2011/05/31 by Bence Toth, Yves Lemperiere, Cyril Deremble +3 · 17 citations
Economics, Econometrics and Finance · Physics and Astronomy · #q-fin.TR #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physrevx.1.021006
published as Physical Review X 1, 021006 (2011) · 16 pages, 7 figures
arxiv created 2011/11/01 · arxiv updated 2011/11/02
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.