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Crossover from Linear to Square-Root Market Impact.

Frédéric Bucci1,2, Michael Benzaquen2,3,4, Fabrizio Lillo5

  • 1Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy.

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We found that order volume determines market impact, shifting from linear to square-root scaling. A dynamical liquidity theory with fast and slow timescales explains this crossover quantitatively.

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Area of Science:

  • Quantitative Finance
  • Market Microstructure
  • Statistical Mechanics

Background:

  • Understanding market impact is crucial for institutional traders.
  • Existing models often simplify the complex dynamics of price formation.
  • Liquidity dynamics are known to exhibit multiple timescales.

Purpose of the Study:

  • To empirically investigate the relationship between order volume and market impact.
  • To test the predictive power of a dynamical theory of liquidity.
  • To identify the key factors governing the crossover in market impact regimes.

Main Methods:

  • Analysis of a large dataset of 8 million U.S. equity institutional trades.
  • Statistical modeling to identify market impact regimes.
  • Comparison of empirical data with predictions from a dynamical liquidity theory.

Main Results:

  • A clear crossover from linear to square-root market impact scaling was observed as a function of order volume.
  • The empirical results align well with the predictions of a dynamical theory of liquidity.
  • Incorporating both fast and slow liquidity timescales achieved quantitative agreement with the data.

Conclusions:

  • Order volume is a critical determinant of market impact regimes.
  • A dynamical theory of liquidity provides a robust framework for understanding market impact.
  • The presence of multiple liquidity timescales is essential for accurately modeling market dynamics.