Robust Static Super-Replication of Barrier Options

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.

"I always felt that Jan Maruhn would be the only person on the globe who knows how to statically hedge barrier options. Now I am even more pleased to see that he is making a fully guided tour available as a book. For decades many papers have been contributed to this core problem by many authors. Many of the suggestions worked well on a piece of paper, none of them ever worked in practice. Jan''s book is the Odyssey of the barrier hedging problem, that ends with a case study on how his solution works and performs in real markets. Anybody researching in or trading barrier options should read this book and pick up the entire numerical toolbox on the way."
Uwe Wystup, CEO MathFinance AG