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A characterisation of cross-impact kernels

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  • Mathieu Rosenbaum
  • Mehdi Tomas

Abstract

Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisations for trading purposes. We focus on kernels that guarantee that prices are martingales and anticipate future order flow (martingale-admissible kernels) and those that ensure there is no possible price manipulation (no-statistical-arbitrage-admissible kernels). We determine the overlap between these two classes and provide formulas for calibration of cross-impact kernels on data. We illustrate our results using SP500 futures data.

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  • Mathieu Rosenbaum & Mehdi Tomas, 2021. "A characterisation of cross-impact kernels," Papers 2107.08684, arXiv.org.
    • Handle: RePEc:arx:papers:2107.08684
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    References listed on IDEAS

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    1. 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.
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    7. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Working Papers hal-03378903, HAL.
    8. 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.
    9. 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.
    10. Thibault Jaisson, 2015. "Market impact as anticipation of the order flow imbalance," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1123-1135, July.
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    13. Aurélien Alfonsi & Alexander Schied & Florian Klöck, 2016. "Multivariate transient price impact and matrix-valued positive definite functions," Post-Print hal-00919895, HAL.
    14. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    15. 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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