  Markovian credit migration models are a reasonably standard tool nowadays,
but there are fundamental difficulties with calibrating them. We show how these
are resolved using a simplified form of matrix generator and explain why
risk-neutral calibration cannot be done without volatility information. We also
show how to use elementary ideas from differential geometry to make general
inferences about calibration stability. This the longer version of an article
published by RISK (Feb 2021).
