Journal of Credit Risk

Markovian credit transition probabilities under inequality constraints: the US portfolio 1984–2004

George A. Christodoulakis


Credit risk transition probabilities between aggregate portfolio classes constitute a very useful tool when individual transition data is not available. Jones (2005) estimates Markovian credit transition matrices using an adjusted least squares method. Given the arguments of Judge and Takayama (1966), a least squares estimator under inequality constraints is consistent but has unknown distribution, thus parameter testing is essentially not immediately available. In this paper, we view transition probabilities as parameters from a Bayesian perspective, which allows us to impose the non-negativity and diagonal dominance constraints to transition probabilities using prior densities and then estimate the model through Monte Carlo integration (MCI). This approach reveals the empirical posterior distribution of transition probabilities and makes statistical inference readily available. Our empirical results as compared with Jones (2005) suggest that least squares-based methods tend to overestimate non-transition and underestimate transition probabilities, especially toward upgrades. Furthermore, in-sample forecast evaluation statistics indicate that our estimator tends to slightly over-predict (under-predict) non-performing (performing) loan proportions consistent with prudent asymmetric preferences and is substantially more accurate in all cases.

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