可交换传染的系统性风险：对欧洲银行体系的应用
Systemic Risk with Exchangeable Contagion: Application to the European Banking System
摘要：
我们提出了一个模型和估计技术来区分系统性风险和传染信用风险。其主要思想是假设，对于一组$d$债务人，一组$d$特质冲击和一个触发所有债务人违约的冲击。所有的冲击被假定为由一个依赖关系，在本文中被假定为可交换和阿基米德。这种方法能够同时包含系统性风险和传染，以马歇尔-奥尔金纯系统性风险模型和阿基米德传染模型作为极端情况。此外，我们表明，假设一个仿射结构的特质和系统性冲击的强度和Gumbel Copula，该方法提供了一个完整的多元分布与指数边际分布。该模型可以通过对二元边缘应用矩匹配过程来估计。我们还提供了一个简单的视觉检查模型的良好规范。该模型适用于选定的样本银行为8个欧洲国家，假设每个国家的共同冲击。该模型被认为是很好地指定为4的8个国家。我们还提供了该模型的理论扩展到不可交换的情况下，我们提出了可能的研究途径的估计。
英文摘要：
We propose a model and an estimation technique to distinguish systemic risk and contagion in credit risk. The main idea is to assume, for a set of $d$ obligors, a set of $d$ idiosyncratic shocks and a shock that triggers the default of all them. All shocks are assumed to be linked by a dependence relationship, that in this paper is assumed to be exchangeable and Archimedean. This approach is able to encompass both systemic risk and contagion, with the Marshall-Olkin pure systemic risk model and the Archimedean contagion model as extreme cases. Moreover, we show that assuming an affine structure for the intensities of idiosyncratic and systemic shocks and a Gumbel copula, the approach delivers a complete multivariate distribution with exponential marginal distributions. The model can be estimated by applying a moment matching procedure to the bivariate marginals. We also provide an easy visual check of the good specification of the model. The model is applied to a selected sample of banks for 8 European countries, assuming a common shock for every country. The model is found to be well specified for 4 of the 8 countries. We also provide the theoretical extension of the model to the non-exchangeable case and we suggest possible avenues of research for the estimation.
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