A model-free approximation for barrier options in a general stochastic volatility framework

For a general stochastic volatility framework with correlation between the spot price and the instantaneous volatility, an analytical approximation for single barrier options with continuous monitoring is given. The approximation is expressed only in terms of market observable implied volatilities and prices. As such the approximation is independent of the specific form and number of parameters of the skew-generating stochastic volatility model.