Journal of Credit Risk

A credit portfolio framework under dependent risk parameters: probability of default, loss given default and exposure at default

Johanna Eckert, Kevin Jakob and Matthias Fischer

  • We provide a new factor model to capture the dependence of PD, EAD and LGD.
  • We develop a Maximum-Likelihood estimation framework for the unknown dependence parameters.
  • Correct specification of the dependence structure between risk parameters in a credit portfolio setting is essential.
  • Both specific systematic and idiosyncratic dependencies can have a significant impact on the respective risk figures.


This paper introduces a credit portfolio framework that allows for dependencies between default probabilities, secured and unsecured recovery rates and exposures at default (EADs). The overall approach is an extension of the factor models of Pykhtin (2003) and Miu and Ozdemir (2006), with respect to differentiated recovery rates and the inclusion of dependent exposures. As there is empirical evidence for dependence between these risk parameters and observations for the EAD, and since the secured and unsecured recovery rates are available only in the case of a default, we propose a multivariate extension of the selection model of Heckman in order to estimate the unknown parameters within a maximum likelihood framework. Finally, we empirically demonstrate the effects of the dependence structure on the portfolio loss distribution and its risk measure for a hypothetical loan portfolio.

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