Modeling of Dependent Credit Rating Transitions Governed by Industry-Specific Markovian Matrices
Two coupling schemes where probabilities of credit rating migrations vary across industry sectors are introduced. Favorable and adverse macroeconomic factors, encoded as values 1 and 0, of credit class- and industry-specific unobserved tendency variables,
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Abstract Two coupling schemes where probabilities of credit rating migrations vary across industry sectors are introduced. Favorable and adverse macroeconomic factors, encoded as values 1 and 0, of credit class- and industry-specific unobserved tendency variables, modify the transition probabilities rendering individual evolutions dependent. Unlike in the known coupling schemes, expansion in some industry sectors and credit classes coexists with shrinkage in the rest. The schemes are tested on Standard and Poor’s data. Maximum likelihood estimators and MATLAB optimization software were used.
1 Motivation Within the CreditMetrics approach, the study of changes in the credit quality of debtors through time is a corner stone, see Gupton et al. [3]. While the credit rating of each of them evolves as a time-homogeneous Markov chain, in order to model the joint distribution of a pool of debtors, a coupling scheme can be suggested. Then, introducing dependence among the migrations, the evolution of every debtor in the pool can be represented as a randomization of an idiosyncratic move and a common component. In particular, the model by Kaniovski and Pflug [4] considers a single common component for all debtors belonging to a credit class, while in the modification by Wozabal and Hochreiter [6] common components are debtorspecific. An intermediate situation, where the same common component affects all debtors characterized by a combination of a credit class and an industry sector, was introduced in Boreiko et al. [2]. In all three cases, the distribution of a common component depends on an unobserved binary tendency variable. It indicates whether D.V. Boreiko · Y.M. Kaniovski (B) Faculty of Economics and Management, Free University of Bozen-Bolzano, Piazza Università 1, 39100 Bolzano, Italy e-mail: [email protected] G.Ch. Pflug Department of Statistics and Decision Support Systems, University of Vienna, Universitätstraße 5, 1090 Vienna, Austria © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_71
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the overall state of the economy is favorable or not for debtors belonging to the credit class in question. In other words, it is assumed that, being credit class-specific, the microeconomic factors affect all industry sectors in the same way. Let us label this pattern of tendency variables as synchronous evolution of industries. In this paper, asynchronously moving industries are analyzed. That is, tendency variables are not synchronized across industry sectors: favorable conditions in some of them can coexist with adversities in the rest. Incorporating the known coupling schemes as particular cases, the settings introduced here could account better for the actually observed variability of the strength and of the direction of the macroeconomic factors across industry sectors. More importantly, industry-specific tendency variables are necessary for implementing the
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