The Impact of White Noise in PD Estimations on Banks' Capital Requirements According to Basel II

47 Pages Posted: 1 Mar 2007

See all articles by Irmhild Kuehn

Irmhild Kuehn

University of Muenster - Finance Center

Andreas Pfingsten

University of Münster - Finance Center Münster

Date Written: March 12, 2007


Regulation requires banks to hold sufficent capital to cover their risks. Within the new framework commonly labeled Basel II, the Internal Ratings Based Approach (IRBA) allows banks to use their own rating systems to determine how much capital they must set aside for their credit risk. These capital charges are concave functions of the debtors' probabilities of default (PDs). Thus, by using noisy PD estimations in the IRBA, banks arrive at lower expected capital requirements than by using PD estimations with the same mean but a higher accuracy. This effect is the target of our investigation. Firstly, the reduction of capital requirements as such is proven mathematically by making use of second order stochastic dominance. Secondly, their extent is quantified by means of several Monte Carlo simulations. We find that the reduction is quite distinct and banks therefore might have an interest to abstain from improving their existing, likely noisy PD estimators or to even worsen them on purpose by deliberately adding noise. Our study focuses, for analytical convenience, on the incentive to intentionally worsen PD estimations because this enables us to choose a suitable functional form for the noise. However, our findings can easily be interpreted for the case of a bank having some noise in its PD estimations accidentally and not intending to improve them. We also discuss regulatory assessments concerning such modifications of banks' internal rating systems. Obviously, it turns out that PD estimations knowingly modified by the addition of noise are not accepted by supervisors. We therefore review feasible ways for banks to hide such manipulations. Finally, we derive some advice for supervisors on how to detect a possible utilization of this unintended opportunity to save regulatory capital.

Keywords: Banking Supervision, Basel II, IRB Approach, Capital Requirements, Estimation Errors

JEL Classification: C15, G21, G28

Suggested Citation

Kuehn, Irmhild and Pfingsten, Andreas, The Impact of White Noise in PD Estimations on Banks' Capital Requirements According to Basel II (March 12, 2007). Available at SSRN: or

Irmhild Kuehn (Contact Author)

University of Muenster - Finance Center ( email )

Universitätsstr. 14-16
48143 Münster

Andreas Pfingsten

University of Münster - Finance Center Münster ( email )

Universitätsstr. 14-16
Muenster, D-48143

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