Basel II Capital Requirement Sensitivity to the Definition of Default
24 Pages Posted: 29 Sep 2008 Last revised: 14 Jun 2016
Date Written: September 26, 2008
The paper is motivated by a disturbing observation according to which the outcome of the regulatory formula significantly depends on the definition of default used to measure the probability of default (PD) and the loss given default (LGD) parameters. Basel II regulatory capital should estimate with certain probability level unexpected credit losses on banking portfolios and so it should not depend on a particular definition of default that does not change real historical and expected losses. We provide an explanation of the phenomenon based on the Merton default model and test it using a Monte Carlo simulation. Moreover we shall develop an analytical method to model LGD unexpected risk and to combine it with the PD unexpected risk. The developed formula and in particular its simplified version could be used to improve the current regulatory formula. The analysis at the same time provides a different insight into the issue of regulatory capital sensitivity on the definition of default. Finally we perform a structural model based simulation to test the hypothesis according to which scoring functions developed with a soft definition of default provide weaker predictive power than the ones developed with a hard definition of default.
Keywords: credit risk, correlation, recovery rate, regulatory capital
JEL Classification: G21, G28, C14
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