The research field of conic finance tries to bridge classical arbitrage and expected utility theory by introducing the acceptability level of stochastic cash flows. The preferences of market participants are modeled using single-parameter distorted expectations. By allowing the price of a cash flow to vary with its trade direction the market’s required level of acceptability leads to theoretical expressions for bid-and-ask prices. In this thesis we try to weaken the law invariance property by introducing the correlation structure with a market variable. We introduce a double-distortion model and establish a link with the work of Buhlmann (1980). In an application on European call and put options we derive formulas for bid-and-ask prices comparable to the Black-Scholes (1973) option prices now taking into account the direction of trade.Using option data we calibrate the required level of acceptability and investigate to what extent a cash flow’s correlation with general market performance is a good predictor of the bid-ask spread. We find several evidence supporting the hypothesis, but recognize that the effects fluctuate heavily over the months in our sample period.