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Optimal dynamic pairs trading of futures under a two-factor mean-reverting model

Author

Listed:
  • Tim Leung

    (Department of Applied Mathematics, University of Washington, Seattle WA 98195, United States)

  • Raphael Yan

    (#x2020;Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada)

Abstract

We study the problem of dynamically trading a pair of futures contracts. We consider a two-factor mean-reverting model, where the spot price tends to evolve around its stochastic equilibrium that is also mean-reverting. We derive the futures price dynamics and determine the optimal futures trading strategy by solving a utility maximization problem. By analyzing the associated Hamilton–Jacobi–Bellman equation, we solve the utility maximization explicitly and provide the optimal trading strategies in closed form. Our strategies are applied to volatility (VIX) futures trading, and illustrated in a series of numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:03:n:s2424786318500275
    DOI: 10.1142/S2424786318500275
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    References listed on IDEAS

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    1. 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.
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    13. 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.
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    18. 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.
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    Citations

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    Cited by:

    1. Tim Leung & Yang Zhou, 2019. "Optimal dynamic futures portfolio in a regime-switching market framework," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-27, December.
    2. Bahman Angoshtari & Tim Leung, 2020. "Optimal trading of a basket of futures contracts," Annals of Finance, Springer, vol. 16(2), pages 253-280, June.
    3. Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
    4. 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..
    5. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    6. Tim Leung & Yang Zhou, 2020. "Optimal dynamic futures portfolio in a regime-switching market framework," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-27, February.
    7. Xiaodong Chen & Tim Leung & Yang Zhou, 2022. "Constrained dynamic futures portfolios with stochastic basis," Annals of Finance, Springer, vol. 18(1), pages 1-33, March.

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