非齐次投资组合的Moody相关二项违约分布
Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios
摘要：
本文将Witt提出的同质（可交换）信用组合的Moody相关二项违约分布推广到非同质信用组合的情形。作为非齐次投资组合，我们考虑两种情况。在第一种情况下，我们处理的资产组合具有一致的违约相关性和非一致的违约概率。第二种情况对应于一个具有非齐次违约相关性的投资组合，我们得到了违约概率分布，并研究了非齐次违约相关性对违约概率分布的影响。资产分为几个不同的部门，部门间和部门内的相关性也不相同。我们构造了联合违约概率，得到了违约概率分布。我们发现，随着每个部门的资产数量减少，部门间的相关性变得比部门内的相关性更重要。我们研究了部门间违约相关性的最大值。我们的推广方法可以应用于任何相关的二项违约分布模型，它有显式的关系，条件的违约概率或条件的违约相关性，如信用风险${}^{+}$，隐含的违约分布。本文还从隐含份额相关性的角度比较了一些流行的CDO定价模型。
英文摘要：
This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than intra-sector correlation. We study the maximum values of the inter-sector default correlation. Our generalization method can be applied to any correlated binomial default distribution model which has explicit relations to the conditional default probabilities or conditional default correlations, e.g. Credit Risk${}^{+}$, implied default distributions. We also compare some popular CDO pricing models from the viewpoint of the range of the implied tranche correlation.
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