Rating Migration Matrix

Definition

A Rating Migration Matrix (also Credit Migration Matrix, Transition Matrix) is a fundamental mathematical object used in the connection of a Credit Rating System that employs a Rating Scale. The matrix captures the probability that a certain obligor will transition (migrate) from one credit state to another over a given time period.

Usage

Migration matrices are used in two major and distinct ways in the field of Credit Risk Modelling:

• As a purely descriptive (empirical) statistic capturing the dynamic behavior of Creditworthiness over time
• As a building block of a probabilistic Risk Model, whereby the credit quality (as expressed in probability of default or credit risk premium) is assumed to follow a Markov Chain

Notation

A Rating migration matrix is essentially a Transition Matrix. A set of rating transition matrices encapsulates the probabilities that a name will move from rating state m at time 0 to state n at time l, i.e.,

$T_{0l}^{mn}=P(R_{l}^{i}=n|F_{0},R_{0}^{i}=m)\,.$

Empirical Estimation

The simplest empirical estimation of a rating migration matrix is a frequency count

Credit Risk Models

A transition matrix can also be used as the basic representation of stochastic credit processes.

See Also

• Transition Matrix

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