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Cross-impact and no-dynamic-arbitrage

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  • M. Schneider
  • F. Lillo

Abstract

We extend the ‘No-dynamic-arbitrage and market impact’-framework of Gatheral [Quant. Finance, 2010, 10(7), 749–759] 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.

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  • M. Schneider & F. Lillo, 2019. "Cross-impact and no-dynamic-arbitrage," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 137-154, January.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:1:p:137-154
    DOI: 10.1080/14697688.2018.1467033
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    Citations

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    Cited by:

    1. Alexander Barzykin & Fabrizio Lillo, 2019. "Optimal VWAP execution under transient price impact," Papers 1901.02327, arXiv.org, revised Jan 2019.
    2. 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.
    3. 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.
    4. Samim Ghamami & Paul Glasserman, 2019. "Submodular Risk Allocation," Management Science, INFORMS, vol. 65(10), pages 4656-4675, October.
    5. 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.
    6. 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.
    7. Mathieu Rosenbaum & Mehdi Tomas, 2021. "A characterisation of cross-impact kernels," Papers 2107.08684, arXiv.org.
    8. 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.
    9. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Cross impact in derivative markets," Post-Print hal-03378903, HAL.
    10. 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.
    11. 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.
    12. Eduardo Abi Jaber & Eyal Neuman & Sturmius Tuschmann, 2024. "Optimal Portfolio Choice with Cross-Impact Propagators," Papers 2403.10273, arXiv.org.
    13. Gerry Tsoukalas & Jiang Wang & Kay Giesecke, 2019. "Dynamic Portfolio Execution," Management Science, INFORMS, vol. 67(5), pages 2015-2040, May.
    14. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    15. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Working Papers hal-03378903, HAL.
    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. 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.
    18. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Papers 2102.02834, arXiv.org, revised Mar 2022.
    19. 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.
    20. 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.

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