New Approaches to Defaultable Term Structure Models

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The goal of this proposal is to explore new approaches in the modelling of dynamic term structures. We focus on defaultable term structure models, while the developed methodologies and results can be applied to other markets with term structures (energy markets, volatility markets, etc.).A critical reflection on the recent financial crisis raises the question, whether the current financial models are capable of capturing all relevant risks that should be reflected by such models. In this research project, we address this problem in two steps: first, we develop a general approach to defaultable term structures, including important economic risk drivers neglected by previous approaches. Second, based on these results, we develop a new viewpoint of term structure approaches by means of a concept known as Knightian uncertainty and suitable generalizations. This approach is close to a model free-framework showing a high degree of robustness towards undetected market risks. Methodologies of this kind have been recently applied to several areas in mathematical finance, however not to term structure models.