Loss Given Default

The loss given default or LGD at the asset level is the amount of money that a bank or other financial institution loses when a borrower defaults on a loan. The value of the debt in the case of a default is based on a debt-restructuring model that assumes that debt holders will forgo some debt to avoid a default because debt holders will receive less if a project is liquidated.

Here, LGD is computed as the averaged loss given default for all the defaulting scenarios.

$$//<![CDATA[ \begin{array}{l}\displaystyle LGD = \sum_{j \in D_{1}}^{}{p_{1,j}\left( t = 1 \right)}\left( 1 - {RecoveryRate}_{j}\left( t = 1 \right) \right)\end{array} //]]>$$

where summation is done over all the defaulting scenarios because there would still be loss even in the soft defaults, and

$$//<![CDATA[ \begin{array}{l}\displaystyle {RecoveryRate}_{j}\left( t \right) = \min\left( 1,\frac{{DebtValu}e_{j}\left( t \right)}{{DebtOutstanding}\left( t \right)} \right)\end{array} //]]>$$