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

Author

Listed:
  • Mehdi Tomas
  • Iacopo Mastromatteo

    (SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies)

  • Michael Benzaquen

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

Abstract

Cross-impact, namely the fact that on average buy (sell) trades on a financial instrument induce positive (negative) price changes in other correlated assets, can be measured from abundant, although noisy, market data. In this paper we propose a principled approach that allows to perform model selection for cross-impact models, showing that symmetries and consistency requirements are particularly effective in reducing the universe of possible models to a much smaller set of viable candidates, thus mitigating the effect of noise on the properties of the inferred model. We review the empirical performance of a large number of cross-impact models, comparing their strengths and weaknesses on a number of asset classes (futures, stocks, calendar spreads). Besides showing which models perform better, we argue that in presence of comparable statistical performance, which is often the case in a noisy world, it is relevant to favor models that provide ex-ante theoretical guarantees on their behavior in limit cases. From this perspective, we advocate that the empirical validation of universal properties (symmetries, invariances) should be regarded as holding a much deeper epistemological value than any measure of statistical performance on specific model instances.

Suggested Citation

  • Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Working Papers hal-02567489, HAL.
  • Handle: RePEc:hal:wpaper:hal-02567489
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-02567489
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    References listed on IDEAS

    as
    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. Paolo Pasquariello & Clara Vega, 2015. "Strategic Cross-Trading in the U.S. Stock Market," Review of Finance, European Finance Association, vol. 19(1), pages 229-282.
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    4. 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.
    5. Thibault Jaisson, 2015. "Market impact as anticipation of the order flow imbalance," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1123-1135, July.
    6. M. Schneider & F. Lillo, 2019. "Cross-impact and no-dynamic-arbitrage," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 137-154, January.
    7. 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.
    8. Olivier Guéant, 2017. "Optimal market making," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02862554, HAL.
    9. 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.
    10. Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
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