Bewertung von Collateralized Debt Obligations mit Hilfe verschiedener 1-Faktor-Copula-Modelle
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Diplomarbeit aus dem Jahr 2014 im Fachbereich Mathematik - Stochastik, Note: 1,3, Universität zu Köln (Mathematisches Institut), Sprache: Deutsch, Abstract: Kreditderivate und alle damit im Zusammenhang stehenden Komponenten wurden seit je her kritisch betrachtet und galten oft als Sinnbild für spekulative und undurchschaubare Finanzgeschäfte. Die weltweite Wirtschaftskrise, welche 2007 ihren Anfang nahm, verschlechterte diesen Ruf zusätzlich. Die platzende Immobilienblase der USA weitete sich zu einer schweren Rezession in vielen Ländern aus. Besonders den synthetischen Collateralized Debt Obligations wird daran eine gro e Mitschuld gegeben. Der Grund hierfür ist, dass diese ohnehin schwer bewertbaren Finanzinstrumente oft durch aufwändige Konstrukte weiter in einander verschachtelt wurden, so dass eine realistische Einschätzung des tatsächlichen Risikos nahezu unmöglich ist. Auch wenn sich die Weltwirtschaft und insbesondere der mitteleuropäische Raum nach und nach wieder von diesem Schlag erholt, bleibt die Tatsache bestehen, dass sich in der Vergangenheit zu wenig mit adäquaten Modellen zur Bewertung von synthetischen Collateralized Debt Obligations befasst wurde. Besonders die Tatsache, dass zwar der Ruf dieser Finanzinstrumente auf einem neuen Tiefpunkt, das entsprechende Handelsvolumen aber so hoch ist wie nie zuvor, belegt die Aktualität dieses Themas. In den letzten Jahren wurden hierzu einige neue mathematische Verfahren entwickelt und bestehende Modelle weiter verfeinert. Der hierbei aktuell am häufigsten verwendete Ansatz ist das von Oldrich Vasicek vorgestellte Faktor-Copula-Modell. Ziel dieser Diplomarbeit ist es, dieses genauer zu behandeln und zu beleuchten. Hierzu sollen, nach einer kurzen Einführung in die benötigten Kapitalmarktprodukte, zunächst stochastische Grundlagen zur Modellierung von Abhängigkeitsstrukturen geschaffen werden. Darauf aufbauend kann die Funktionsweise des Faktor-Copula-Modells verständlich gemacht und aktuelle Variationen vo
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