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Optimal mean-reverting spread trading: nonlinear integral equation approach

Author

Listed:
  • Yerkin Kitapbayev

    (Boston University)

  • Tim Leung

    (University of Washington)

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 (J Theor Probab 18:499–535, 2005a) and derive the nonlinear integral equations of Volterra-type that uniquely characterize 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

  • 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.
    • Handle: RePEc:kap:annfin:v:13:y:2017:i:2:d:10.1007_s10436-017-0295-y
    DOI: 10.1007/s10436-017-0295-y
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    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.
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    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, August.
    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.
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    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.
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    Cited by:

    1. 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.
    2. Jize Zhang & Tim Leung & Aleksandr Y. Aravkin, 2018. "Mean Reverting Portfolios via Penalized OU-Likelihood Estimation," Papers 1803.06460, arXiv.org.
    3. D'Auria, Bernardo & 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. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    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. Azze, A. & D’Auria, B. & García-Portugués, E., 2024. "Optimal stopping of an Ornstein–Uhlenbeck bridge," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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    More about this item

    Keywords

    Spread trading; Optimal stopping; Free-boundary problem; Local time; Integral equation;
    All these keywords.

    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

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