Robust Static Super-Replication of Barrier Options

1. Auflage 2009
ISBN: 978-3-11-020468-1
Verlag: De Gruyter

Buch, Englisch, Band 7, 197 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 547 g

Reihe: Radon Series on Computational and Applied Mathematics

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.

Zielgruppe

Academic and professional

Autoren/Hrsg.

Maruhn, Jan H.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

Inhaltsverzeichnis

Frontmatter
Contents
1. Theoretical Background
2. Static Hedging of Barrier Options
3. An Optimization Approach to Static Super-Replication
4. Reformulation as a Semi-Infinite Problem
5. Eliminating Model Parameter Uncertainty
6. Modifications and Extensions
7. Avoiding Model Errors
8. Empirical Hedge Performance
9. Summary and Outlook
A. General Existence Theorem
B. Source Code
Backmatter

Über Autor(innen)

Maruhn, Jan H.
Jan H. Maruhn, UniCredit Markets & Investment Banking, Munich, Germany.