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

13 Pages Posted: 11 May 2011

See all articles by Bence Toth

Bence Toth

Santa Fe Institute

Yves Lemperiere

Capital Fund Management

Cyril Deremble

Capital Fund Management

Joachim de Lataillade

Capital Fund Management

Julien Kockelkoren

Capital Fund Management

Jean-Philippe Bouchaud

Capital Fund Management

Date Written: May 9, 2011

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.

Suggested Citation

Toth, Bence and Lemperiere, Yves and Deremble, Cyril and de Lataillade, Joachim and Kockelkoren, Julien and Bouchaud, Jean-Philippe, Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets (May 9, 2011). Available at SSRN: https://ssrn.com/abstract=1836508 or http://dx.doi.org/10.2139/ssrn.1836508

Bence Toth (Contact Author)

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Yves Lemperiere

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Cyril Deremble

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Joachim De Lataillade

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Julien Kockelkoren

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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