Modeling the Dependence between Extreme Operational Losses and Economic Factors: A Conditional Semi-Parametric Generalized Pareto Approach

We model the severity distribution of operational loss data, conditionally to some covariates. Indeed, previous studies suggest that this distribution might be influenced by firm-specific factors. We introduce a conditional Generalized Pareto model for the tail of the severity distribution, where the shape parameter is an unknown function of a linear combination of the covariates. More precisely, we rely on a single-index assumption to perform a dimension reduction that enables to use univariate nonparametric techniques. Hence, we suffer neither from too strong parametric assumption nor from the curse of dimensionality. We apply this methodology on a novel database provided by the bank UniCredit. We use firm-specific factors to estimate the conditional shape parameter. Our analysis suggests that the leverage ratio of the company and the proportion of the revenue coming from fees have an important impact on the probability of suffering from large operational losses.