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From the Fermi–Dirac distribution to PD curves

From the Fermi–Dirac distribution to PD curves In machine learning applications, and in credit risk modeling in particular, model performance is usually measured by using cumulative accuracy profile (CAP) and receiving operating characteristic curves. The purpose of this paper is to use the statistics of the CAP curve to provide a new method for credit PD curves calibration that are not based on arbitrary choices as the ones that are used in the industry.Design/methodology/approachThe author maps CAP curves to a ball–box problem and uses statistical physics techniques to compute the statistics of the CAP curve from which the author derives the shape of PD curves.FindingsThis approach leads to a new type of shape for PD curves that have not been considered in the literature yet, namely, the Fermi–Dirac function which is a two-parameter function depending on the target default rate of the portfolio and the target accuracy ratio of the scoring model. The author shows that this type of PD curve shape is likely to outperform the logistic PD curve that practitioners often use.Practical implicationsThis paper has some practical implications for practitioners in banks. The author shows that the logistic function which is widely used, in particular in the field of retail banking, should be replaced by the Fermi–Dirac function. This has an impact on pricing, the granting policy and risk management.Social implicationsMeasuring credit risk accurately benefits the bank of course and the customers as well. Indeed, granting is based on a fair evaluation of risk, and pricing is done accordingly. Additionally, it provides better tools to supervisors to assess the risk of the bank and the financial system as a whole through the stress testing exercises.Originality/valueThe author suggests that practitioners should stop using logistic PD curves and should adopt the Fermi–Dirac function to improve the accuracy of their credit risk measurement. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Risk Finance Emerald Publishing

From the Fermi–Dirac distribution to PD curves

Brunel, Vivien
The Journal of Risk Finance , Volume 20 (2): 17 – Jul 8, 2019
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References (14)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1526-5943
DOI
10.1108/jrf-01-2018-0009
Publisher site
See Article on Publisher Site

Abstract

In machine learning applications, and in credit risk modeling in particular, model performance is usually measured by using cumulative accuracy profile (CAP) and receiving operating characteristic curves. The purpose of this paper is to use the statistics of the CAP curve to provide a new method for credit PD curves calibration that are not based on arbitrary choices as the ones that are used in the industry.Design/methodology/approachThe author maps CAP curves to a ball–box problem and uses statistical physics techniques to compute the statistics of the CAP curve from which the author derives the shape of PD curves.FindingsThis approach leads to a new type of shape for PD curves that have not been considered in the literature yet, namely, the Fermi–Dirac function which is a two-parameter function depending on the target default rate of the portfolio and the target accuracy ratio of the scoring model. The author shows that this type of PD curve shape is likely to outperform the logistic PD curve that practitioners often use.Practical implicationsThis paper has some practical implications for practitioners in banks. The author shows that the logistic function which is widely used, in particular in the field of retail banking, should be replaced by the Fermi–Dirac function. This has an impact on pricing, the granting policy and risk management.Social implicationsMeasuring credit risk accurately benefits the bank of course and the customers as well. Indeed, granting is based on a fair evaluation of risk, and pricing is done accordingly. Additionally, it provides better tools to supervisors to assess the risk of the bank and the financial system as a whole through the stress testing exercises.Originality/valueThe author suggests that practitioners should stop using logistic PD curves and should adopt the Fermi–Dirac function to improve the accuracy of their credit risk measurement.

Journal

The Journal of Risk Finance – Emerald Publishing

Published: Jul 8, 2019

Keywords: Credit risk; Machine learning; Fermi–Dirac; Logistic function; PD calibration; Scoring

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