Robust static hedging of barrier options in stochastic volatility models

Static hedge portfolios for barrier options are extremely sensitive with respect to changes in the parameters of the underlying financial market model. In this paper we develop a new semi-infinite programming formulation of the static super-replication problem in stochastic volatility models which allows to incorporate the model parameter uncertainty in the sense of a worst case design. After proving existence of robust hedge portfolios and presenting an algorithm to numerically solve the underlying optimization problem, we apply the approach to a detailed real world example. Surprisingly, the optimal robust static hedge portfolios are only marginally more expensive than the barrier option itself although they offer protection for a broad range of model parameters.