Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets

Abstract

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and 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.

A Fully Consistent, Minimal Model for Non-Linear Market Impact

“…time independent [7]. As now firmly established by many independent empirical studies, the average price change induced by the sequential execution of a total volume Q (which we call meta-order ) appears to follow a sub-linear, approximate √ Q law [2,3,5,[8][9][10][11][12][13]. At the end of the meta-order, impact is furthermore observed to decay (partially or completely) towards the unimpacted price [11][12][13][14].…”

“…The quantity L −1 is the analogue, within a LLOB, of Kyle's "lambda" for a flat order book. In terms of order of magnitudes, it is reasonable to expect that the latent order book has a memory time ν of several hours to several days [3] -remember that we are speaking here of slow actors, not of market makers contributing to the high-frequency dynamics of the revealed order book. Taking D to be of the order of the price volatility, the width of the linear region γ −1 is found to be of the order of 1% of the price (see Eq.…”

“…Our starting point is the zero-intelligence model of Smith et al [20], reformulated in the context of the latent order book in [3] and independently in [21]. We assume that each trading (buy/sell) intention of market participant is characterized by a reservation price and a volume.…”

“…t -where the density of buy/sell orders vanishes -has an intrinsic non-zero width even in the limit κ → ∞ [22], corresponding to the average distance a − b between the highest buy order x = b and the lowest sell order x = a. 3 The instantaneous price can then be conventionally be defined as p inst. t = (a + b)/2, but will in general not coincide with the coarse-grained price p t defined by the average shape of the latent order book through Eq.…”

“…But as often in science, it is the empirical discovery of a genuinely surprising result that explains the recent spree of activity on the subject (see e.g. [2][3][4][5][6] and refs. therein).…”