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Cross impact in derivative markets

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Listed:
  • Mehdi Tomas

    (LadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Iacopo Mastromatteo

    (Auteur indépendant)

  • Michael Benzaquen

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

Abstract

We introduce a linear cross-impact framework in a setting in which the price of some given financial instruments (derivatives) is a deterministic function of one or more, possibly tradeable, stochastic factors (underlying). We show that a particular cross-impact model, the multivariate Kyle model, prevents arbitrage and aggregates (potentially non-stationary) traded order flows on derivatives into (roughly stationary) liquidity pools aggregating order flows traded on both derivatives and underlying. Using E-Mini futures and options along with VIX futures, we provide empirical evidence that the price formation process from order flows on derivatives is driven by cross-impact and confirm that the simple Kyle cross-impact model is successful at capturing parsimoniously such empirical phenomenology. Our framework may be used in practice for estimating execution costs, in particular hedging costs.

Suggested Citation

  • Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Cross impact in derivative markets," Post-Print hal-03378903, HAL.
    • Handle: RePEc:hal:journl:hal-03378903
    Note: View the original document on HAL open archive server: https://hal.science/hal-03378903
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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. 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.
    3. Emilio Said, 2019. "How Option Hedging Shapes Market Impact," Papers 1910.05056, arXiv.org, revised Nov 2019.
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    5. Bence Toth & Zoltan Eisler & Jean-Philippe Bouchaud, 2016. "The square-root impact law also holds for option markets," Papers 1602.03043, arXiv.org.
    6. 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.
    7. Bruno Bouchard & G. Loeper & Y. Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01611790, HAL.
    8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    9. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Tóth, 2018. "Linear models for the impact of order flow on prices. I. History dependent impact models," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 903-915, June.
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    11. 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.
    12. 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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