  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.

Pricing of Securities;Probability