Joint Default

Definition

Joint Default denotes an composite risk event where two borrowers (legal entities) default on debt obligations within the Risk Horizon under consideration. The joint realization need not imply a causal relationship between the two individual defaults.

The likelihood of a joint default event is influenced by the degree of Default Dependency or Default Correlation between entities.

Formula

The general formula capturing the joint probability of default over a period k for two entities whose rating state becomes the default state D is

$\mbox{JDP}_k = \mathbb{P}(R^i_k = D, R^j_k = D)$

From Asset Correlation

A long standing Credit Portfolio Model infers the joint default probability from the Asset Correlation Matrix

$\mbox{JDP} = \mathbb{P}(A^i < H_i, A^j < H_j) = N_2(H_i, H_j, \rho_{ij})$

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