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Optimal switching for pairs trading rule: a viscosity solutions approach

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  • Minh Man Ngo
  • Huyen Pham

Abstract

This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat position (no holding stocks), long one short the other and short one long the other. A fixed commission cost is charged with each transaction. We use a viscosity solutions approach to prove the existence and the explicit characterization of cut-off points via the resolution of quasi-algebraic equations. We illustrate our results by numerical simulations.

Suggested Citation

  • Minh Man Ngo & Huyen Pham, 2014. "Optimal switching for pairs trading rule: a viscosity solutions approach," Papers 1412.7649, arXiv.org.
    • Handle: RePEc:arx:papers:1412.7649
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    References listed on IDEAS

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    1. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    2. 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.
    3. 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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    Cited by:

    1. Thomas Nanfeng Li & Agnès Tourin, 2016. "Optimal pairs trading with time-varying volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-29, September.
    2. Zequn Li & Agnès Tourin, 2022. "A Finite Difference Scheme for Pairs Trading with Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 601-632, August.
    3. T. N. Li & A. Tourin, 2021. "Optimal Pairs Trading with Time-Varying Volatility," Papers 2111.02834, arXiv.org.

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