Default probability of an underlying deliverable obligation refers to the chance that it would not fulfill during the life of the contract. It can be obtained using CDS quotes: default probability is backed out from the observed CDS spread.
Spread (in bps) = (1- R) × q
Where:
q is default probability (probability of a credit event).
R is the value of the reference entity/ obligor (e.g., a sovereign debt) following a credit event (the recovery rate).
The default and recovery rate are assumed to be independent.
For a given recovery rate (R) and a spread, the implied probability is given by:
q = spread/(1-R)
For example, if the observed 5-year CDS spread is 1,500 basis points (= 15%) and the assumed recovery rate is 75%, then the implied default probability is:
q= 15%/(1- 75%) = 60%
