  This paper elaborates on the validation requirements for rating systems and
probabilities of default (PDs) which were introduced with the New Capital
Standards (Basel II). We start in Section 2 with some introductory remarks on
the topics and approaches that will be discussed later on. Then we have a view
on the developments in banking regulation that have enforced the interest of
the public in validation techniques. When doing so, we put the main emphasis on
the issues with quantitative validation. The techniques discussed here could be
used in order to meet the quantitative regulatory requirements. However, their
appropriateness will depend on the specific conditions under which they are
applied. In order to have a common ground for the description of the different
techniques, we introduce in Section 3 a theoretical framework that will be the
basis for the further considerations. Intuitively, a good rating system should
show higher probabilities of default for the less creditworthy rating grades.
Therefore, in Section 4, we discuss how this monotonicity property is reflected
in the theoretical framework from Section 3. In Section 5, we study the meaning
of discriminatory power and some tools for measuring it in some detail. We will
see that there are tools that might be more appropriate than others for the
purpose of regulatory validation of discriminatory power. The topic in Section
6 is calibration of rating systems. We introduce some of the tests that can be
used for checking correct calibration and discuss the properties of the
different tests. We then conclude in Section 7 with some comments on the
question which tools might be most appropriate for quantitative validation of
rating systems and probabilities of default.
