# Credit Curve

From Open Risk Manual

## Definition

**Credit Curve** denotes a *grouping* of different possible Credit Risk metrics (Risk Rarameters) that provide quantitative estimates capturing possible legal entity Credit Event over different time periods.

## Characteristics

- A credit curve is a type of Term Structure.
- It may refer purely to the likelihood of a default or it may incorporate also a loss estimate
- It may be empirical (historical) in nature (expressing statistical likelihood of defaulting over a period of time) or derived from models and/or market data

## Notation

The credit curve (default curve) at timepoint is the collection of credit default expectation probabilities at the various future timepoints.

## Relation with Transition Matrices

A Multi-Period Transition Matrix is a collection of square (n x n) matrixes representing the transition probabilities of a stochastic system (e.g. a Markov Chain) over several successive periods.

- In cases where the Credit Event captured by the Credit Curve can be conceptually represented as a State Space transition a credit curve can be considered as a subset of the corresponding transition rates
- A credit curve may capture complext / composite risk premia (e.g. Expected Credit Loss) in which case its relationship with a transition matrix representation may not be well defined