Robust calibration of the Libor market model and pricing of derivative products [Elektronische Ressource] / Dennis Schätz

ECOD·ODNEICS·MLUTÄTUniversitat UlmInstitut fur FinanzmathematikRobust Calibration of the Libor Market ModelandPricing of Derivative ProductsDissertationzur Erlangung des DoktorgradesDr. rer. nat.der Fakultat fur Mathematik und Wirtschaftswissenschaften an der Universitat Ulmvorgelegt vonDipl.-Math. oec. Dennis Schatzaus IllertissenUlm, 2011ISREVINU·ODNARUC·ODNAmtierender Dekan: Professor Dr. Werner Kratz1. Gutachter: Professor Dr. Rudiger Kiesel, Universitat Duisburg-Essen2. Gutachter: Dr. Ulrich Rieder, Universitat UlmTag der Promotion: 28.02.2011AbstractThe Libor market model has established itself as the benchmark model for interest ratederivatives. If the observed correlation and volatility surfaces cannot be reproduced bya model, we cannot hope to get meaningful prices, therefore the crucial task, beforeit comes to pricing and hedging, is to calibrate the model to given market data. Anoverview of the Libor market model is given and it is shown how to obtain a robustcalibration. The big disadvantage of the model is that it cannot reproduce the typicallyobserved implied volatility smile.We show how to extend the model to include the market smile by making use ofstochastic volatility. For these stochastic volatility Libor market models a new timehomogeneous skew parametrization is introduced which has the capability of tting theobserved market data very well.