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URN: urn:nbn:de:bsz:25-opus-4723
URL: http://www.freidok.uni-freiburg.de/volltexte/472/

Özkan, Fehmi

Lévy processes in credit risk and market models

Lévy Prozesse in Kreditrisiko- und Libormodellen

Kurzfassung in Deutsch

Mathematical credit risk models in the literature are mainly models based on Brownian motion although it is known that real-life financial data provides a different statistical behavior than that implied by these models. Lévy processes are an appropriate tool to increase accuracy of models in finance. They have been used to model stock prices, and term structures of interest rates, thus allowing more accurate derivative pricing and risk management.
This study shows how Lévy processes can be applied to credit risk and market models.

Chapter 1 is a brief survey of some aspects of credit risk, generalized hyperbolic distributions and Lévy processes. In the overview of the structural approach, it is shown how Lévy processes can be used to generalize the classical structural approach. The second chapter contains a generalization of the software package CreditRisk+ to a class of heavy-tailed distributions.
Chapter 3 contains an intensity-based credit risk Heath-Jarrow-Morton-framework based on Lévy processes. In Chapter 4 it is explained how the market practice of pricing caplets with the Black formula can be pushed further to a model where the driving process is a Lévy process.