Most models for barrier pricing are designed to let a market maker tune themodel-implied covariance between moves in the asset spot price and moves in theimplied volatility skew. This is often implemented with a localvolatility/stochastic volatility mixture model, where the mixture parametertunes that covariance. This paper defines an alternate model where thespot/volatility correlation is a separate mean-reverting stochastic variablewhich is itself correlated with spot. We also develop an efficientapproximation for barrier option and one touch pricing in the model based onsemi-static vega replication and compare it with Monte Carlo pricing. Theapproximation works well in markets where the risk neutral drift is modest.
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