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Kolmogorov–Smirnov‐type testing for the partial homogeneity of Markov processes—with application to credit risk
Author(s) -
Weißbach Rafael,
Dette Holger
Publication year - 2007
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.667
Subject(s) - markov chain , homogeneity (statistics) , econometrics , censoring (clinical trials) , mathematics , credit risk , actuarial science , statistics , economics
In banking, the default behaviour of the counterpart is not only of interest for the pricing of transactions under credit risk but also for the assessment of a portfolio credit risk. We develop a test against the hypothesis that default intensities are chronologically constant within a group of similar counterparts, e.g. a rating class. The Kolmogorov–Smirnov‐type test builds up on the asymptotic normality of counting processes in event history analysis. The right censoring accommodates for Markov processes with more than one no‐absorbing state. A simulation study and two examples of rating systems demonstrate that partial homogeneity can be assumed, however occasionally, certain migrations must be modelled and estimated inhomogeneously. Copyright © 2007 John Wiley & Sons, Ltd.