The Double Default Value-of-the-Firm Model

In the new Basel Accord, banks have the possibility to consider the double default effect of a guaranteed exposure, which is when both the obligor and the guarantor fail to meet their obligations. This question is currently taken into account by a multivariate value-of-the-firm model, with increased asset correlations between the obligor and the guarantor, in order to capture the additional link created by the guarantee. Such an approach is misleading, since the obligor and guarantor are treated in a symmetric way, whereas the link between obligor and guarantor is clearly asymmetric. Moreover, their joint default involves an over-the-counter price of the guarantee, whose existence and uniqueness have to be analyzed. The aim of our paper is to specify this link in detail, to discuss how it depends on the type of guarantee and the seniorities of the components of the debts, and to deduce its implications in terms of risk management.