No-dynamic-arbitrage and market impact

Jim Gatheral

Quantitative Finance, 2010, vol. 10, issue 7, 749-759

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: Stochastic volatility; Volatility modelling; Volatility smile fitting; Volatility surfaces; Stochastic jumps; Options volatility; Options pricing (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (142)

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DOI: 10.1080/14697680903373692

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