Kolmogorv-Smirnov-type testing for the partial homogeneity of Markov processes - with application to credit risk

Abstract

In banking the default behaviour of the counterpart is of interest not only for the pricing of transactions under credit risk but also for the assessment of portfolio credit risk. We develop a test against the hypothesis that default intensities are constant over time within a homogeneous group of counterparts under investigation, e.g. a rating class. The Kolmogorov-Smirnov-type test builds on the asymptotic normality of counting processes in event history analysis. Right-censoring accommodates for Markov process with more than one no-absorbing state. A simulation study and an example of rating migrations support the usefulness of the test.