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How to build a cross-impact model from first principles: Theoretical requirements and empirical results

Author

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  • Mehdi Tomas
  • Iacopo Mastromatteo
  • Michael Benzaquen

Abstract

Trading a financial instrument pushes its price and those of other assets, a phenomenon known as cross-impact. To be of use, cross-impact models must fit data and be well-behaved so they can be applied in applications such as optimal trading. To address these issues, we introduce a set of desirable properties which constrain cross-impact models. We classify cross-impact models according to which properties they satisfy and stress them on three different asset classes to evaluate goodness-of-fit. We find that two models are robust across markets, but only one satisfies all desirable properties and is appropriate for applications.

Suggested Citation

  • Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Papers 2004.01624, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2004.01624
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    References listed on IDEAS

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    1. M. Schneider & F. Lillo, 2019. "Cross-impact and no-dynamic-arbitrage," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 137-154, January.
    2. 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.
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    5. 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.
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    7. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    8. Luis Carlos Garc'ia del Molino & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2018. "The Multivariate Kyle model: More is different," Papers 1806.07791, arXiv.org, revised Dec 2018.
    9. Aurélien Alfonsi & Alexander Schied & Florian Klöck, 2016. "Multivariate transient price impact and matrix-valued positive definite functions," Post-Print hal-00919895, HAL.
    10. Iacopo Mastromatteo & Bence Toth & Jean-Philippe Bouchaud, 2013. "Agent-based models for latent liquidity and concave price impact," Papers 1311.6262, arXiv.org, revised Dec 2014.
    11. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    12. Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
    13. 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.
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    Cited by:

    1. Eduardo Abi Jaber & Eyal Neuman & Sturmius Tuschmann, 2024. "Optimal Portfolio Choice with Cross-Impact Propagators," Papers 2403.10273, arXiv.org.
    2. Philippe van der Beck & Jean-Philippe Bouchaud & Dario Villamaina, 2024. "Ponzi Funds," Papers 2405.12768, arXiv.org.

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