Loss Distribution Function

Definition

A Loss Distribution Function is a cumulative Risk Distribution function that captures the probability that a Random Variable $L$ representing the Credit Loss of a Credit Portfolio takes on a value less than or equal to $x$.

The loss distribution function (and the related default rate distribution function that focuses exclusively on Default Event counts) is a fundamental object in quantitative Credit Portfolio Management. Important risk metrics are formed as the low moments (mean, variance) of that distribution and quantile estimates are informing risk capital calculations

• Expected Loss
• Default Rate Volatility

Formula

Single Period Loss Distribution function:

$F_L(x) = \operatorname{P}(L\leq x)$

A multiperiod Loss Distribution Function is a generalization of the above to a Loss Process that is modelled over more than one periods (possibly continuously)