Changes in Migration Matrices and Credit VAR - A New Class of Difference Indices

In credit risk management migration matrices are major inputs for many applications, including the determination of Value-at-Risk or derivative pricing. After reviewing distance measures for migration matrices we motivate and propose new directed difference indices to measure changes in migration behavior in a more risk-sensitive way. We quantify the changes in rating migration matrices by applying the classical distance measures as well as the derived distance indices based on twenty years of Moody's credit migration history. We further study the relationship between changes in migration behavior, business cycle effects and changes in risk capital for an exemplary credit portfolio. Our findings strongly support the usefulness of the derived distance indices and its capability to relate changes in migration behavior to the business cycle and Value-of-Risk of a credit portfolio. We particularly recommend the use of the indices in risk management for internal credit and loan portfolios of a bank