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URN: urn:nbn:de:bsz:25-opus-72539
URL: http://www.freidok.uni-freiburg.de/volltexte/7253/


Grbac, Zorana

Credit risk in LÚvy Libor Modeling: rating based approach

Kreditrisiken dargestellt durch LÚvy Libor Modelle: Ratingbasierter Ansatz

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Kurzfassung in Englisch

Modeling of credit risk has become a very important and rapidly expanding field of mathematical finance in the last fifteen years. In this thesis we study credit risk modeling in the Libor framework and develop the rating based LÚvy Libor model and a credit portfolio market model, based on time-inhomogeneous LÚvy processes and general semimartingales as driving processes.

In the first part of the thesis, we consider modeling of the defaultable forward Libor rates related to defaultable bonds with credit ratings and develop the rating based LÚvy Libor model with a time-inhomogeneous LÚvy process as a driving process. It can be seen as a generalization of the default-free Libor market models found in the literature, and moreover it extends the LÚvy Libor model with default risk to multiple credit ratings with migration. Conditional Markov processes are used to model this migration and we provide a detailed analysis of their properties and behavior under forward Libor measures. Furthermore, we calculate the correlations of the rating-dependent Libor rates and study the pricing of credit derivatives. We also consider an application of the defaultable LÚvy Libor model to counterparty risk and derive a valuation formula for vulnerable European call options based on Fourier transform methods.

In the second part, we study credit portfolio risk in the Libor market models and introduce a very general market model for CDOs which allows contagion in the portfolio and a direct dependence of the risk-free interest rates and the aggregate loss process. The model is driven by a special semimartingale whose components are time-inhomogeneous LÚvy processes and the aggregate loss process of the considered portfolio. We derive conditions for the absence of arbitrage in the model and provide pricing formulae for CDOs in this framework.


Kurzfassung in Deutsch

Kreditrisikomodellierung geh÷rt zu den wichtigsten und sich am schnellsten entwickelnden Gebieten der Finanzmathematik in den letzten fŘnfzehn Jahren. In dieser Arbeit werden verschiedene Arten von Kreditrisiken durch Libor Modelle dargestellt und zwei Modelle prńsentiert: das LÚvy Libor Kreditrisikomodell im Ratingbasierten Ansatz und das Libor Kreditportfoliomodell, die von zeit-inhomogenen LÚvy-Prozessen und allgemeinen Semimartingalen getrieben werden.


SWD-Schlagwörter: Finanzmathematik , Kreditrisiko , Stochastische Analysis , Semimartingal , LÚvy-Prozess
Freie Schlagwörter (deutsch): Bonitńtsbeurteilung , Libor-Modell , Kreditportfoliomodell , Bedingte Markov-Prozesse
Freie Schlagwörter (englisch): Credit rating , Libor model , credit portfolio model , conditional Markov processes
MSC Klassifikation 91G40 , 91G30 , 60G51 , 60J27 , 60J75
Institut: Institut fŘr Mathematische Stochastik
Fakultät: Fakultńt fŘr Mathematik und Physik
DDC-Sachgruppe: Mathematik
Dokumentart: Dissertation
Erstgutachter: Eberlein, Ernst (Prof. Dr.)
Sprache: Englisch
Tag der mündlichen Prüfung: 22.01.2010
Erstellungsjahr: 2009
Publikationsdatum: 24.02.2010
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