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

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  • Mehdi Tomas
  • Iacopo Mastromatteo
  • Michael Benzaquen

Abstract

Trading a financial instrument induces a price response on itself and on other correlated instruments, a phenomenon known as cross-impact. Unfortunately, empirical measures of cross-impact are affected by a large estimation error due to both the large number of interactions to infer and the strongly fluctuating nature of price returns. In this study we propose a principled approach that leverages simple consistency criteria (symmetries, no-arbitrage conditions, correlation and liquidity limit-case properties) in order to impose ex-ante properties that might be required for practical applications. We validate our approach on empirical data for several asset classes, thus determining which properties are desirable across multiple markets. In particular, our results show that two cross-impact models perform well in all markets studied but only one is suitable for other applications, such as optimal execution.

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 Sep 2020.
    • Handle: RePEc:arx:papers:2004.01624
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    References listed on IDEAS

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    1. Aurélien Alfonsi & Alexander Schied & Florian Klöck, 2016. "Multivariate transient price impact and matrix-valued positive definite functions," Post-Print hal-00919895, HAL.
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    3. 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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    7. 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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    9. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    10. 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.
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