Credit Risk Modeling Using Excel and VBA with DVD

3

Transition Matrices

A credit rating system uses a limited number of rating grades to rank borrowers according to their default probability. Ratings are assigned by rating agencies such as Fitch, Moody's and Standard & Poor's, but also by financial institutions. Rating assignments can be based on a qualitative process or on default probabilities estimated with a scoring model (see Chapter 1), a structural model (see Chapter 2) or other means. To translate default probability estimates into ratings, one defines a set of rating grade boundaries, e.g., rules that borrowers are assigned to grade AAA if their probability of default is lower than 0.02%, to grade AA if their probability of default is between 0.02% and 0.05% and so on.

In this chapter, we introduce methods for answering questions such as: ‘With what probability will the credit risk rating of a borrower decrease by a given degree?’ In credit risk lingo, we show how to estimate probabilities of rating transition or rating migration. They are usually presented in transition matrices.

Consider a rating system with two rating classes A and B, and a default category D. The transition matrix for this rating system is a table listing the probabilities that a borrower rated A at the start of a period has rating A, B or D at the end of the period; analogously for B-rated companies. Table 3.1 illustrates the transition matrix for this simple rating system.

Row headers give the rating at the beginning of the time period, column headers ...