The estimation error in the Basel II IRB approach: floors to the estimated parameters

Risk measures, like the Value-at-Risk or the Expected Shortfall, are usually dependent on model’s parameters that are unknown and must be estimated. This introduces an additional source of uncertainty that is easily not accounted for. The Prudential Regulation has formally raised the issue of errors stemming from the internal model estimation process in the context of credit risk, calling for margins of conservatism to cover possible underestimation in capital. We investigated the effect of the estimation error in the context of the Internal-Ratings Based (IRB) approach and we also suggested how to introduce the margin of conservativism called by the Regulation. A feature of this approach is that it does not require introducing additional elements in the Asymptotic Single Risk Factor model like prior distributions or other parameters which, having to be estimated, would introduce other sources of estimation error. In this paper we further investigate along the lines suggested above by studying what happens when dealing with low probabilities of default. This in turn leads to study another aspect of the Prudential Regulation which is the setting of floors to the estimated parameters. These floors are heuristically justified by the difficulties to estimate the parameters when the default event becomes rare. Moreover we provide a more robust justification to the floors as well as a framework that would enable to calibrate the floors depending on other parameters.