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# A Bayesian derivation of the square root law of market impact

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Date Updated
2023/03/16
Category
q-fin.TR
Date Published
2023/03/15
Date Retrieved
2023/03/17
Description
We show that the main empirical findings on the impact of a sequence of transactions on prices of financial assets can be recovered within a surprisingly simple model with fully Bayesian market expectations. This includes {\em i)} the square-root behavior of the expected price variation with the total volume traded, {\em ii)} it's crossover to a linear regime for small volumes, and {\em iii)} the impact decay back to equilibrium, after the sequence of trades is over. The simplicity of this derivation lends further support to its robustness and universality, and it sheds light on its origin. In particular, it suggests that the square-root impact law originates from the over-estimation of order flows originating from meta-orders.
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