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Pairs Trading: An Optimal Selling Rule with Constraints

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Listed:
  • Ruyi Liu
  • Jingzhi Tie
  • Zhen Wu
  • Qing Zhang

Abstract

The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the optimal time to sell the long position and repurchase the short position in order to close the pairs position. The paper presents an optimal pairs-trading selling rule with trading constraints. In particular, the underlying stock prices evolve according to a two dimensional geometric Brownian motion and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold curve which is obtained by solving the associated HJB equations (quasi-variational inequalities). A closed form solution is obtained. A verification theorem is provided. Numerical experiments are also reported to demonstrate the optimal policies and value functions.

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  • Ruyi Liu & Jingzhi Tie & Zhen Wu & Qing Zhang, 2023. "Pairs Trading: An Optimal Selling Rule with Constraints," Papers 2307.15300, arXiv.org.
    • Handle: RePEc:arx:papers:2307.15300
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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. 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.
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