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Optimal Transport and Risk Aversion in Kyle's Model of Informed Trading

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  • Kerry Back
  • Francois Cocquemas
  • Ibrahim Ekren
  • Abraham Lioui

Abstract

We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections to extend the model to multiple assets, general distributions, and risk-averse market makers. With risk-averse market makers, liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean reverting. We illustrate the model by showing that implied volatilities predict stock returns when there is informed trading in stocks and options and market makers are risk averse.

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  • Kerry Back & Francois Cocquemas & Ibrahim Ekren & Abraham Lioui, 2020. "Optimal Transport and Risk Aversion in Kyle's Model of Informed Trading," Papers 2006.09518, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2006.09518
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    References listed on IDEAS

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    1. Jean-Charles Rochet & Jean-Luc Vila, 1994. "Insider Trading without Normality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 131-152.
    2. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2020. "The Multivariate Kyle model: More is different," Post-Print hal-02323433, HAL.
    3. Pierre Collin‐Dufresne & Vyacheslav Fos, 2016. "Insider Trading, Stochastic Liquidity, and Equilibrium Prices," Econometrica, Econometric Society, vol. 84, pages 1441-1475, July.
    4. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    5. Dmitry Kramkov & Yan Xu, 2019. "An optimal transport problem with backward martingale constraints motivated by insider trading," Papers 1906.03309, arXiv.org.
    6. Biais, Bruno & Hillion, Pierre, 1994. "Insider and Liquidity Trading in Stock and Options Markets," The Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 743-780.
    7. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    8. Kacperczyk, Marcin & Pagnotta, Emiliano, 2019. "Becker Meets Kyle: Inside Insider Trading," CEPR Discussion Papers 13928, C.E.P.R. Discussion Papers.
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    Cited by:

    1. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    2. Shreya Bose & Ibrahim Ekren, 2020. "Kyle-Back Models with risk aversion and non-Gaussian Beliefs," Papers 2008.06377, arXiv.org, revised Oct 2022.
    3. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    4. Guo, Mng, 2023. "Dampening effect and market efficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 148(C).

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