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
Date Written: March 26, 2009
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
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