This is the final of five articles – each explaining at a high level one each of the five credit risk models in the PRMIA handbook. This write-up deals with the actuarial, or the ‘CreditRisk+’ model.Credit Risk +, or the actuarial approach.
Under the actuarial approach, default is an ‘end-of-game’ surprise with a known probability that follows the Poisson distribution. (For a quick 1-minute reminder of what the Poisson distribution is, click here). The actuarial method ignores all other factors such as leverage, volatility of asset returns, or even downgrade risk, and considers defaults to ‘arrive’ at a certain rate per unit of time (say years) and considers them distributed according to the Poisson distribution.
The probability of default is assumed to be constant from one period to the next, and generally very small at the individual issuer level. Thus, the distribution of defaults during a given period of time is represented by the Poisson distribution as follows, where μ is the mean number of defaults each year, with a variance of μ as well.
The mean number of defaults per year (μ) itself varies from year to year, for example, due to the effects of the business cycle.
It assumes:
- The probability of default for an individual obligor is small, ie μ is a small number,
- The probability of default stays same from month to month, and
- The number of defaults in any period are independent of the defaults in the previous period.
- The mean default rate, μ, itself is stochastic and varies from year to year
There are three steps to implementing the model:
- The portfolio is classified by exposure size so that all obligors of a certain size range are bucketed together in ‘bands’,
- The default distribution is calculated for each band, and
- The bands are aggregated together to get the loss distribution for the entire portfolio.
Limitations:
- The model ignores downgrade or migration risk, ie, the fall in the price of the security as a result of declines in credit quality are ignored.
- Causes of default, the capital structure of the firm are ignored too.
- The approach does not work for non-linear portfolios where exposures vary in a non-linear way with the market.