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Analytic value function for optimal regime-switching pairs trading rules

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  • Yang Bai
  • Lan Wu

Abstract

We introduce a regime-switching Ornstein–Uhlenbeck (O–U) model to address an optimal investment problem. Our study gives a closed-form expression for a regime-switching pairs trading value function consisting of probability and expectation of the double boundary stopping time of the Markov-modulated O–U process. We derive analytic solutions for the homogenous and non-homogenous ODE systems with initial value conditions for probability and expectation of the double boundary stopping time, and translate the solutions with boundary value conditions into solutions with initial value conditions. Based on the smoothness and continuity of the value function, we can obtain the optimum of the value function with thresholds and guarantee the existence of optimal thresholds in a finite closed interval. Our numerical analysis illustrates the rationality of theoretical model and the shape of transition probability and expected stopping time, as well as discusses sensitivity analysis in both one-state and two-state regime-switching models. We find that the optimal expected return per unit time in the two-state regime-switching model is higher than that of one-state regime-switching model. Likewise, the regime-switching model’s optimal thresholds are closer and more symmetric to the long-term mean.

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  • Yang Bai & Lan Wu, 2018. "Analytic value function for optimal regime-switching pairs trading rules," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 637-654, April.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:4:p:637-654
    DOI: 10.1080/14697688.2017.1336281
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    Cited by:

    1. Li Chen & Guang Zhang, 2022. "COVID-19 Effects on Arbitrage Trading in the Energy Market," Energies, MDPI, vol. 15(13), pages 1-13, June.
    2. Alexander Lipton & Marcos Lopez de Prado, 2020. "A closed-form solution for optimal mean-reverting trading strategies," Papers 2003.10502, arXiv.org.
    3. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.
    4. Guang Zhang, 2020. "Pairs Trading with Nonlinear and Non-Gaussian State Space Models," Papers 2005.09794, arXiv.org.
    5. Weiliang Lu & Alexis Arrigoni & Anatoliy Swishchuk & Stéphane Goutte, 2021. "Modelling of Fuel- and Energy-Switching Prices by Mean-Reverting Processes and Their Applications to Alberta Energy Markets," Mathematics, MDPI, vol. 9(7), pages 1-24, March.
    6. Vladimír Holý & Michal Černý, 2022. "Bertram’s pairs trading strategy with bounded risk," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 667-682, June.
    7. Endres, Sylvia & Stübinger, Johannes, 2018. "A flexible regime switching model with pairs trading application to the S&P 500 high-frequency stock returns," FAU Discussion Papers in Economics 07/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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