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一种用于信用风险的随机矩阵方法。

A random matrix approach to credit risk.

作者信息

Münnix Michael C, Schäfer Rudi, Guhr Thomas

机构信息

Faculty of Physics, University of Duisburg-Essen, Essen, Germany.

出版信息

PLoS One. 2014 May 22;9(5):e98030. doi: 10.1371/journal.pone.0098030. eCollection 2014.

DOI:10.1371/journal.pone.0098030
PMID:24853864
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4031172/
Abstract

We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.

摘要

我们通过考虑相关矩阵的集合来估计结构化信用风险模型的一般统计特性。该集合是根据随机矩阵理论建立的。我们通过分析证明，如果相关性不全为零，相关性的存在会严重限制信用投资组合中的分散化效果。相关性的存在会显著改变损失分布的尾部，即使其平均值为零。在相关性随机波动的假设下，给出了损失分布估计的下限。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/ad6ff3e74815/pone.0098030.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/030a3f3a8c26/pone.0098030.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/2f015231b026/pone.0098030.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/37f450468ddd/pone.0098030.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/ad6ff3e74815/pone.0098030.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/030a3f3a8c26/pone.0098030.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/2f015231b026/pone.0098030.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/37f450468ddd/pone.0098030.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/38d9/4031172/ad6ff3e74815/pone.0098030.g004.jpg

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本文引用的文献

1
Default risk modeling beyond the first-passage approximation: extended Black-Cox model.
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2
Spectral properties of empirical covariance matrices for data with power-law tails.具有幂律尾部的数据的经验协方差矩阵的谱特性。
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Oct;74(4 Pt 1):041129. doi: 10.1103/PhysRevE.74.041129. Epub 2006 Oct 31.
PLoS One. 2018 Feb 9;13(2):e0190263. doi: 10.1371/journal.pone.0190263. eCollection 2018.