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%