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Let annual losses be $L={\sum }_{i=1}^N{X}_i$ with $N\sim \mathrm{Poisson}(\lambda )$ independent of identically distributed nonnegative loss given default amounts of mean $\mu$ and variance ${\sigma }^2$. Conditional expectation and variance give $\mathbb{E}L=\lambda \mu$ and $\mathrm{Var}L=\lambda ({\sigma }^2+{\mu }^2)$. A many-event normal approximation yields the displayed quantile; the actual loss distribution has a zero atom and depends on the entire severity law. For rare events or extreme tails, the moment-based normal approximation need not be accurate.

Credit risk is the risk of loss through a counterparty's inability or failure to meet a financial obligation, or deterioration in its credit quality. A loss model distinguishes credit default frequency from loss given default; shared exposures or systematic factors may produce dependence beyond an independent Poisson model.

A credit rating is an agency's ordered assessment of an issuer's or particular obligation's capacity and willingness to meet its promised payments. Corporate and sovereign issuers are classified on letter scales, with finer notches, broad investment-grade and speculative-grade groupings, and default categories. Agencies such as Standard & Poor's, Moody's and Fitch also revise ratings as information changes; sovereign assessments involve public finances and institutional or political factors as well as debt-servicing capacity.

A credit rating summarizes relative creditworthiness rather than specifying an exact, immutable credit default probability. Historical defaults and migrations within rating classes can inform a statistical model. Assuming a homogeneous Poisson process within one class is a simplifying choice: it posits a constant event intensity and independent increments, neither of which follows merely from a shared rating. The credit risk model must also distinguish default frequency from loss given default severity.