Estimation of rating classes and default probabilities in credit risk models with dependencies

Daniel Tillich and Dietmar Ferger

Applied Stochastic Models in Business and Industry, 2015, vol. 31, issue 6, 762-781

Abstract: Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m. In the literature, estimators for the three parameters of m, that is, the breakpoint θ and the levels a and b, are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y. The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.

Date: 2015
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https://doi.org/10.1002/asmb.2089

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:31:y:2015:i:6:p:762-781

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