Smooth-Transition Regression Models for Non-Stationary Extremes

We introduce a smooth-transition generalized Pareto (GP) regression model to study the time-varying dependence structure between extreme losses and a set of economic factors. In this model, the distribution of the loss size is approximated by a GP distribution, and its parameters are related to explanatory variables through regression functions, which themselves depend on a time-varying predictor of structural changes. We use this approach to study the dynamics in the monthly severity distribution of operational losses at a major European bank. Using the VIX as a transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past are indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the growth rate of the economy seems to be a relevant predictor of the likelihood of extreme losses.