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Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion

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  • SANGMIN LEE

    (Department of Finance and Risk Engineering, New York University, Brooklyn, New York, 11201, United States)

  • ANDREW PAPANICOLAOU

    (Department of Finance and Risk Engineering, New York University, Brooklyn, New York, 11201, United States)

Abstract

This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset's drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the investor has only partial information. We solve the control problem under both full and partial informations for utility function U(x) = x1−γ/(1 − γ), and we make comparisons. We show the existence of stable solution to the associated matrix Riccati equations in both cases for γ > 1, but for 0 < γ < 1 there remains potential for infinite value functions in finite time. Also, we quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper.

Suggested Citation

  • Sangmin Lee & Andrew Papanicolaou, 2016. "Pairs Trading Of Two Assets With Uncertainty In Co-Integration'S Level Of Mean Reversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-36, December.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:08:n:s0219024916500540
    DOI: 10.1142/S0219024916500540
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    References listed on IDEAS

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    Cited by:

    1. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    2. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    3. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    4. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    5. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697, arXiv.org, revised Sep 2018.
    6. Viviana Fanelli & Claudio Fontana & Francesco Rotondi, 2023. "A hidden Markov model for statistical arbitrage in international crude oil futures markets," Papers 2309.00875, arXiv.org.
    7. Sühan Altay & Katia Colaneri & Zehra Eksi, 2021. "Optimal convergence trading with unobservable pricing errors," Annals of Operations Research, Springer, vol. 299(1), pages 133-161, April.
    8. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    9. Flavio Angelini & Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "Implicit incentives for fund managers with partial information," Computational Management Science, Springer, vol. 18(4), pages 539-561, October.
    10. E. Boguslavskaya & M. Boguslavsky & D. Muravey, 2020. "Trading multiple mean reversion," Papers 2009.09816, arXiv.org.
    11. Suhan Altay & Katia Colaneri & Zehra Eksi, 2019. "Optimal Convergence Trading with Unobservable Pricing Errors," Papers 1910.01438, arXiv.org, revised Oct 2019.
    12. T. N. Li & A. Papanicolaou, 2019. "Statistical Arbitrage for Multiple Co-Integrated Stocks," Papers 1908.02164, arXiv.org, revised Feb 2022.

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