Journal of Credit Risk

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A latent variable credit risk model comprising nonlinear dependencies in a sector framework with a stochastically dependent loss given default

Jakob Maciag and Matthias Löderbusch

  • We propose a latent variable credit risk model for large loan sector-type portfolios with stochastically dependent Loss Given Default, using the concept of nested Archimedean copulas.
  • Employing non-Gaussian copulas in a sector-type portfolio model can be accompanied by a significant increase in terms of measured riskiness.
  • When employing non-Gaussian Copulas, value at risks are highly sensitive to the calibration method, although some degree of convergence ensues if the copulas are calibrated on default correlations.
  • Moving from a homogenous portfolio to a heterogeneous sector model has only a small impact on portfolio tail risk.
  • For most of the copulas, a copula-dependent stochastic LGD increases the portfolio tail risk remarkably.

In this paper, we propose a latent variable credit risk model for large loan port- folios. It employs the concept of nested Archimedean copulas to account for both a sector-type dependence structure and a copula-dependent stochastic loss given default (LGD). Using this framework, we conduct an extensive Monte Carlo simulation study and analyze the impact of various nested Archimedean and elliptical copulas, the sector-type dependence structure and a stochastically dependent LGD on portfolio tail risk. Further, we examine the effect of calibrating the different copulas, either on default correlations or on a measure of global coherence. We find that employing non-Gaussian copulas in a sector-type portfolio model can be accompanied by a significant increase in terms of measured riskiness. Although the value-at-risk (VaR) measurements partially converge when the copulas are calibrated on default correlations, substantial differences between the (nested) copulas remain. We compare homogeneous and heterogeneous sector-type portfolios and find the latter yielding slightly smaller VaRs. Moreover, the restrictions of the nested copula model can attenuate the impact of heavy-tailed copulas on portfolio tail risk. By contrast, for most of the (nested) copulas, a copula-dependent stochastic LGD increases the measured riskiness of the portfolio’s loss rate distribution remarkably.

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