Variance estimation for the quantification of the margin of conservatism category C

Financial institutions have to add a margin of conservatism of type C (MoC C) to their estimates of probability of default in order to account for the statistical uncertainty involved. European banking supervisors expect MoC C to increase with a decreasing number of observations. In 2023, Casellina, Landini and Uberti determined MoC C of probability of default estimates based on a confidence interval of the long-run average default rate. Although their approach disregards the number of obligors, they conclude that their approach is compliant with the European banking supervisors’ expectations. Our paper makes a twofold contribution to the literature. First, we express the variance of the long-run average default rate as a function of, among other input parameters, the number of obligors. Second, we compare this estimator with two alternative approaches, complying with supervisory expectations, in a simulation experiment. Our simulation results indicate that the newly developed estimator has a lower bias and variance than the other two approaches for a broad set of parameter values. An accurate and efficient estimation of the long-run average default rate’s variance is essential, in particular, for MoC C quantification. Further, internal validation functions and external banking supervisors can employ our estimator in order to challenge the level of MoC C determined by model developers.