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There is question from 2017 here but the answer given doesn't really go into any detail.

How correlated is volume with price impact? Especially with regard to wash trading; For example, wash trading is extremely prevalent in crypto markets and yet, despite this, one can still a clear correlation between volume and price impact.

Is there a nice formula that can break down the relationship?

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  • $\begingroup$ Related topics: volume/dollar bars, net volume. $\endgroup$ Mar 19, 2021 at 9:33
  • $\begingroup$ It is a classic observation in many markets that there is a relation between volume and the absolute value of the price change. See for example this review article by Karpoff 1987 jstor.org/stable/2330874?seq=1 $\endgroup$
    – nbbo2
    Mar 19, 2021 at 13:55

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Market impact corresponds to price moves due to the intensity of trading in one direction. As you mention: when a market participant trades in size in one direction, the price usually follows.

They are two reasons:

  1. the first one is informational: the trader is right to buy (or sell), he or she understood the price will go up (or down). Hence in this case, a relation with volume is not needed: the price will move.
  2. the second one is mechanical: it is the one you mention. The pressure of the buying flow moves the price. In such a case the relation between the traded quantity $Q$ and the price move $\Delta P$ is square root (Bacry, Emmanuel, Adrian Iuga, Matthieu Lasnier, and C-A L. "Market impacts and the life cycle of investors orders" Market Microstructure and Liquidity 1, no. 02 (2015)): $$\Delta P\propto \sigma\sqrt{Q\over V} + a\,\psi,$$ where $\sigma$ is the volatility of the specific instrument, $\psi$ its bid-ask spread, and $V$ its traded volume.

JP Bouchaud explains the two effects quite well in his Introduction to Part II. Price Impact: Information Revelation or Self- Fulfilling Prophecies? to Capponi, Agostino, and C-A L, eds. Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices Cambridge University Press, 2023.

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