Analyse der von Copulas erzeugten Ausfallabhängigkeiten und deren Auswirkungen auf das Risikomanagement
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Diplomarbeit aus dem Jahr 2005 im Fachbereich BWL - Investition und Finanzierung, Note: 1,3, Universität Karlsruhe (TH) (Willkommen am Lehrstuhl für Financial Engineering und Derivate), Sprache: Deutsch, Abstract: Die Modellierung von Ausfallabhängigkeit ist ein zentrales Thema im Kreditrisiko-Management. Seit Mitte der Neunziger Jahre werden Copula-Funktionen als Alternative zur Abbildung von Ausfallabhängigkeit eingesetzt. Sie besitzen die sehr praktische Eigenschaft, die gemeinsame Abhängigkeitsstruktur der Zufallsvariablen untereinander separat von ihren individuellen Randverteilungen zu betrachten. Zwei der am häufigsten verwendeten Copulaklassen sind die sogenannten elliptischen und die Archimedischen Copulas. Normalerweise werden in der Literatur nur generelle Eigenschaften bezüglich der Struktur bzw. der Konstruktion von Copulas diskutiert. Es existieren jedoch keine Kriterien für oder gegen die Wahl einer speziellen Copula-Funktion. An diesem Punkt setzt die vorliegende Arbeit an und beleuchtet diesen Aspekt näher. Es wird im ersten Schritt untersucht, welche Abhängigkeiten von welchen Copula-Funktionen erzeugt werden können bzw. welche Copulas Ausfallabhängigkeiten adäquat abbilden können. Dabei wird genauer betrachtet, wovon die Ausfallabhängigkeiten jeweils determiniert werden und wie sie über die Parameter der Copula-Funktionen gesteuert werden können. Der zweite Teil untersucht den Einfluss von Copula-Funktionen auf das Kreditrisiko-Management. In einer Simulationsstudie werden für die dynamischen Modellansätze von Li (2000) und Schönbucher/Schubert (2001) die Kreditspreads von ausfallbehafteten Nullkuponanleihen und die Preise von korrelationssensitiven nth-to-Default Swaps für verschiedene Copula-Funktionen ermittelt und in Abhängigkeit des Ausfallabhängigkeitsniveaus verglichen. Hieraus lassen sich sodann Rückschlüsse auf Bewertungsunterschiede ziehen, so dass einige Auswahlkriterien für eine geeignete Copula-Funktion im Kreditrisiko-Management ide
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