Understanding the Economic Determinants of the Severity of Operational Losses: A Regularized Generalized Pareto Regression Approach

Abstract

We investigate a novel database of 10,217 extreme operational losses from the Italian bank UniCredit. Our goal is to shed light on the dependence between the severity distribution of these losses and a set of a set of macroeconomic, financial and firmspecific factors. To do so, we use Generalized Pareto regression techniques, where both the scale and shape parameters are assumed to be functions of these explanatory variables. We perform the selection of the relevant covariates with a state-of-the-art penalized-likelihood estimation procedure relying on L 1 -penalty terms. A simulation study indicates that this approach efficiently selects covariates of interest and tackles spurious regression issues encountered when dealing with integrated time series. Lastly, we illustrate the impact of different economic scenarios on the requested capital for operational risk. Our results have important implications in terms of risk management and regulatory policy.

LASSO-type penalization in the framework of generalized additive models for location, scale and shape

“…The second setting uses different numbers of observations since the generalized Pareto is not an easy distribution to model. For example, Hambuckers et al (2018) encountered problems if the number of observations is small. We chose this setup in order to investigate how sensible the estimation of the generalized Pareto model is, if the sample size becomes small.…”

“…Here, we study the same data as in Hambuckers et al (2018). This data set consists of 10,217 extreme operational losses registered by the Italian bank UniCredit, between January 2005 and June 2014.…”

“…An alternative strategy for variable selection, which is mainly designed for linear covariate effects, uses L 1 -type penalties. A first attempt for such a penalization-based, regularized estimation in the high-dimensional GAMLSS framework is proposed in Hambuckers et al (2018). There, only linear effects are considered, so in fact a generalized linear model for location, scale and shape is regarded.…”

“…The conventional least absolute shrinkage and selection operator (LASSO; Tibshirani, 1996) for metric covariates is then applied on Generalized Pareto distributed extreme operational loss data from the Italian bank UniCredit. For the implementation of the estimation procedure, Hambuckers et al (2018) follow Zou and Li (2008) and Oelker and Tutz (2017) and use local quadratic approximations of the penalty terms. Relying on this approximation, the maximization problem can be linearized and solved with usual Newton methods.…”

“…The second data set is a database of 10,217 extreme operational losses from the Italian bank UniCredit, covering a period of 10 years and 7 different event types. These data have recently been analyzed in Hambuckers et al (2018).…”