Credit risk and the instability of the financial system: An ensemble approach

Abstract

The instability of the financial system as experienced in recent years and in previous periods is often linked to credit defaults, i.e., to the failure of obligors to make promised payments. Given the large number of credit contracts, this problem is amenable to be treated with approaches developed in statistical physics. We introduce the idea of ensemble averaging and thereby uncover generic features of credit risk. We then show that the often advertised concept of diversification, i.e., reducing the risk by distributing it, is deeply flawed when it comes to credit risk. The risk of extreme losses remains due to the ever present correlations, implying a substantial and persistent intrinsic danger to the financial system.

Constructing analytically tractable ensembles of stochastic covariances with an application to financial data

“…With the help of Eq. (14), the results (17,19) are easily seen to coincide. Having extracted the covariance matrix for the total time interval from the data, we can proceed with the determination of the deformation functions.…”

“…-In the context of finance, we recently put forward a random ma- * Electronic address: frederik.meudt@uni-due.de † Electronic address: martin.theissen@stud.uni-due.de ‡ Electronic address: rudi.schaefer@uni-due.de § Electronic address: thomas.guhr@uni-due.de trix approach to tackle these issues [16]. We also succesfully applied it in a study of credit risk and its impact on systemic stability [17]. Inspite of the conceptual differences, random matrix theory [18,19] formally has much in common with statistical mechanics.…”

Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

“…Recently, we also applied it in the context of credit risk (Schmitt et al 2014) leading to the computation of an averaged loss distribution for credit portfolios.…”

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

“…The covariance and correlation matrix of asset values changes in time [57,53,38,44] exhibiting an important example of the non-stationarity which is always present in financial markets. The approach we review here [46,47,48,52] uses the fact that the set of different correlation matrices measured in a smaller time window that slides through a longer dataset can be modeled by an ensemble of random correlation matrices. The asset values are found to be distributed according to a correlation averaged multivariate distribution [8,46,47,48].…”

“…The approach we review here [46,47,48,52] uses the fact that the set of different correlation matrices measured in a smaller time window that slides through a longer dataset can be modeled by an ensemble of random correlation matrices. The asset values are found to be distributed according to a correlation averaged multivariate distribution [8,46,47,48]. This assumption is confirmed by detailed empirical studies.…”