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Anomalous impact in reaction-diffusion models

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  • Iacopo Mastromatteo
  • Bence Toth
  • Jean-Philippe Bouchaud

Abstract

We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.

Suggested Citation

  • Iacopo Mastromatteo & Bence Toth & Jean-Philippe Bouchaud, 2014. "Anomalous impact in reaction-diffusion models," Papers 1403.3571, arXiv.org.
    • Handle: RePEc:arx:papers:1403.3571
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    File URL: http://arxiv.org/pdf/1403.3571
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    Cited by:

    1. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Post-Print hal-01277584, HAL.
    2. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," Papers 1503.06704, arXiv.org, revised Oct 2015.
    3. Jonathan Donier & Jean-Philippe Bouchaud, 2015. "Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-11, October.
    4. Jean-Philippe Bouchaud, 2021. "The Inelastic Market Hypothesis: A Microstructural Interpretation," Papers 2108.00242, arXiv.org, revised Jan 2022.
    5. Bolster, Diogo & Benson, David A. & Singha, Kamini, 2017. "Upscaling chemical reactions in multicontinuum systems: When might time fractional equations work?," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 414-425.
    6. Jonathan Donier & Julius Bonart, 2014. "A Million Metaorder Analysis of Market Impact on the Bitcoin," Papers 1412.4503, arXiv.org, revised Sep 2015.

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