Smooth Transition Regression Models for Non-Stationary Extremes

Abstract

We introduce a smooth transition Generalized Pareto (GP) regression model to study the link between extreme losses and the economic context. The advantage of our approach consists in specifying a time-varying dependence structure between financial factors and the severity distribution of the losses. To do so, the parameters of the GP distribution are related to explanatory variables through regression functions which themselves depend on a time-varying predictor of structural changes. We use this technique to study the dynamics in the monthly severity distribution of losses at UniCredit. Using the VIX as transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past is indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the economy’s growth rate seems to be a relevant predictor of the likelihood of extreme losses