Logistic distribution maps credit score to probability of default (PD)

The logistic function can be used to transform a credit score into a probability of default (PD). The advantages of the logistic are (i) it easy to calculate and (ii) as a cumulative distribution function (CDF) the output is, appropriately, a probability between 0 and 1.0. In this video, I show two approaches to the exponent, which itself is the negative of a product of vectors (-b*x). First, the two-factor linear probability model that produces a “credit score;” the credit score is then transformed into a PD. Second, an illustrated usage which starts with “internal credit ratings” from 0 to 100, with 100 representing perfect credit quality; in this case, the internal credit rating is adjusted to a scale usable to the logistic, then the logistic function is again used to compute a PD. The spreadsheet is available on our website!

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