The measure of model risk in credit capital requirements

TL;DR

This paper quantifies how uncertainty in key parameters affects credit capital requirements, showing that accounting for estimation risk can significantly increase regulatory capital needs by up to 66%.

Contribution

It introduces a method to compute and incorporate estimation risk of default probability and loss-given-default into credit capital regulation.

Findings

Estimation risk can increase capital requirements by 38-66%.

Parameter dependency significantly raises tail risk in capital calculations.

Statistical tests validate the impact of estimation uncertainty on capital estimates.

Abstract

Credit capital requirements in Internal Rating Based approaches require the calibration of two key parameters: the probability of default and the loss-given-default. This letter considers the uncertainty about these two parameters and models this uncertainty in an elementary way: it shows how this estimation risk can be computed and properly taken into account in regulatory capital. We analyse two standard real datasets: one composed by all corporates rated by Moody's and one limited only to the speculative grade ones. We statistically test model hypotheses on both marginal distributions and parameter dependency. We compute the estimation risk impact and observe that parameter dependency raises substantially the tail risk in capital requirements. The results are striking with a required increase in regulatory capital in the range $38\%$-$66\%$.