Static hedge portfolios for barrier options are very sensitive with respect to changes of the
volatility surface. To prevent potentially significant hedging losses this book develops a
static super-replication strategy with market-typical robustness against volatility skew and
liquidity risk as well as model errors. Empirical results and various numerical examples
confirm that the static superhedge successfully eliminates the risk of a changing volatility
surface. Combined with associated sub-replication strategies this leads to robust price bounds
for barrier options which are also relevant in the context of dynamic hedging. The mathematical
techniques used to prove appropriate existence duality and convergence results range from
financial mathematics stochastic and semi-infinite optimization convex analysis and partial
differential equations to semidefinite programming.
