Credit risk: taking fluctuating asset correlations into account

Schmitt, Thilo A.; afer, Rudi Sch; Guhr, Thomas

doi:10.21314/jcr.2015.196

Cited by 9 publications

(20 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This goal can be achieved by using the random matrix approach for the asset correlations, discussed in Section 2. Based on (Schmitt et al 2014(Schmitt et al , 2015, we discuss the Merton model together with the random matrix approach in Section 3.1. In Section 3.2, we reveal the results for the average loss distribution of a credit portfolio.…”

Section: Modeling Fluctuating Asset Correlations In Credit Riskmentioning

confidence: 99%

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

Mühlbacher

Guhr

2018

Risks

Self Cite

View full text Add to dashboard Cite

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used, the correlations of which have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary, which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results, which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model.

show abstract

Section: Modeling Fluctuating Asset Correlations In Credit Riskmentioning

confidence: 99%

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

Mühlbacher

Guhr

2018

Risks

Self Cite

View full text Add to dashboard Cite

show abstract

“…2. Based on [47,48], we discuss the Merton model together with the random matrix approach in Sec. 3.1.…”

Section: Modeling Fluctuating Asset Correlations In Credit Riskmentioning

confidence: 99%

“…This corresponds to the case N → ∞. Second, we use fluctuating asset correlations, employing a parameter value of N eff = 5 in accordance with the findings of [48] for an effective correlation matrix, see Tab. 1.…”

Section: Simulation Setupmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Mühlbacher

Guhr

2018

SSRN Journal

Self Cite

View full text Add to dashboard Cite

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model. * andreas.muehlbacher@uni-due.de arXiv:1803.00261v1 [q-fin.RM]

show abstract

Multivariate analysis of short time series in terms of ensembles of correlation matrices

Vyas¹,

Guhr²,

Seligman³

2018

Sci Rep

View full text Add to dashboard Cite

When dealing with non-stationary systems, for which many time series are available, it is common to divide time in epochs, i.e. smaller time intervals and deal with short time series in the hope to have some form of approximate stationarity on that time scale. We can then study time evolution by looking at properties as a function of the epochs. This leads to singular correlation matrices and thus poor statistics. In the present paper, we propose an ensemble technique to deal with a large set of short time series without any consideration of non-stationarity. Given a singular data matrix, we randomly select subsets of time series and thus create an ensemble of non-singular correlation matrices. As the selection possibilities are binomially large, we will obtain good statistics for eigenvalues of correlation matrices, which are typically not independent. Once we defined the ensemble, we analyze its behavior for constant and block-diagonal correlations and compare numerics with analytic results for the corresponding correlated Wishart ensembles. We discuss differences resulting from spurious correlations due to repetitive use of time-series. The usefulness of this technique should extend beyond the stationary case if, on the time scale of the epochs, we have quasi-stationarity at least for most epochs.

show abstract

Credit risk: taking fluctuating asset correlations into account

Cited by 9 publications

References 20 publications

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

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

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

Multivariate analysis of short time series in terms of ensembles of correlation matrices

Contact Info

Product

Resources

About