Difference between revisions of "Marginal Default Probability"

Revision as of 11:35, 31 March 2021

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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 * In terms of the [[Cumulative Default Probability]] we have <math>p_k = q_k - q_{k-1} </math> where we denote with <math>q_k</math> the cumulative default probability up to time <math>t_k</math>
-* In terms of the [[Marginal Default Probability]] we have  <math>p_k = h_k / (1 - q_{k-1}) </math> where <math>h_k</math> is the marginal default probability during period <math>[t_{k-1}, t_k]</math>. The marginal default probability is also denoted the [[Hazard Rate]]
+* In terms of the [[Incremental Default Probability]] we have  <math>j_k = p_k / (1 - q_{k-1}) </math> where <math>p_k</math> is the incremental default probability during period <math>[t_{k-1}, t_k]</math>.
 * In terms of the [[Survival Probability]] we have  <math>p_k = S_{k-1} - S_k </math> where <math>S_k</math> is the survival probability up to point <math>t_k</math>
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 [[Category:Credit Curve]]