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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Eckert et al. (2016) studied this question.