1. Introduction

This chapter elaborates on the validation requirements for rating systems and probabilities of default (PDs) that were introduced with the New Capital Standards (commonly called Basel II , cf. BCBS, 2004). 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 to meet the quantitative regulatory requirements. However, their appropriateness will depend on the specific conditions under which they are applied.

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 further considerations. Intuitively, a good rating system should show higher PDs 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...