Probability of default (PD)
Probability of default (PD) is the likelihood that a borrower defaults within a defined horizon, often 12 months. Default is commonly defined as 90 or more days past due or as the borrower being unlikely to pay. A lender estimates PD from a score or rating grade, then compares the estimate with observed defaults.
Example
For illustration, suppose a scorecard assigns odds of 19 good borrowers to 1 bad borrower at a score. The bad share is 1/(19+1), or 5%, so the estimated PD for that score is 5% over the specified horizon.
How scores, horizons and through-the-cycle or point-in-time PDs differ
A lender maps a score or rating grade to an estimated PD. The estimate depends on the chosen definition of default and the horizon. A common definition is 90 or more days past due, or being unlikely to pay, measured over a 12-month horizon.
Through-the-cycle and point-in-time are two ways of framing PD estimates. The label alone does not specify the default definition or horizon, so the model methodology matters when interpreting or comparing estimates.
How lenders use PD for expected loss, pricing and limits
PD is one input to expected loss: PD × loss given default × exposure at default. For illustration, a 5% PD, 40% loss given default and $1,000 exposure at default produce $20 in expected loss.
Lenders can also use PD when setting pricing and credit limits. The lender sets its own policy. To check estimates, back-testing compares each grade’s assigned PD with the share of that grade that defaulted. A binomial or Jeffreys test asks whether the gap is more than chance.
Questions we get asked
How is a PD different from a credit score?
A credit score is used to estimate risk, while PD expresses the estimated likelihood of default over a set horizon. A scorecard can assign good-to-bad odds at each score, from which the bad share gives the PD.
Does a 5% PD mean a borrower will default?
No. A 5% PD is an estimated likelihood over the specified horizon, not certainty about an individual borrower. Lenders check estimates against defaults observed for the relevant grade.
What do binomial and Jeffreys tests tell you about a PD estimate?
They test whether the difference between a grade’s assigned PD and its observed default share is more than chance. Back-testing compares those two figures for each grade.
Decisimo’s PD calibration calculator tests each rating grade’s PD against observed bads using Jeffreys and binomial tests, with portfolio and Hosmer-Lemeshow results.
