Modeling Extreme Events: Time-Varying Extreme Tail Shape

66 Pages Posted: 5 Mar 2021

See all articles by Bernd Schwaab

Bernd Schwaab

European Central Bank (ECB) - Directorate General Research

Andre Lucas

Vrije Universiteit Amsterdam; Tinbergen Institute

Xin Zhang

Sveriges Riksbank - Research Division

Multiple version iconThere are 2 versions of this paper

Date Written: February 1, 2021

Abstract

We propose a dynamic semi-parametric framework to study time variation in tail parameters. 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 that Eurosystem sovereign bond purchases during the euro area sovereign debt crisis had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

JEL Classification: C22, G11

Suggested Citation

Schwaab, Bernd and Lucas, Andre and Zhang, Xin, Modeling Extreme Events: Time-Varying Extreme Tail Shape (February 1, 2021). ECB Working Paper No. 2021/2524, Available at SSRN: https://ssrn.com/abstract=3797144 or http://dx.doi.org/10.2139/ssrn.3797144

Bernd Schwaab (Contact Author)

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

Kaiserstrasse 29
D-60311 Frankfurt am Main
Germany

Andre Lucas

Vrije Universiteit Amsterdam ( email )

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

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

Xin Zhang

Sveriges Riksbank - Research Division ( email )

S-103 37 Stockholm
Sweden

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