Under the actuarial (or CreditRisk+) based modeling of defaults, what is the probability of 4 defaults in a retail portfolio where the number of expected defaults is 2?
The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.
The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.
Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.
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