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

Abstract

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.