Metrics for Comparing Credit Migration Matrices
Credit migration or transition matrices, which characterize the expected changes in credit quality of obligors, are cardinal inputs to applications such as asset pricing and risk management. We propose a new metric for comparing these matrices (a mobility index) by first subtracting the identity matrix, focusing the analysis on the dynamics, and then taking the average of the singular values for the resulting matrix. This yields a metric which has an intuitively-appealing “size” related to the average probability of migration of the original matrix. We also propose a new mobility index performance criterion which is particularly relevant for credit migration matrices, namely that it be distribution discriminatory, i.e. sensitive to the distribution of off-diagonal probability mass. We demonstrate the advantages of the proposed metric over more traditional cell-by-cell distance metrics and eigenvalue-based mobility indices. We then apply these metrics to credit rating histories of S&P rated U.S. obligors from 1981-2001.
|Date of creation:||Mar 2003|
|Date of revision:|
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- Til Schuermann & Yusuf Jafry, 2003. "Measurement and Estimation of Credit Migration Matrices," Center for Financial Institutions Working Papers 03-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Anil Bangia & Francis X. Diebold & Til Schuermann, 2000.
"Ratings Migration and the Business Cycle, With Application to Credit Portfolio Stress Testing,"
Center for Financial Institutions Working Papers
00-26, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
- Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
- Geweke, John & Marshall, Robert C & Zarkin, Gary A, 1986. "Mobility Indices in Continuous Time Markov Chains," Econometrica, Econometric Society, vol. 54(6), pages 1407-23, November.
- Robert B. Israel & Jeffrey S. Rosenthal & Jason Z. Wei, 2001. "Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 245-265.
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