Smooth Transition Regression Models for Non-Stationary Extremes

43 Pages Posted: 16 Mar 2020 Last revised: 19 Jan 2021

See all articles by Julien Hambuckers

Julien Hambuckers

University of Liège - HEC Liège

T. Kneib

University of Goettingen (Göttingen)

Date Written: February 20, 2020


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

Keywords: Extreme value theory, generalized Pareto distribution, operational risk, VIX

JEL Classification: C24, C46, C58, G21

Suggested Citation

Hambuckers, Julien and Kneib, T., Smooth Transition Regression Models for Non-Stationary Extremes (February 20, 2020). Available at SSRN: or

Julien Hambuckers (Contact Author)

University of Liège - HEC Liège ( email )

rue Louvrex 14
Liège, 4000

T. Kneib

University of Goettingen (Göttingen)

Platz der Gottinger Sieben 3
Gottingen, D-37073

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