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An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions

Author

Listed:
  • Jingzhi Tie

    (University of Georgia)

  • Hanqin Zhang

    (Academia Sinica
    National University of Singapore)

  • Qing Zhang

    (University of Georgia)

Abstract

This paper is concerned with an optimal strategy for simultaneously trading of a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by their prices divergence and consists of a pair of positions to short the strong stock and to long the weak one. Such a strategy bets on the reversal of their price strengths. From the viewpoint of technical tractability, typical pairs-trading models usually assume a difference of the stock prices satisfies a mean-reversion equation. In this paper, we consider the optimal pairs-trading problem by allowing the stock prices to follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. The optimal policy is characterized by threshold curves obtained by solving the associated HJB equations. Numerical examples are included to demonstrate the dependence of our trading rules on various parameters and to illustrate how to implement the results in practice.

Suggested Citation

  • Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-017-1065-8
    DOI: 10.1007/s10957-017-1065-8
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    References listed on IDEAS

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    1. Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
    2. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    3. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    4. 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.
    5. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. Amit Sinha, 2024. "Daily and Weekly Geometric Brownian Motion Stock Index Forecasts," JRFM, MDPI, vol. 17(10), pages 1-22, September.
    2. Chung-Han Hsieh & Xin-Yu Wang, 2023. "Robust Trading in a Generalized Lattice Market," Papers 2310.11023, arXiv.org.
    3. Ruyi Liu & Jingzhi Tie & Zhen Wu & Qing Zhang, 2023. "Pairs Trading: An Optimal Selling Rule with Constraints," Papers 2307.15300, arXiv.org.
    4. Chung-Han Hsieh, 2022. "On Robustness of Double Linear Trading with Transaction Costs," Papers 2209.12383, arXiv.org.
    5. Yen-Sheng Lee, 2022. "Representative Bias and Pairs Trade: Evidence From S&P 500 and Russell 2000 Indexes," SAGE Open, , vol. 12(3), pages 21582440221, August.
    6. Chung-Han Hsieh, 2022. "From Semi-Infinite Constraints to Structured Robust Policies: Optimal Gain Selection for Financial Systems," Papers 2202.02300, arXiv.org, revised Jan 2025.
    7. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.

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