A hidden Markov model of credit quality. (English) Zbl 1181.91326

Korolkiewicz, Małgorzata W.; Elliott, Robert J.

J. Econ. Dyn. Control 32, No. 12, 3807-3819 (2008).

Summary: This paper presents a hidden Markov model of credit quality dynamics, and highlights the use of filtering-based estimation methods for models of this kind. We suppose that the Markov chain governing the “true” credit quality evolution is hidden in “noisy” or incomplete observations represented by posted credit ratings. Parameters of the model, namely credit transition probabilities, are estimated using the EM algorithm. Filtering methods provide recursive updates of optimal estimates so the model is “self-calibrating”. The estimation procedure is illustrated with an application to a data set of Standard & Poor’s credit ratings.

MSC:

91G40	Credit risk
91G70	Statistical methods; risk measures
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

credit quality; filtering; hidden Markov models; EM algorithm

Software:

astsa

References:

[1]	Altman, E.I., The importance and subtlety of credit rating migration, Journal of banking and finance, 22, 1231-1247, (1998)
[2]	Altman, E.I.; Kao, D.L., Rating drift in high-yield bonds, Journal of fixed income, 2, 15-20, (1992)
[3]	Bangia, A.; Diebold, F.X.; Schuermann, T., Rating migration and the business cycle, with application to credit portfolio stress testing, Journal of banking and finance, 26, 445-474, (2002)
[4]	Basel Committee on Banking Supervision, 2000. Credit ratings and complementary sources of credit quality information. BCBS Publications No. 3, Bank for International Settlements.
[5]	Basel Committee on Banking Supervision, 2001. A new capital adequacy framework, Basel.
[6]	Basel Committee on Banking Supervision, 2005. Studies on validation of internal rating systems. BCBS Publications No. 14, Bank for International Settlements.
[7]	Carey, M.; Hrycay, M., Parametrizing credit risk models with rating data, Journal of banking and finance, 25, 197-270, (2001)
[8]	Delianedis, G., Geske, R., 2003. Credit risk and risk neutral default probabilities: information about rating migrations and defaults. In: EFA Annual Conference Paper No. 962. Available at SSRN \(\langle\)http://ssrn.com/abstract=424301⟩.
[9]	Elliott, R.J.; Krishnamurthy, V., New finite-dimensional filters for parameter estimation of discrete-time linear Gaussian models, IEEE transactions on automatic control, 44, 938-951, (1999) · Zbl 0959.93055
[10]	Elliott, R.J.; Aggoun, L.; Moore, J.B., Hidden Markov models. estimation and control, (1995), Springer Berlin · Zbl 0819.60045
[11]	Krishnamurthy, V.; Chung, S.H., Signal processing based on hidden Markov models for extracting small channel currents, ()
[12]	Lando, D.; Skødeberg, T., Analyzing rating transitions and rating drift with continuous observations, Journal of banking and finance, 26, 423-444, (2002)
[13]	Löffler, G., An anatomy of rating through the cycle, Journal of banking and finance, 28, 695-720, (2004)
[14]	Löffler, G., Avoiding the rating bounce: why rating agencies are slow to react to new information, Journal of economic behavior and organization, 56, 365-381, (2004)
[15]	Shumway, R.H.; Stoffer, D.S., Time series analysis and its applications with R examples, (2006), Springer Berlin · Zbl 0502.62085
[16]	Standard & Poor’s, 2000. Standard & Poor’s COMPUSTAT (North America) User’s Guide. Standard & Poor’s, Englewood, CO.
[17]	Wendin, J.; McNeil, A.J., Dependent credit migrations, Journal of credit risk, 2, 87-114, (2006)