Quantification of margin of conservatism category C: Correlations and quantification levels

Financial institutions are required to incorporate a margin of conservatism for the general estimation error (MoC C) into their probability of default (PD) estimates. This paper presents three key contributions to the quantification of MoC C. First, the European banking regulation allows financial institutions to choose between overlapping and nonoverlapping one-year default rates for calculating their calibration targets, i.e., their long run average default rates (LRADRs). When overlapping one-year default rates are used, it is crucial to account for temporal dependencies to accurately calculate MoC C. We provide a MoC C quantification for overlapping one-year default rates. Second, the European Central Bank has established MoC C quantification at grade level rather than at calibration segment level as the standard. However, many financial institutions calculate their LRADRs at calibration segment level rather than at grade level. Therefore, we approximate the confidence level for MoC C quantification at grade level to achieve the same sum of risk weighted exposure amounts as the MoC C at calibration segment level. Third, we corroborate that the common practice of using the maximum likelihood estimator of asset correlation on samples with varying PDs results in a downward bias. We compensate for this downward bias using a simulation approach.