Joint extreme Value-at-Risk and Expected Shortfall dynamics with a single integrated tail shape parameter

Enzo D'Innocenzo, Andre Lucas, Bernd Schwaab and Xin Zhang
Additional contact information
Enzo D'Innocenzo: University of Bologna
Bernd Schwaab: European Central Bank
Xin Zhang: Sveriges Riksbank

No 24-069/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: dynamic tail risk; integrated score-driven models; extreme value theory (search for similar items in EconPapers)
JEL-codes: C22 G11 (search for similar items in EconPapers)
Date: 2024-11-08
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://papers.tinbergen.nl/24069.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20240069

Access Statistics for this paper

More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Bibliographic data for series maintained by Tinbergen Office +31 (0)10-4088900 ().