dorsal/arxiv
View SchemaMoody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios
| Authors | S. Mori, K. Kitsukawa, M. Hisakado |
|---|---|
| Categories | |
| ArXiv ID | physics/0603036 |
| URL | https://arxiv.org/abs/physics/0603036 |
| DOI | 10.1080/14697680903419685 |
| Journal | Quantitative Finance, vol.11,No.3(2011)391-405 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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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"abstract": "This paper generalizes Moody\u0027s correlated binomial default distribution for\nhomogeneous (exchangeable) credit portfolio, which is introduced by Witt, to\nthe case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider\ntwo cases. In the first case, we treat a portfolio whose assets have uniform\ndefault correlation and non-uniform default probabilities. We obtain the\ndefault probability distribution and study the effect of the inhomogeneity on\nit. The second case corresponds to a portfolio with inhomogeneous default\ncorrelation. Assets are categorized in several different sectors and the\ninter-sector and intra-sector correlations are not the same. We construct the\njoint default probabilities and obtain the default probability distribution. We\nshow that as the number of assets in each sector decreases, inter-sector\ncorrelation becomes more important than intra-sector correlation. We study the\nmaximum values of the inter-sector default correlation. Our generalization\nmethod can be applied to any correlated binomial default distribution model\nwhich has explicit relations to the conditional default probabilities or\nconditional default correlations, e.g. Credit Risk${}^{+}$, implied default\ndistributions. We also compare some popular CDO pricing models from the\nviewpoint of the range of the implied tranche correlation.",
"arxiv_id": "physics/0603036",
"authors": [
"S. Mori",
"K. Kitsukawa",
"M. Hisakado"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1080/14697680903419685",
"journal_ref": "Quantitative Finance, vol.11,No.3(2011)391-405",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Moody\u0027s Correlated Binomial Default Distributions for Inhomogeneous Portfolios",
"url": "https://arxiv.org/abs/physics/0603036"
},
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