# 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 defined Credit Event *up to a particular timepoint*.

## Notation

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