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Cross-impact and no-dynamic-arbitrage

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  • Michael Schneider
  • Fabrizio Lillo

Abstract

We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset $i$ to asset $j$ must be equal to the one from $j$ to $i$. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.

Suggested Citation

  • Michael Schneider & Fabrizio Lillo, 2016. "Cross-impact and no-dynamic-arbitrage," Papers 1612.07742, arXiv.org, revised Aug 2017.
    • Handle: RePEc:arx:papers:1612.07742
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    Cited by:

    1. Seungki Min & Costis Maglaras & Ciamac C. Moallemi, 2018. "Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and their Effect on Portfolio Execution," Papers 1811.05524, arXiv.org.
    2. 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.
    3. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2025. "Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework," Papers 2503.05594, arXiv.org.
    4. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    5. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327, arXiv.org, revised Jan 2019.
    6. Mathieu Rosenbaum & Mehdi Tomas, 2021. "A characterisation of cross-impact kernels," Papers 2107.08684, arXiv.org.
    7. 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.
    8. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2023. "Cross impact in derivative markets," Post-Print hal-03378903, HAL.
    9. 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.
    10. Yi Li & Ju’e Guo & Kin Keung Lai & Jinzhao Shi, 2022. "Optimal portfolio liquidation with cross-price impacts on trading," Operational Research, Springer, vol. 22(2), pages 1083-1102, April.
    11. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    12. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Working Papers hal-03378903, HAL.
    13. Francesco Cordoni & Fabrizio Lillo, 2024. "Instabilities in multi-asset and multi-agent market impact games," Annals of Operations Research, Springer, vol. 336(1), pages 505-539, May.
    14. Siu, Chi Chung & Guo, Ivan & Zhu, Song-Ping & Elliott, Robert J., 2019. "Optimal execution with regime-switching market resilience," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 17-40.
    15. Gerardo Ferrara & Maria Flora & Roberto Renò, 2025. "The Impact of COVID-19 on Italian Sovereign Bond Market Quality," Journal of Financial Services Research, Springer;Western Finance Association, vol. 67(1), pages 55-71, April.
    16. Francesco Cordoni & Fabrizio Lillo, 2020. "Instabilities in Multi-Asset and Multi-Agent Market Impact Games," Papers 2004.03546, arXiv.org, revised Nov 2021.
    17. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.
    18. Yutong Lu & Gesine Reinert & Mihai Cucuringu, 2023. "Co-trading networks for modeling dynamic interdependency structures and estimating high-dimensional covariances in US equity markets," Papers 2302.09382, arXiv.org, revised May 2024.
    19. L. C. Garcia Del Molino & I. Mastromatteo & Michael Benzaquen & J.-P. Bouchaud, 2019. "The Multivariate Kyle model: More is different," Working Papers hal-02323433, HAL.
    20. Cedric Schuhmann & Benjamin Kohler & Anton J. Heckens & Thomas Guhr, 2025. "A New Traders' Game? -- Response Functions in a Historical Perspective," Papers 2503.01629, arXiv.org.
    21. Eduardo Abi Jaber & Eyal Neuman & Sturmius Tuschmann, 2024. "Optimal Portfolio Choice with Cross-Impact Propagators," Papers 2403.10273, arXiv.org.
    22. Samim Ghamami & Paul Glasserman, 2019. "Submodular Risk Allocation," Management Science, INFORMS, vol. 65(10), pages 4656-4675, October.
    23. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.
    24. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Papers 2102.02834, arXiv.org, revised Mar 2022.

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