Simple arbitrage

Christian Bender

Papers from arXiv.org

Abstract: We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of \epsilon, if the investor trades at all. For continuous stock models, we provide an equivalent condition for absence of 0-admissible simple arbitrage in terms of a property of the fine structure of the paths, which we call "two-way crossing." This property can be verified for many models by the law of the iterated logarithm. As an application we show that the mixed fractional Black-Scholes model, with Hurst parameter bigger than a half, is free of simple arbitrage on a compact time horizon. More generally, we discuss the absence of simple arbitrage for stochastic volatility models and local volatility models which are perturbed by an independent 1/2-H\"{o}lder continuous process.

Date: 2012-10
New Economics Papers: this item is included in nep-mst
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Citations: View citations in EconPapers (5)

Published in Annals of Applied Probability 2012, Vol. 22, No. 5, 2067-2085

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1210.5391

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