# Cumulative Default Probability

From Open Risk Manual

## Definition

The term **Cumulative Default Probability** is used in the context of multi-period credit risk analysis to denote the likelihood that a legal entity is observed to have experienced a Credit Event up to a particular timepoint.

The cumulative default probability can be considered as the primary representation of the Credit Curve as a set of non-decreasing probabilities

- In terms of the Incremental Default Probability we have where we denote with the incremental default probability during time
- In terms of the Marginal Default Probability we have where is the marginal default probability during period . The marginal default probability is also denoted the Hazard Rate
- In terms of the Survival Probability we have where is the survival probability up to point