PD-2 Modeling the dependence between extreme operational losses and economic covariates: statistical developments, model comparisons and empirical study based on conditional generalized Pareto regression

Postdoc: Julien Hambuckers

In this research project, we focus on modeling the conditional severity distribution of extreme operational losses in the banking industry. Indeed, such a tool would allow banking instutions to have a pro-active management of their operational risks exposure and capital requirements. To this end, we start from the extreme value theory to assume that the conditional severity follows a Generalized Pareto distribution (GDP). Then, we introduce a dependency between the GPD parameters and the covariates. Several statistical problems are therefore faced: how can we model explicitly the link function between the parameters and the covariates in the parametric case? In the nonparametric case, which regression approach should we use to estimate them? How can we escape the curse of dimensionality? How can we adapt usual bandwidth selection strategies in the GPD case? Is it possible to select a conditional threshod parameter? To answer to these questions, we use two particular specifications: either generalized additive models (GAM) or single-index based models, specificaly taylored for GPD. Both approaches have been introduced in Chavez-Demoulin et al. (2015) and Hambuckers et al. (2016). We aim at comparing both approaches and to find solutions to their existing failure: lack of good (cross-validated) bandwidth selection procedure, absence of variable selection procedure, confidence intervals computation, etc. Besides, we use these results to perform a wide empirical study on the determinant of extreme operational losses severity, using a unique database of 40,000 financial losses, provided by the bank UniCredit. We study the effect of 46 different economic variables (GDP growth, unemployment rate, financial ratios, interest rates, risk classes, type of regulation...) on the shape parameter, to determine when we can expect larger losses.