# Default Rate Process

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## Definition

Default Rate Process is any stochastic process that aims to model the arrival of default events in a Credit Portfolio

A default rate process is related to the corresponding Credit Loss Process which incorporates additional Loss Given Default considerations

## Formula

A default rate process is modelled as the cumulation of individual transitions of Credit Rating into the defaulted state. The individual default indicator for an entity ${\displaystyle i}$ is simply

${\displaystyle {\mbox{d}}_{k}^{i}=1_{\{R_{k}^{i}=D\}}}$

where ${\displaystyle R_{k}^{i}}$ is the rating state at observation point k

The default rate process is the sum (defined on a fixed cohort basis) of individual random variables ${\displaystyle {\mbox{d}}_{k}^{i}}$

${\displaystyle {\mbox{DR}}_{k}=\sum _{i=1}^{N}{\mbox{d}}_{k}^{i}}$