Credit migration modelling
Credit ratings summarise a range of qualitative and quantitative information about the credit worthiness of debt issuers and are therefore a convenient signal for the credit quality of the debtor. The estimation of credit quality transition matrices is at the core of credit risk measures with applications to pricing and portfolio risk management. In view of pending regulations regarding the calculation of capital requirements for banks, there is continued interest in the efficiency of credit ratings as indicators of credit quality and models of their dynamics.
In the study of credit quality dynamics, it is convenient to assume that the credit rating process is a time-homogeneous Markov chain, which then implies that the rating process should have no memory of its past behaviour. In other words, predictions of future rating evolution based on the past rating history and a current rating should be no better than predictions based on the current rating only. However, the assumptions of time homogeneity and Markovian behaviour of the rating process have been challenged by some empirical studies; in particular, it has been suggested that ratings exhibit 'rating momentum' or 'drift', where a rating change in response to a change in credit quality does not fully reflect that change in credit quality, perhaps as a result of some of the agenciesÃ rating policies, such as rating through-the-cycle and avoiding rating reversals.
In our research into the dynamics of credit ratings, the credit rating process is assumed to be a hidden Markov model (HMM), with 'true' credit quality hidden in 'noisy' observations represented by posted credit ratings. We employ hidden Markov filtering and estimation techniques and use the filter-based EM (Expectation Maximization) algorithm to estimate the parameters of the model. By construction parameters are revised as new information is obtained so the resulting filters are adaptive and 'self-tuning'. Dependence between noise terms in the signal ('true' credit quality) and observation (posted credit ratings) processes is also considered, thus explicitly allowing for the presence of 'rating momentum' in posted credit ratings.
Contact: Malgorzata Korolkiewicz
MW Korolkiewicz, 'A dependent hidden Markov model of credit quality', International Journal of Stochastic Analysis, in press.
MW Korolkiewicz & RJ Elliott, RJ, 'A hidden Markov model of credit quality', Journal of Economic Dynamics and Control, 32( 12):3807-3819, 2008.
MW Korolkiewicz & RJ Elliott, 'Smoothed Parameter Estimates for a Hidden Markov Chain of Credit Quality', in Hidden Markov Models in Finance, RS Mamon & RJ Elliott (eds), Springer Science+Business Media, LLC, New York, 2007.
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