The measures of probability of default (PD) used in banks are done on the aggregated level, that means that companies are grouped in rating classes and a specific value of PD is assigned to each class. Internal rating systems use the methodology called PIT (Point in Time). In practice it is necessary to re-calibrate models and estimate the PDs every time the state of economy changes. Fortunately, the study of credit rating dynamics can be reduced to the analysis of migration matrices. It is convenient to consider migration process as a stationary Markov chain to obtain  stable estimates. However,  ratings don’t have the properties of stationary Markov processes. There are many proposals of the so-called non-Markov processes, such as: "rating drifts", hidden Markov chains, Markov Mixture Models.

In this paper, the authors would like to present the model of Markov process based on the direct link between the transition matrix and  time. Temporal changes occur relatively slowly, and we can assume the properties of defaults are close to exponential distribution. This is the reason of existence an intensity matrix for a Markov process which allows to enter hazard space. The intensity matrix defines the levels of hazard in the space corresponding to the ratings. In general, the levels are deterministic functions of time or stochastic processes such as random walks. The transition from the intensity of the migration matrix requires Monte Carlo simulations. The authors tried to link the resulting model with external factors such as the state of the economy "crisis/development." Inferences were drawn based on simulated data.

Literature:

1.      H. Frydman, T. Schuermann (2007), „Credit Rating Dynamics and Markov Mixture Models”,  Wharton;

2.      G. Giampieri, M. Davis, M. Crowder (2005), “A Hidden Markov Model of default interaction”, Quantitative Finance;

3.      D .Lando,  T. Skødeberg (2002), “Analyzing Ratings Transitions and Rating Drift with Continuous Observations,” Journal of B&F;

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