We investigate financial markets under model risk caused by uncertain

volatilities. For this purpose we consider a financial market that

features volatility uncertainty. To have a mathematical consistent

framework we use the notion of G–expectation and its corresponding

G–Brownian motion recently introduced by Peng (2007). Our financial

market consists of a riskless asset and a risky stock with price

process modeled by a geometric G–Brownian motion. We adapt the

notion of arbitrage to this more complex situation and consider stock

price dynamics which exclude arbitrage opportunities. Due to volatility

uncertainty the market is not complete any more. We establish the

interval of no–arbitrage prices for general European contingent claims

and deduce explicit results in a Markovian setting.