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...

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the...

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...