Cumulative Default Probability

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 $q_{k}$.

Relationships with related measures

• In terms of the Incremental Default Probability we have $q_{T}=\sum _{k=1}^{T}{p_{k}}$ where we denote with $p_{k}$ the incremental default probability during time $[t_{k-1},t_{k}]$
• In terms of the Marginal Default Probability we have $q_{T}=1-\prod _{k=1}^{T}(1-h_{k})$ where $h_{k}$ is the marginal default probability during period $[t_{k-1},t_{k}]$. The marginal default probability is also denoted the Hazard Rate
• In terms of the Survival Probability we have $q_{k}=1-S_{k}$ where $S_{k}$ is the survival probability up to point $t_{k}$

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