Modeling Extreme Events: Time-Varying Extreme Tail Shape
Tinbergen Institute Discussion Paper 2020-076/III
63 Pages Posted: 4 Jan 2021
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: Suggested Citation