New Approaches to Defaultable Term Structure Models

这项提议的目标是探索动态期限结构建模的新方法。我们专注于可违约期限结构模型，而开发的方法和结果可以应用于其他具有期限结构的市场(能源市场、波动市场等)。对最近的金融危机的批判性反思提出了一个问题，即当前的金融模型是否能够捕捉这些模型应该反映的所有相关风险。在这个研究项目中，我们分两步解决这个问题：首先，我们开发了一个通用的方法来处理可违约的期限结构，包括被以前的方法忽视的重要的经济风险驱动因素。其次，在这些结果的基础上，我们通过奈特不确定性的概念和适当的推广，发展了期限结构方法的新观点。这种方法接近于一种无模型框架，显示出对未发现的市场风险具有高度的稳健性。这类方法最近已被应用于数学金融的几个领域，但不适用于期限结构模型。

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.