Rating Migration Matrix
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.
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
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.,
The simplest empirical estimation of a rating migration matrix is simply a frequency count
Credit Risk Models
A transition matrix can also be used as the basic representation of stochastic credit processes.