1. The standard approach here is to calculate some conventional ratios.
These ratios can afterwards be used along with regression analysis to estimate the default probability.
2. To acquire the migration matrix for a particular credit rating once could look at the past ratings data on all corporate and calculate the statistical estimates for the transition probabilities from one rating to another in a given time period.
3. There are several credit ratings and each credit comes with a migration matrix. Using past data one can as well calculate the joint probabilities that two or more credits migrate to a different rating.