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A Singular Stochastic Control Approach for Optimal Pairs Trading with Proportional Transaction Costs

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  • Haipeng Xing

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA)

Abstract

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies that determine optimally both trade times and number of shares in a pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem that involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.

Suggested Citation

  • Haipeng Xing, 2022. "A Singular Stochastic Control Approach for Optimal Pairs Trading with Proportional Transaction Costs," JRFM, MDPI, vol. 15(4), pages 1-23, March.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:4:p:147-:d:777349
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    References listed on IDEAS

    as
    1. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    2. Lei, Yaoting & Xu, Jing, 2015. "Costly arbitrage through pairs trading," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 1-19.
    3. Tourin, Agnès & Yan, Raphael, 2013. "Dynamic pairs trading using the stochastic control approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1972-1981.
    4. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
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