Measurement and Estimation of Credit Migration Matrices

Abstract

Credit migration matrices are cardinal inputs to many risk management applications. Their accurate estimation is therefore critical. We explore three approaches, cohort and two variants of duration - time homogeneous and non-homogeneous - and the resulting differences, both statistically through matrix norms and economically through credit portfolio and credit derivative models. We develop a testing procedure to assess statistically the differences between migration matrices using bootstrap techniques. The method can have substantial economic import: economic credit risk capital differences between economic regimes, recession vs. expansion, can be as large as difference implied by different estimation techniques. Ignoring the efficiency gain inherent in the duration methods by using the cohort method instead is more damaging that making a (possibly false) assumption of time-homogeneity.

Keywords: Credit risk, risk management, matrix norms, bootstrapping, credit derivatives

JEL Classification: C15, C41, G21, G28