An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions

Jingzhi Tie University of Georgia Hanqin Zhang National University of Singapore Qing Zhang University of Georgia

Optimization and Control mathscidoc:1702.27001

Journal of Optimization Theory and Applications, 2017
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.
Pairs trading · Optimal policy · Quasi-variational inequalities
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  • DOI 10.1007/s10957-017-1065-8
@inproceedings{jingzhi2017an,
  title={An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions},
  author={Jingzhi Tie, Hanqin Zhang, and Qing Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202112338201825152},
  booktitle={Journal of Optimization Theory and Applications},
  year={2017},
}
Jingzhi Tie, Hanqin Zhang, and Qing Zhang. An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions. 2017. In Journal of Optimization Theory and Applications. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170202112338201825152.
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