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Estimating discriminatory power and PD curves when the number of defaults is small


  • Dirk Tasche


The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory power. In the second phase of the approach, the raw PD curve is calibrated to fit a target unconditional PD. The concepts and techniques presented include a discussion of different definitions of area under the curve (AUC) and accuracy ratio (AR), a simulation study on the performance of confidence interval estimators for AUC, a discussion of the one-parametric approach to the estimation of PD curves by van der Burgt (2008) and alternative approaches, as well as a simulation study on the performance of the presented PD curve estimators. The topics are treated in depth in order to provide the full rationale behind them and to produce results that can be implemented immediately.

Suggested Citation

  • Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928,, revised Mar 2010.
  • Handle: RePEc:arx:papers:0905.3928

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    References listed on IDEAS

    1. Stephen Satchel & Wei Xia, 2006. "Analytic Models of the ROC Curve: Applications to Credit Rating Model Validation," Research Paper Series 181, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, March.
    3. Roger Newson, 2006. "Confidence intervals for rank statistics: Percentile slopes, differences, and ratios," Stata Journal, StataCorp LP, vol. 6(4), pages 497-520, December.
    4. Roger Newson, 2002. "Parameters behind "nonparametric" statistics: Kendall's tau,Somers' D and median differences," Stata Journal, StataCorp LP, vol. 2(1), pages 45-64, February.
    5. Roger Newson, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 309-334, September.
    6. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036, March.
    7. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
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    Cited by:

    1. Dirk Tasche, 2011. "Bayesian estimation of probabilities of default for low default portfolios," Papers 1112.5550,, revised Aug 2013.
    2. Dirk Tasche, 2012. "Bounds for rating override rates," Papers 1203.2287,, revised Aug 2012.
    3. Dirk Tasche, 2012. "The art of probability-of-default curve calibration," Papers 1212.3716,, revised Nov 2013.

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