Estimation of rating classes and default probabilities in credit risk models with dependencies |
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Authors: | Daniel Tillich Dietmar Ferger |
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Institution: | 1. Chair of Quantitative Methods, esp. Statistics, Technische Universit?t Dresden, Dresden, Germany;2. Institute of Mathematical Stochastics, Technische Universit?t Dresden, Dresden, Germany |
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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. |
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Keywords: | regression with jump change point default probability rating class dependence strong consistency |
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