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How Option Hedging Shapes Market Impact

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  • Emilio Said

    (FiQuant, MICS)

Abstract

We present a perturbation theory of the market impact based on an extension of the framework proposed by [Loeper, 2018] -- originally based on [Liu and Yong, 2005] -- in which we consider only local linear market impact. We study the execution process of hedging derivatives and show how these hedging metaorders can explain some stylized facts observed in the empirical market impact literature. As we are interested in the execution process of hedging we will establish that the arbitrage opportunities that exist in the discrete time setting vanish when the trading frequency goes to infinity letting us to derive a pricing equation. Furthermore our approach retrieves several results already established in the option pricing literature such that the spot dynamics modified by the market impact. We also study the relaxation of our hedging metaorders based on the fair pricing hypothesis and establish a relation between the immediate impact and the permanent impact which is in agreement with recent empirical studies on the subject.

Suggested Citation

  • Emilio Said, 2019. "How Option Hedging Shapes Market Impact," Papers 1910.05056, arXiv.org, revised Nov 2019.
    • Handle: RePEc:arx:papers:1910.05056
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    References listed on IDEAS

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    1. Nataliya Bershova & Dmitry Rakhlin, 2013. "The non-linear market impact of large trades: evidence from buy-side order flow," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1759-1778, November.
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    11. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
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    13. Bence Toth & Zoltan Eisler & Jean-Philippe Bouchaud, 2016. "The square-root impact law also holds for option markets," Papers 1602.03043, arXiv.org.
    14. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    15. Emilio Said & Ahmed Bel Hadj Ayed & Alexandre Husson & Frédéric Abergel, 2018. "Market Impact: A systematic study of limit orders," Working Papers hal-01561128, HAL.
    16. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
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    18. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2023. "Cross impact in derivative markets," Post-Print hal-03378903, HAL.
    2. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Working Papers hal-03378903, HAL.
    3. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2021. "Cross impact in derivative markets," Papers 2102.02834, arXiv.org, revised Mar 2022.
    4. Behzad Alimoradian & Karim Barigou & Anne Eyraud-Loisel, 2022. "Derivatives under market impact: Disentangling cost and information," Working Papers hal-03668432, HAL.

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