Modeling extreme events: Time-varying extreme tail shape - Bernd Schwaab; Xin Zhang; André Lucas (Sveriges Riksbank, 2020)
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.
Keywords: C22; G11; 330; dynamic tail risk; observation-driven models; extreme value theory; European Central Bank (ECB); Securities Markets Programme (SMP)