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The Multivariate Kyle model: More is different

Author

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  • L. C. Garcia Del Molino
  • I. Mastromatteo
  • Michael Benzaquen

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • J.-P. Bouchaud

Abstract

We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its interpretation. We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:hal-02323433
    Note: View the original document on HAL open archive server: https://hal.science/hal-02323433
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    References listed on IDEAS

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    1. Iacopo Mastromatteo & Michael Benzaquen & Zoltan Eisler & Jean-Philippe Bouchaud, 2017. "Trading Lightly: Cross-Impact and Optimal Portfolio Execution," Papers 1702.03838, arXiv.org, revised Aug 2017.
    2. Guillaume Lasserre, 2004. "Asymmetric information and imperfect competition in a continuous time multivariate security model," Finance and Stochastics, Springer, vol. 8(2), pages 285-309, May.
    3. Shanshan Wang & Rudi Schäfer & Thomas Guhr, 2016. "Cross-response in correlated financial markets: individual stocks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(4), pages 1-16, April.
    4. Shanshan Wang & Rudi Schafer & Thomas Guhr, 2016. "Cross-response in correlated financial markets: individual stocks," Papers 1603.01580, arXiv.org, revised Apr 2016.
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    6. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    7. Hasbrouck, Joel & Seppi, Duane J., 2001. "Common factors in prices, order flows, and liquidity," Journal of Financial Economics, Elsevier, vol. 59(3), pages 383-411, March.
    8. Vitale, Paolo, 2012. "Risk-averse insider trading in multi-asset sequential auction markets," Economics Letters, Elsevier, vol. 117(3), pages 673-675.
    9. Aurélien Alfonsi & Florian Klöck & Alexander Schied, 2016. "Multivariate Transient Price Impact and Matrix-Valued Positive Definite Functions," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 914-934, August.
    10. Caballe, Jordi & Krishnan, Murugappa, 1994. "Imperfect Competition in a Multi-security Market with Risk Neutrality," Econometrica, Econometric Society, vol. 62(3), pages 695-704, May.
    11. Aurélien Alfonsi & Alexander Schied & Florian Klöck, 2016. "Multivariate transient price impact and matrix-valued positive definite functions," Post-Print hal-00919895, HAL.
    12. Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Working Papers hal-03378903, HAL.
    2. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Papers 2102.02834, arXiv.org, revised Mar 2022.
    3. Ibrahim Ekren & Brad Mostowski & Gordan v{Z}itkovi'c, 2022. "Kyle's Model with Stochastic Liquidity," Papers 2204.11069, arXiv.org.
    4. Luciano Somoza & Antoine Didisheim, 2022. "The End of the Crypto-Diversification Myth," Swiss Finance Institute Research Paper Series 22-53, Swiss Finance Institute.
    5. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Cross impact in derivative markets," Post-Print hal-03378903, HAL.
    6. Shreya Bose & Ibrahim Ekren, 2021. "Multidimensional Kyle-Back model with a risk averse informed trader," Papers 2111.01957, arXiv.org.
    7. Charles-Albert Lehalle & Eyal Neuman & Segev Shlomov, 2021. "Phase Transitions in Kyle's Model with Market Maker Profit Incentives," Papers 2103.04481, arXiv.org.
    8. 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.

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