Examples of Migration Matrices Models and their Performance in Credit Risk Analysis

• Authors: U. Grzybowska , M. Karwański , A. Orłowski
• Languages of publication: EN

Abstracts

EN

Credit risk models used in banks are based on probability models for occurrence of default. A vast class of the models used in practice (e.g., Credit Metrics) is based on the notion of intensity. In 1997 Jarrow applied Markov chain approach to analyze intensities. The key problem that arises is the selection of appropriate estimators. Within the Markov approach among the most frequently used estimators of a migration matrix are cohort and duration estimators. Migration matrices can also be obtained with help of statistical longitudinal models (GLMM) in which states (rating classes) in discrete time points are regarded as matched pairs. In this paper we compare Markov chain models and GLMM models and the influence of their application on bank portfolio evaluation.

Keywords

EN

02.50.Ga; 87.55.N-; 02.10.Yn

Discipline

• 02.10.Yn: Matrix theory
• 02.50.Ga: Markov processes
• 87.55.N-: Radiation monitoring, control, and safety

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 2B
• Pages: B-40-B-46

Dates

published

2012-02

Contributors

author

U. Grzybowska

• Katedra Informatyki SGGW, Nowoursynowska 159,02-776 Warszawa, Poland

author

M. Karwański

• Katedra Informatyki SGGW, Nowoursynowska 159,02-776 Warszawa, Poland

author

A. Orłowski

• Katedra Informatyki SGGW, Nowoursynowska 159,02-776 Warszawa, Poland
• Instytut Fizyki PAN, al. Lotników 32/46,02-668 Warszawa, Poland

References

• [1] R. A Jarrow, D.Lando, S. M.Turnbull, A Markov model for the term structure of credit risk spreads, Review of Financial Studies, 10, 2 (1997)
• [2] W. Feller, Wstęp do rachunku prawdopodobieństwa, PWN, Warszawa 1966
• [3] M. Iosifoscu, Skończone łańcuchy Markowa, WNT, Warszawa 1987
• [4] S&P, www.standardandpoors.com/ratings/en/eu
• [5] Moody's Investors Service, Historical Default Rates of Corporate Bond Issuers, 1920-1999, p. 25, Special Comment 2000
• [6] Moody's, www.moodys.com
• [7] Basel Committee on Banking Supervision, The Internal Ratings-Based Approach. Consultative Document, 2001, www.bis.org/publ/bcbsca05.pdf
• [8] A. Saunders, Metody pomiaru ryzyka kredytowego, Oficyna Ekonomiczna Kraków 2001
• [9] H. Frydman, J. G. Kallberg, L. D. Kao, Testing the Adequacy of Markov Chain and Mover-Stayer Models as Representations of Credit Behavior, Operations Research 33, 6 (1985)
• [10] H. Frydman, Maximum Likelihood Estimation in the Mover-Stayer Model, J. American Statistical Association, 79, 632 (1984)
• [11] M. T. Jones, Estimating Markov Transition Matrices Using Proportions Data: An Application to Credit Risk, IMF Working Paper WP/05/219, http://www.imf.org/external/pubs/cat/longres.aspx?sk=18387.0
• [12] S. Höse, S. Huschens, R. Wania, Rating Migrations, in: Applied Quantitative Finance: Theory and Computational Tools, Eds. W. Härdle, T. Kleinow, G. Stahl, Springer, Berlin 2002
• [13] Y. Jafry, T. Schuermann, Measurement, estimation and comparison of credit migration matrices, J. Banking and Finance, 28, 11 (2004)
• [14] D. Lando, T. M. Skodeberg, Analyzing rating transitions and rating drift with continuous observations, J. Banking and Finance, 26, 423 (2002)
• [15] T. Schuermann, Credit Migration Matrices in: Encyclopedia Quantitative Risk Analysis and Assessment, www.wiley.com//wileychi/risk/
• [16] R. B. Israel, J. S. Rosentahl, J. Z. Wei, Finding generators for Markov Chains via empirical transition matrices, with applications to credit rating, Mathematical Finance, 11, 2 (2001)
• [17] S. T. Rachev, S. Trueck, Rating Based Modeling of Credit Risk Theory and Application of Migration Matrices, Elsevier Inc, Amsterdam 2009
• [18] A. Agresti, Categorical Data Analysis, Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., Hoboken, New Jersey 2002
• [19] P. Diggle, Analysis of Longitudinal Data, Oxford University Press, New York, 2002
• [20] B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, New York 1993

Identifiers

DOI

10.12693/APhysPolA.121.B-40