# Incremental Default Probability

From Open Risk Manual

## 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 , the incremental default probability is denoted .

In the context of a Credit Rating System, incremental default probabilities} during period k, given an initial rating of m, are denoted by

- In terms of the Cumulative Default Probability we have where we denote with the cumulative default probability up to time
- In terms of the Marginal Default Probability we have where is the marginal default probability during period . The marginal default probability is also denoted the Hazard Rate
- 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 incremental default probability from the Marginal Default Probability which is conditional on no default prior to the current period.