Risk Management Beyond Correlation

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Dissertation an der Fakultät für Mathematik, Informatik und Statistik der Ludwig-Maximilians-Universität München. - Effects of dependencies are an important component of risk management in an aggregate setting, for example, when different risk types or business lines are to be modeled jointly. Classical approaches to portfolio theory rely on the notion of linear correlation and thus on the ellipticity of the underlying distribution - a requirement which is typically not fulfilled in a risk management context. For each of market, credit and operational risks, this thesis examines situations where linear correlation reaches its limits and may lead to an underestimation of or counterintuitive effects on aggregate risk. Copulas and tail dependence coefficients are considered, estimated and analyzed as alternatives to correlation. These measures are able to detect extremal dependence structures otherwise neglected. However, due to restrictions by sample sizes and asymptotic considerations, there is no "one-size-fits-all" approach to measuring dependencies among extremes. Instead, this thesis suggests a joint consideration of parametric and nonparametric methods in order to gain a picture of aggregate risk as comprehensive as possible. - Aus der Schriftenreihe zu Statistik und Ökonometrie Herausgeber: Prof. Stefan Mittnik, Ph.D.: