Modeling Extreme Events: Time-Varying Extreme Tail Shape

Tinbergen Institute Discussion Paper 2020-076/III

63 Pages Posted: 4 Jan 2021

See all articles by Bernd Schwaab

Bernd Schwaab

European Central Bank (ECB) - Directorate General Research

Xin Zhang

Sveriges Riksbank - Research Division; BIS Innovation Hub

Andre Lucas

Vrije Universiteit Amsterdam; Tinbergen Institute

Multiple version iconThere are 2 versions of this paper

Date Written: November 10, 2020


A dynamic semi-parametric framework is proposed to study time variation in tail fatness of sovereign bond yield changes during the 2010--2012 euro area sovereign debt crisis measured at a high (15-minute) frequency. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail shape parameters. The score-driven updates used improve the expected Kullback-Leibler divergence between the model and the true data generating process on every step even if the GPD only fits approximately and the model is mis-specified, as will be the case in any finite sample. This is confirmed in simulations. Using the model, we find the ECB program had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

Keywords: Dynamic Tail Risk, Observation-Driven Models, Extreme Value Theory, European Central Bank (ECB), Securities Markets Programme (SMP)

JEL Classification: C22, G11

Suggested Citation

Schwaab, Bernd and Zhang, Xin (Kelvin) and Lucas, Andre, Modeling Extreme Events: Time-Varying Extreme Tail Shape (November 10, 2020). Tinbergen Institute Discussion Paper 2020-076/III, Available at SSRN: or

Bernd Schwaab (Contact Author)

European Central Bank (ECB) - Directorate General Research ( email )

Kaiserstrasse 29
D-60311 Frankfurt am Main

Xin (Kelvin) Zhang

Sveriges Riksbank - Research Division ( email )

S-103 37 Stockholm

BIS Innovation Hub

Mäster Samuelsgatan 36
Stockholm, 111 57

Andre Lucas

Vrije Universiteit Amsterdam ( email )

SBE/EDS, De Boelelaan 1105
Amsterdam, 1081 HV
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)


Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB


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