Difference between revisions of "Marginal Default Probability"
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The marginal default probability <math>h_k</math> is identical in meaning with the [[Hazard Rate]]. | The marginal default probability <math>h_k</math> is identical in meaning with the [[Hazard Rate]]. | ||
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== Relationships with related measures == | == Relationships with related measures == | ||
* 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 [[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 [[Incremental Default Probability]] we have <math> | + | * In terms of the [[Incremental Default Probability]] we have <math>h_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> | * 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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+ | == Issues and Challenges == | ||
+ | * 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.''' | ||
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[[Category:Credit Curve]] | [[Category:Credit Curve]] |
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 is identical in meaning with the Hazard Rate.
- In terms of the Cumulative Default Probability we have where we denote with the cumulative default probability up to time
- In terms of the Incremental Default Probability we have where is the incremental default probability during period .
- In terms of the Survival Probability we have where is the survival probability up to point
Issues and Challenges
- 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.