Modelling the Risk of CDO dynamics

CDO部分定价的市场标准模型是单因素高斯Copula模型。然而，该模型不能再现市场价格，人们观察到众所周知的隐含相关性微笑，见图1。许多论文都是关于解释经验微笑效应的模型。更复杂的模型为固定的时间点解释了这一事实，但到目前为止未能正确地描述时变的相依结构。鉴于我们在自适应估计时变参数方面的共同经验，以及在CDO建模和定价方面的专业知识，我们可以成功地将这些技术转移到时变CDO风险分析中。我们的目标是研究市场隐含相关表面或等价的定价表面在其时变背景下在不同估值模型中的动态行为。为了实现这一目标，我们将使用现代统计技术(自适应半参数估计)和高级定价模型，并将创建用于定价和预测CDO风险的高效算法。该项目是柏林和GIEüen之间的一个联合项目，因为在衍生品估值和信用风险测量的数学建模方面的专业知识属于德国数学金融组，金融时间序列和时变(高维)相关性模型的统计专业知识是与C.A.S.E.-应用统计和经济中心以及柏林洪堡大学的统计和计量经济学研究所一起设计的。这两个专业中心的结合对于拟议的研究项目的成功是不可或缺的。在洪堡大学创建洪堡校园米特(HCM)，即所谓的综合研究所(IRI)的研究战略中，C.A.S.E.也是一个重要因素。

The market standard model for pricing the CDO tranches is the one factor Gaussian Copula Model. The model however cannot reproduce the market prices and one observes the well known implied correlation smile, see Figure 1. Many papers have been written on models explaining the empirical smile effect. More complex models explain this fact for fixed point in time but so far fail in correctly describing the time varying dependence structure. Given our joint experience with adaptively estimated time varying parameters and the expertise on modeling and pricing CDOs we can successfully transfer these technologies to time varying CDO risk analysis.Our aim is to study the dynamic behavior of the market implied correlation surface or equivalently the pricing surface in different valuation models in its time varying context. We will use for this aim modem statistical techniques (adaptive semi parametric estimation) and advanced pricing models and will create efficient algorithms for pricing and predicting CDO risks.The project is designed as a joint project between Berlin and Gießen since the expertise in mathematical modeling of derivative valuation and risk measurements in credit lies within the Mathematical Finance Group at the Universität Gießen and the statistical expertise for financial time series and time varying (high dimensional) dependency models is with C.A.S.E. - Centre for Applied Statistics and Economics and Institute of Statistics and Econometrics at Humboldt-Universität zu Berlin. A combination of these two centers of expertise is indispensable for the success of the proposed research project. C.A.S.E. is also a comerstone in the Humboldt University research strategy in creating a Humboldt Campus Mitte (HCM), a so called integrative research institute (IRI).