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A General Framework for Pairs Trading with a Control-Theoretic Point of View

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  • Atul Deshpande
  • B. Ross Barmish

Abstract

Pairs trading is a market-neutral strategy that exploits historical correlation between stocks to achieve statistical arbitrage. Existing pairs-trading algorithms in the literature require rather restrictive assumptions on the underlying stochastic stock-price processes and the so-called spread function. In contrast to existing literature, we consider an algorithm for pairs trading which requires less restrictive assumptions than heretofore considered. Since our point of view is control-theoretic in nature, the analysis and results are straightforward to follow by a non-expert in finance. To this end, we describe a general pairs-trading algorithm which allows the user to define a rather arbitrary spread function which is used in a feedback context to modify the investment levels dynamically over time. When this function, in combination with the price process, satisfies a certain mean-reversion condition, we deem the stocks to be a tradeable pair. For such a case, we prove that our control-inspired trading algorithm results in positive expected growth in account value. Finally, we describe tests of our algorithm on historical trading data by fitting stock price pairs to a popular spread function used in literature. Simulation results from these tests demonstrate robust growth while avoiding huge drawdowns.

Suggested Citation

  • Atul Deshpande & B. Ross Barmish, 2016. "A General Framework for Pairs Trading with a Control-Theoretic Point of View," Papers 1608.03636, arXiv.org.
    • Handle: RePEc:arx:papers:1608.03636
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    References listed on IDEAS

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    1. Binh Do & Robert Faff, 2012. "Are Pairs Trading Profits Robust To Trading Costs?," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 35(2), pages 261-287, June.
    2. 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.
    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.
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    Cited by:

    1. Yuji Yamada & James A. Primbs, 2018. "Model Predictive Control for Optimal Pairs Trading Portfolio with Gross Exposure and Transaction Cost Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(1), pages 1-21, March.
    2. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    3. Atul Deshpande & B. Ross Barmish, 2018. "A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control," Papers 1803.04591, arXiv.org.
    4. Atul Deshpande & John A Gubner & B. Ross Barmish, 2020. "On Simultaneous Long-Short Stock Trading Controllers with Cross-Coupling," Papers 2011.09109, arXiv.org.

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