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

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  • Dirk Tasche

Abstract

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, arXiv.org, revised Mar 2010.
    • Handle: RePEc:arx:papers:0905.3928
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    References listed on IDEAS

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    1. 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.
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    7. 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.
    8. 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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    Cited by:

    1. Dirk Tasche, 2012. "Bounds for rating override rates," Papers 1203.2287, arXiv.org, revised Aug 2012.
    2. Dirk Tasche, 2015. "Fitting a distribution to Value-at-Risk and Expected Shortfall, with an application to covered bonds," Papers 1505.07484, arXiv.org, revised Nov 2015.
    3. Marat Z. Kurbangaleev & Victor A. Lapshin & Zinaida V. Seleznyova, 2018. "Studying The Replicability Of Aggregate External Credit Assessments Using Public Information," HSE Working papers WP BRP 71/FE/2018, National Research University Higher School of Economics.
    4. Wosnitza, Jan Henrik, 2022. "Calibration alternatives to logistic regression and their potential for transferring the dispersion of discriminatory power into uncertainties of probabilities of default," Discussion Papers 04/2022, Deutsche Bundesbank.
    5. Tasche, Dirk, 2013. "Bayesian estimation of probabilities of default for low default portfolios," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 6(3), pages 302-326, July.
    6. Dirk Tasche, 2012. "The art of probability-of-default curve calibration," Papers 1212.3716, arXiv.org, revised Nov 2013.
    7. M. V. Pomazanov, 2022. "Second-order accuracy metrics for scoring models and their practical use," Papers 2204.07989, arXiv.org, revised Nov 2022.
    8. Lukasz Prorokowski, 2016. "Rank-order statistics for validating discriminative power of credit risk models," Bank i Kredyt, Narodowy Bank Polski, vol. 47(3), pages 227-250.

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