Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Focus Session: Large Deviations and Rare Events II

DY 15.10: Talk

Monday, March 9, 2026, 17:45–18:00, ZEU/0114

Extreme Value Analysis for Finite, Multivariate and Correlated Systems with Finance as an Example — •Benjamin Köhler, Anton J Heckens, and Thomas Guhr — Universität Duisburg-Essen, Germany

Extreme values and the tail behaviour of probability distributions are essential for quantifying and mitigating risk in complex environmental and socio-economic systems. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for truly infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of time series.
We study the extremal behavior of high-frequency stock returns after rotating them into the eigenbasis of the correlation matrix. This separates information on the market as a whole and on sectoral behavior while allowing us to use univariate tools of extreme value analysis, even for high-frequency data where discretization effects normally complicate analysis.
Using a Peaks–over–threshold approach, we estimate the tail shape of the rotated returns while explicitly accounting for non-stationarity, a key feature in finance and many other complex systems. Our framework allows for tail risk estimation relative to larger trends and intraday seasonalities at both market and sectoral levels.

Keywords: Extreme Events; Economics; Financial Markets; Risk Management; Nonstationarity