Why PD curves calibrated from scoring models should have a Fermi-Dirac shape?

Scoring model performance measurement is usualy achieved by using CAP and ROC curves. We map CAP curves to a ball-box problem and we use statistical physics techniques to compute the number of CAP curves that correspond to a... [ view full abstract ]

Scoring model performance measurement is usualy achieved by using CAP and ROC curves. We map CAP curves to a ball-box problem and we use statistical physics techniques to compute the number of CAP curves that correspond to a given accuracy ratio. We derive the probability of default curve for a scoring model as a function of the portfolio target default rate and the target accuracy ratio of the scoring model, without any additional arbitrary choice. We show that practitioners should stop using logistic PD curves and should adopt the Fermi-Dirac function to improve the accuracy of their credit risk measurement.