochastic control approach for optimal pairs trading with proportional transaction costs," Papers 1911.10450, arXiv.org.
    18. Ahmet Göncü & Erdinc Akyildirim, 2016. "A stochastic model for commodity pairs trading," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1843-1857, December.
    19. Huck, Nicolas, 2009. "Pairs selection and outranking: An application to the S&P 100 index," European Journal of Operational Research, Elsevier, vol. 196(2), pages 819-825, July.
    20. Terence D.Agbeyegbe & Elena Goldman, 2005. "Estimation of threshold time series models using efficient jump MCMC," Economics Working Paper Archive at Hunter College 406, Hunter College Department of Economics, revised 2005.

    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:1706.07021. 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.