Time-inhomogeneous Lévy processes in interest rate and credit risk models

In this thesis, we present interest rate models and a credit risk model, all driven <br>by time-inhomogeneous Lévy processes, i.e. stochastic processes whose increments <br>are independent but in general not stationary. <br> <br>In the interest rate part, we discuss a Heath-Jarrow-Morton forward rate <br>model (the Lévy term structure model), a model for forward bond prices (the <br>Lévy forward price model) and a Libor model (the Lévy Libor model) which <br>generalizes the Libor market model. In all of these models, explicit valuation <br>formulae are established for the most liquid interest rate derivatives, namely <br>caps, floors, and swaptions. The formulae can numerically be evaluated fast and <br>thus allow to calibrate the models to market data. In the Lévy term structure <br>model, we also price floating range notes. Their payoffs are path-dependent. <br> <br>In the credit risk part, the Lévy Libor model (and therewith, as a special <br>case, the Libor market model) is extended to defaultable forward Libor rates. <br>We present a rigorous construction of the model and price some of the most <br>heavily traded credit derivatives, namely credit default swaps, total rate of <br>return swaps, credit spread options and credit default swaptions.

Author dc:creator

• Kluge, Wolfgang

Contributors dc:contributor

• Eberlein, Ernst

• Zinsderivate
• Kreditderivate
• Zeit-inhomogene Lévy-Prozesse
• Modellkalibrierung
• Laplace-Transformation
• interest rate derivatives
• credit derivatives
• time-inhomogeneous Lévy processes
• model calibration
• Laplace transformation

Repository record source_url

https://freidok.uni-freiburg.de/data/2090

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:2090