Robust Static Super-Replication of Barrier Options

Jan H. Maruhn

Published by De Gruyter 2009

Robust Static Super-Replication of Barrier Options

Jan H. Maruhn

Volume 7 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110208511

Overview
Contents

About this book

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.

Author information

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

Reviews

"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

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Contents Requires Authentication Unlicensed Licensed Download PDF	xi
1. Theoretical Background Requires Authentication Unlicensed Licensed Download PDF	1
2. Static Hedging of Barrier Options Requires Authentication Unlicensed Licensed Download PDF	15
3. An Optimization Approach to Static Super-Replication Requires Authentication Unlicensed Licensed Download PDF	32
4. Reformulation as a Semi-Infinite Problem Requires Authentication Unlicensed Licensed Download PDF	50
5. Eliminating Model Parameter Uncertainty Requires Authentication Unlicensed Licensed Download PDF	70
6. Modifications and Extensions Requires Authentication Unlicensed Licensed Download PDF	103
7. Avoiding Model Errors Requires Authentication Unlicensed Licensed Download PDF	123
8. Empirical Hedge Performance Requires Authentication Unlicensed Licensed Download PDF	144
9. Summary and Outlook Requires Authentication Unlicensed Licensed Download PDF	163
A. General Existence Theorem Requires Authentication Unlicensed Licensed Download PDF	167
B. Source Code Requires Authentication Unlicensed Licensed Download PDF	172
Backmatter Requires Authentication Unlicensed Licensed Download PDF	181

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers; Practitioners; Graduate Students of Mathematics; Academic Libraries
Pages
- Front matter: 12
- Main content: 197
Illustrations
- Other: Figs. and tabs.
Keywords: Static Hedging; Barrier Options; Robust Optimization; Stochastic Volatility; Semi-infinite Optimization; Semidefinite Programming.

eBook

Published: July 14, 2009
ISBN: 9783110208511

Hardcover

Published: July 15, 2009
ISBN: 9783110204681