  PD curve calibration refers to the transformation of a set of rating grade
level probabilities of default (PDs) to another average PD level that is
determined by a change of the underlying portfolio-wide PD. This paper presents
a framework that allows to explore a variety of calibration approaches and the
conditions under which they are fit for purpose. We test the approaches
discussed by applying them to publicly available datasets of agency rating and
default statistics that can be considered typical for the scope of application
of the approaches. We show that the popular 'scaled PDs' approach is
theoretically questionable and identify an alternative calibration approach
('scaled likelihood ratio') that is both theoretically sound and performs
better on the test datasets.
  Keywords: Probability of default, calibration, likelihood ratio, Bayes'
formula, rating profile, binary classification.
