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Optimal Pairs Trading Strategies: A Stochastic Mean–Variance Approach

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Abstract

In this paper, we consider optimal pairs trading strategies in terms of static optimality and dynamic optimality under mean–variance criterion. The spread of the entity pairs is assumed to be mean-reverting and follows an Ornstein–Uhlenbeck process. A constrained optimal control problem is considered, and the Lagrange multiplier technique is adopted to transform the primal problem into a family of linear-quadratic optimal control problems that can be solved by the classical dynamic programming principle. Both solutions for static and dynamic optimal pairs trading problems are derived and discussed. We show that the “static and dynamic optimality” is a viable approach to the time-inconsistent control problem. Furthermore, numerical experiments are presented to demonstrate the performance of the optimal pairs trading strategies.

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Notes

  1. In practice, the value of \(\gamma \) is important to the pairs trading strategies and can be determined by co-integration test. For more detailed discussion, we refer to [10]. If the two securities are stocks from the same financial sector (like two banking stocks), one may take this ratio to be unity.

  2. The formation is not the focus of this paper, so we omit the details here. For more discussions about the selection of pair of assets, please refer to [10, 11] and [13].

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Acknowledgements

The authors would like to thank the two anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (No. 11671158, 11801262), the Research Grants Council of Hong Kong, GRF Grant (No. 17301522), the Gruangdong Basic and Applied Basic Research Foundation 2021A (No. 1515010031), Shenzhen Humanities and Social Sciences Key Research Bases, IMR and Seed Funding Research Grant, the University of Hong Kong.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, TU Delft, 2628 CD, Delft, The Netherlands

    Fenghui Yu

  2. Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

    Wai-Ki Ching & Chufang Wu

  3. Hughes Hall, Wollaston Road, Cambridge, UK

    Wai-Ki Ching

  4. Department of Mathematics, Southern University of Science and Technology, Shenzhen, China

    Chufang Wu & Jia-Wen Gu

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  1. Fenghui Yu
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  2. Wai-Ki Ching
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  4. Jia-Wen Gu
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Correspondence to Chufang Wu.

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Communicated by Klaus Reiner Schenk-Hoppe.

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Yu, F., Ching, WK., Wu, C. et al. Optimal Pairs Trading Strategies: A Stochastic Mean–Variance Approach. J Optim Theory Appl 196, 36–55 (2023). https://doi.org/10.1007/s10957-022-02131-x

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  • DOI: https://doi.org/10.1007/s10957-022-02131-x

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