Quantification of margin of conservatism category C: correlations and quantification levels
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- This paper quantifies margin of conservatism type C for probability of default estimates based on overlapping default rates.
- We study the aggregation of best estimate PDs and MoC C to derive conservative PDs.
- We convert the MoC C at calibration segment level into MoC C at grade level.
Financial institutions are required to incorporate a margin of conservatism of type C (MoC C) for the general estimation error into their probability of default estimates. This paper makes 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 (ie, their long-run average default rates). When overlapping one-year default rates are used, it is crucial to account for temporal dependencies to accurately calculate MoC C. We provide an 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 the calibration segment level, as the standard. However, many financial institutions calculate their long-run average default rates at the calibration segment 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 the calibration segment level. Third, we corroborate that the common practice of using the maximum likelihood estimator of asset correlation on samples with varying probability of default results in a downward bias. We compensate for this downward bias using a simulation approach.
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