Difference between revisions of "Incremental Default Probability"

Revision as of 11:28, 31 March 2021

Definition

The term Incremental 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 Credit Event during a defined period of time.

The incremental default probability can be considered as another building block of the Credit Curve, alternative to the Cumulative Default Probability representation.

Notation

Observing whether an entity is defaulted over a period $[t_{k-1}, t_k]$ , the incremental default probability is denoted $p_k$ . Incremental default probabilities} during period k, given an initial rating of m, are denoted by

\mbox{PD}^{m}_{t,k} = p^m_k = 1_E [ 1_{\{ R_{k} = D \}} | F_t, R_0=m] = P(R_k=D | F_t, R_0=m)

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 Marginal Default Probability we have $p_k = h_k / (1 - q_{k-1})$ 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 $p_k = S_{k-1} - S_k$ where $S_k$ is the survival probability up to point $t_k$

Issues and Challenges

It is important to distinguish the incremental default probability from the Marginal Default Probability which is conditional on no default prior to the current period.

@@ Line 1: / Line 1: @@
 == Definition ==
-The term '''Incremental 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 [[Credit Event]] during a defined period of time.
+The term '''Incremental 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 [[Credit Event]] ''during a defined period of time''.
-The incremental default probability can be considered as the building block of the [[Credit Curve]].  Observing whether an entity is defaulted over a period  <math>[t_{k-1}, t_k]</math>, the incremental default probability is denoted <math>p_k</math>
+The incremental default probability can be considered as another building block of the [[Credit Curve]], alternative to the  [[Cumulative Default Probability]] representation.
-'''NB: It is important to distinguish the incremental default probability from the [[Marginal Default Probability]] which is conditional on no default prior to the current period.'''
 == Notation ==
+Observing whether an entity is defaulted over a period  <math>[t_{k-1}, t_k]</math>, the incremental default probability is denoted <math>p_k</math>. Incremental default probabilities} during period k, given an initial rating of m, are denoted by
-Incremental default probabilities} during period k, given an initial rating of m, are denoted by
 :<math>
 \mbox{PD}^{m}_{t,k} = p^m_k = 1_E [ 1_{\{ R_{k} = D \}} | F_t, R_0=m] = P(R_k=D | F_t, R_0=m)
@@ Line 17: / Line 14: @@
 * 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 [[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>
+== Issues and Challenges ==
+* It is important to distinguish the incremental default probability from the [[Marginal Default Probability]] which is conditional on no default prior to the current period.'''
 ----
 [[Category:Credit Curve]]
 [[Category:Credit Network]]