Abstract: In this talk we discuss the dual representation for measures of the  model risk in option hedging that is due to market `frictions’ such as  illiquid markets or stochastic volatility . Starting point is the observation that  superhedging prices for options in the presence of market frictions can be described by nonlinear versions of the classical Black Scholes equation. We apply duality theory to show that this equation can be interpreted as a dynamic programming equation and we discuss existence and comparison principles. We show that the superhedging price gives rise to a convex risk measure on the set of all continuous terminal value claims whose dual representation has a very intuitive interpretation.   We consider next  asymptotic properties of this measure as market frictions get large. Finally we propose an approach for discussing the  pricing of individual contracts relative to a book of derivatives and we discuss open research questions.