Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2024-11-08
Number: 24-069/III
Author-Name: Enzo D'Innocenzo
Author-Workplace-Name: University of Bologna
Author-Name: Andre Lucas
Author-Workplace-Name: Vrije Universiteit Amsterdam and Tinbergen Institute
Author-Name: Bernd Schwaab
Author-Workplace-Name: European Central Bank
Author-Name: Xin Zhang
Author-Workplace-Name: Sveriges Riksbank
Title: Joint extreme Value-at-Risk and Expected Shortfall dynamics with a single integrated tail shape parameter
Abstract: We propose a robust semi-parametric framework for persistent time-varying extreme tail behavior, including extreme Value-at-Risk (VaR) and Expected Shortfall (ES). The framework builds on Extreme Value Theory and uses a conditional version of the Generalized Pareto Distribution (GPD) for peaks-over-threshold (POT) dynamics. Unlike earlier approaches, our model (i) has unit root-like, i.e., integrated autoregressive dynamics for the GPD tail shape, and (ii) re-scales POTs by their thresholds to obtain a more parsimonious model with only one time-varying parameter to describe the entire tail. We establish parameter regions for stationarity, ergodicity, and invertibility for the integrated time-varying parameter model and its filter, and formulate conditions for consistency and asymptotic normality of the maximum likelihood estimator. Using four exchange rate series, we illustrate how the new model captures the dynamics of extreme VaR and ES.
Classification-JEL: C22, G11
Keywords: dynamic tail risk, integrated score-driven models, extreme value theory
File-URL: https://papers.tinbergen.nl/24069.pdf
File-Format: application/pdf
File-Size: 15.960.685 bytes
Handle: RePEc:tin:wpaper:20240069