Marginal Default Probability

Definition

The term Marginal Default Probability is used in the context of multi-period credit risk analysis to denote the likelihood that a legal entity is observed to experience a Credit Event during a defined period of time (hence conditional on not having defaulted prior to that period).

The marginal default probability $h_k$ is identical in meaning with the Hazard Rate.

NB: It is important to distinguish the marginal default probability from the Incremental Default Probability which measures the observed default rate during a given period without conditioning on no default prior to the current period.

Relationships with related measures

• In terms of the Cumulative Default Probability we have $p_k = q_k - q_{k-1}$ where we denote with $q_k$ the cumulative default probability up to time $t_k$
• In terms of the Incremental Default Probability we have $j_k = p_k / (1 - q_{k-1})$ where $p_k$ is the incremental default probability during period $[t_{k-1}, t_k]$.
• In terms of the Survival Probability we have $p_k = S_{k-1} - S_k$ where $S_k$ is the survival probability up to point $t_k$

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