No-Dynamic-Arbitrage and Market Impact

Quantitative Finance, Vol. 10, No. 7, pp. 749-759, 2010

28 Pages Posted: 31 Oct 2008 Last revised: 19 Oct 2015

Jim Gatheral

CUNY Baruch College

Date Written: March 26, 2009

Abstract

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely-assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that empirically, these inequalities are typically close to being equalities.

Keywords: Market impact, dynamic-no-arbitrage

Suggested Citation

Gatheral, Jim, No-Dynamic-Arbitrage and Market Impact (March 26, 2009). Quantitative Finance, Vol. 10, No. 7, pp. 749-759, 2010. Available at SSRN: https://ssrn.com/abstract=1292353

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

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