Modeling the dependence between extreme operational losses and economic factors: a conditional semi-parametric Generalized Pareto approach

In this paper, we model the severity distribution of operational losses data, condi-
tional on some covariates. Indeed, previous studies [Chernobai et al., 2011, Cope et al.,
2012, Chavez-Demoulin et al., 2014a] suggest that this distribution might be in uenced
by macroeconomic and rm-speci c factors. We introduce a conditional Generalized
Pareto model, where the shape parameter is an unknown function of a linear combina-
tion 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 su er neither from too strong parametric assumption nor from the curse of dimen-
sionality. Then, we develop an iterative approach to estimate this model, based on the
maximisation of a semiparametric likelihood function. Finally, we apply this method-
ology on a novel database provided by the bank UniCredit. We use rm-speci c factors
to estimate the conditional shape parameter of the severity distribution. Our analysis
suggests that the leverage ratio of the company, the proportion of the revenue coming
from fees as well as the risk category have an important impact on the tail thickness
of this distribution and thus on the probability of su ering from large operational losses.