Members: Jakob Stöber and Claudia Czado
Description: The recent financial crisis demonstrated once more that modeling of extremal events and abrupt changes in behavior is a key challenge for modern risk management. Empirically financial returns have been shown to exhibit tail dependence; extreme events are highly correlated and cluster together. Classic models, like the multivariate Gaussian distribution are unable to capture these dependencies and consequently copula models have gained attention over the last years, with a rich class of copulas, particularly in the bivariate case, having been developed. A flexible and efficient way of constructing high dimensional copulas which exhibit features like asymmetric tail dependence is through the use of vine copulas. Assuming a fixed copula structure for a time series i soften too restrictive a model. In extreme situations dependence properties might change completely. Examples for such structural changes are panic reactions in stock markets which lead to a situation where there are no buyers or central banks intervening in currency markets. To describe these features in the one or low dimensional case regime switching models such as Markov switching models have been developed. The goal of this research project is to combine regime switching models with vine copulas thus extending them to high dimensional problems where complex dependence properties are also present. In order to achieve this goal methodologies for selecting appropriate dependence structures must also be developed and constitute an interesting research question in their own right. Applications of this research are not restricted to risk management in finance and insurance but can be useful in any context where dependence structures change over time.