Anomalous price impact and the critical nature of liquidity in financial markets

TL;DR

This paper develops a dynamical theory of market liquidity showing that supply/demand profiles are V-shaped and vanish at the current price, explaining stylized facts like order fragmentation, long-memory, and the square-root impact law.

Contribution

It introduces a minimal dynamical model of liquidity that accounts for the V-shaped supply/demand profile and the anomalous impact of trades, supported by empirical and numerical evidence.

Findings

Supply/demand profile is V-shaped and vanishes at the current price.

Large metaorders are fragmented, leading to long-memory in order flow.

Small order impact diverges, explaining the square-root law.

Abstract

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.