Robust Static Super-replication of Barrier Options (Radon series on computational and applied mathematics, 7)

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. Read more... Abstract: Presents hedging strategies for a class of financial options. This book places emphasis on theoretical and numerical aspects, such as the consideration of appropriate existence, duality and convergence results. Read more...

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.

Main description: 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. Combined with associated sub-replication strategies this leads to empirically robust price bounds for barrier options which are also relevant in the context of dynamic hedging Frontmatter 1 Contents 11 1. Theoretical Background 13 2. Static Hedging of Barrier Options 27 3. An Optimization Approach to Static Super-Replication 44 4. Reformulation as a Semi-Infinite Problem 62 5. Eliminating Model Parameter Uncertainty 82 6. Modifications and Extensions 115 7. Avoiding Model Errors 135 8. Empirical Hedge Performance 156 9. Summary and Outlook 175 A. General Existence Theorem 179 B. Source Code 184 Backmatter 193