Migration matrices

Credit rating transition is the migration of a corporate or governmental bond from one rating to another. The well-known industrial application is the CreditMetrics approach. It provides a risk modeling tool for bond portfolios to estimate the Conditional Value-at-Risk (CVaR) and credit spreads of a portfolio due to downgrade and upgrading. In this section, we show how to calculate credit spreads from a transition matrix.

We have to define the loss given default (lgd), the ratings (in this example: A, B, and D) and the one year transition matrix to compute credit spreads:

> library(CreditMetrics)
> lgd <- 0.5
> rc <- c( "A", "B", "D")
> M <- matrix(c(85, 13, 2, 5, 80, 15, 0, 0, 100 ) /100, 3, 3,
+          dimnames = list(rc, rc), byrow = TRUE)

The command cm.cs calculates the credit spreads from the migration matrix:

> cm.cs(M, lgd)
         A          B
0.01005034 0.07796154

According to this example, a debt instrument with the rating "A" has around...