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Remarks on the monotonicity of default probabilities


  • Dirk Tasche


The consultative papers for the Basel II Accord require rating systems to provide a ranking of obligors in the sense that the rating categories indicate the creditworthiness in terms of default probabilities. As a consequence, the default probabilities ought to present a monotonous function of the ordered rating categories. This requirement appears quite intuitive. In this paper, however, we show that the intuition can be founded on mathematical facts. We prove that, in the closely related context of a continuous score function, monotonicity of the conditional default probabilities is equivalent to optimality of the corresponding decision rules in the test-theoretic sense. As a consequence, the optimality can be checked by inspection of the ordinal dominance graph (also called Receiver Operating Characteristic curve) of the score function: it obtains if and only if the curve is concave. We conclude the paper by exploring the connection between the area under the ordinal dominance graph and the so-called Information Value which is used by some vendors of scoring systems. Keywords: Conditional default probability, score function, most powerful test, Information Value, Accuracy Ratio.

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  • Dirk Tasche, 2002. "Remarks on the monotonicity of default probabilities," Papers cond-mat/0207555,
  • Handle: RePEc:arx:papers:cond-mat/0207555

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    References listed on IDEAS

    1. Krahnen, Jan Pieter & Weber, Martin, 2001. "Generally accepted rating principles: A primer," Journal of Banking & Finance, Elsevier, vol. 25(1), pages 3-23, January.
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    Cited by:

    1. Dirk Tasche, 2006. "Validation of internal rating systems and PD estimates," Papers physics/0606071,
    2. Raffaella Calabrese, 2011. "Cost-sensitive classification for rare events: an application to the credit rating model validation for SMEs," Working Papers 201134, Geary Institute, University College Dublin.
    3. Raffaella Calabrese, 2012. "Improving Classifier Performance Assessment of Credit Scoring Models," Working Papers 201204, Geary Institute, University College Dublin.
    4. Engelmann, Bernd & Hayden, Evelyn & Tasche, Dirk, 2003. "Measuring the Discriminative Power of Rating Systems," Discussion Paper Series 2: Banking and Financial Studies 2003,01, Deutsche Bundesbank.

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