During the last decade, the dependencies between financial assets have increased due to globalization effects and relaxed market regulation. The standard industrial methodologies like RiskMetrics and CreditMetrics model the dependence structure in the derivatives or in the credit portfolio by assuming multivariate normality of the underlying risk factors. It has been well recognized that many financial assets exhibit a number of features which contradict the normality assumption - namely asymmetry, skewness and heavy tails. Moreover, asset return data suggests also a dependence structure which is quite different from the Gaussian. Recent empirical studies indicate that especially during highly volatile and bear markets the probability for joint extreme events leading to simultaneous losses in a portfolio could be seriously underestimated under the normality assumption. Theoretically, Embrechts et al. show that the traditional dependence measure (the linear correlation coefficient) is not always suited for a proper understanding of the dependency in financial markets. When it comes to measuring the dependence between extreme losses, other measures (e.g. the tail dependence coefficient) are more appropriate. This is particularly important in the credit risk framework, where the risk factors actually enter the model only to introduce a dependence structure in the portfolio. Clearly, appropriate multivariate models suited for extreme events are needed. In this thesis, we consider a portfolio credit risk model in the spirit of CreditMetrics. With respect to the marginal losses, we retain and enhance all features of that model and we incorporate not only the default risk, but also the rating migrations, the credit spread volatility and the recovery risk. The dependence structure in the portfolio is given by a set of underlying risk factors which we model by a general multivariate elliptical distribution. On the one hand, this model retains the standard Gaussian model as a special case. On the other hand, by introducing a heavy-tailed "global shock" affecting the credits simultaneously across regions and business sectors, we obtain a more exible model for joint extreme losses. The goals of the thesis are twofold. First, we consider the calibration of the model. The main result is a new method for statistical estimation of the dependence structure (the copula) of a random vector with arbitrary marginals and elliptical copula. Within our method, we calibrate the linear correlation coefficients using the whole available sample of observations and the non-linear (tail) dependence coefficients using only the extreme observations. Special attention is put to the estimation of the tail dependence coefficients, where additional results aiming at a lower variance of the estimates are provided. The particular application of the method to the calibration of the credit risk model is given in detail, and several simulation studies and real data examples are presented. Second, we investigate the portfolio loss distribution. In particular, we derive an upper bound of its tail, which is especially accurate at high loss levels. Given the complexity of our model, we obtain this result using a mixture of analytic techniques and Monte Carlo simulation. An approximation of the Value-at-Risk and a new method to determine the contributions of the individual credits to the overall portfolio risk is provided. The impact of the heavy-tailed model on the overall portfolio risk and on the risk structure as given by the risk contributions is investigated. We conclude that the heavy-tailed assumption has important consequences in all aspects of risk management.     «

During the last decade, the dependencies between financial assets have increased due to globalization effects and relaxed market regulation. The standard industrial methodologies like RiskMetrics and CreditMetrics model the dependence structure in the derivatives or in the credit portfolio by assuming multivariate normality of the underlying risk factors. It has been well recognized that many financial assets exhibit a number of features which contradict the normality assumption - namely asymmet...     »

Während des letzten Jahrzehnts haben die Abhängigkeiten zwischen den finanziellen Vermögenswerten weltweit auf Grund von Globalisierungseffekten zugenommen. In dieser Dissertation betrachten wir ein Portfoliokreditrisikomodell nach dem Vorbild von CreditMetrics (1997). Unser Modell ist eine Verallgemeinerung des CreditMetrics Modells: durch Einführen eines zufälligen globalen Schocks, der die Kredite gleichzeitig über Wirtschaftsregionen und Geschäftssektoren beeinflusst, erhalten wir ein flexibleres Modell für grosse Kreditausfälle. Zuerst beschäftigen wir uns mit der Kalibrierung unseres neuen Modells. Das Hauptergebnis hier ist eine neue Methode für die statistische Schätzung der Abhängigkeitstruktur der Komponenten eines Zufallsvektor mit beliebigen Randverteilungen und elliptischer Copula. Für unser Modell kalibrieren wir einerseits die linearen Korrelationskoeffizienten klassisch mit der ganzen verfügbaren Stichprobe von Beobachtungen; die nichtlinearen abhängigkeitskoeffizienten zwischen sehr grossen Kreditens schätzen wir auf Basis der grössten Beobachtungen. Danach bestimmen wir die Portfolioverlustverteilung. Gegeben die Komplexität unseres Modells benutzen wir eine Mischung aus analytischen Verfahren und Monte Carlo Simulation. Eine Approximation des Value-at-Risk und eine neue Methode, die Beiträge der einzelnen Kredite zum Gesamtportfoliorisiko zu berechnen, runden unsere Untersuchungen ab.     «

Während des letzten Jahrzehnts haben die Abhängigkeiten zwischen den finanziellen Vermögenswerten weltweit auf Grund von Globalisierungseffekten zugenommen. In dieser Dissertation betrachten wir ein Portfoliokreditrisikomodell nach dem Vorbild von CreditMetrics (1997). Unser Modell ist eine Verallgemeinerung des CreditMetrics Modells: durch Einführen eines zufälligen globalen Schocks, der die Kredite gleichzeitig über Wirtschaftsregionen und Geschäftssektoren beeinflusst, erhalten wir ein flexib...     »