Extreme Value Analysis for Finite, Multivariate and Correlated Systems with Finance as an Example

TL;DR

This paper introduces a practical framework for analyzing the extreme value behavior of finite, correlated multivariate systems, exemplified through high-frequency stock returns, enabling better tail risk estimation in complex systems.

Contribution

It develops a novel approach for multivariate extreme value analysis that accounts for correlations and nonstationarity, applicable to finite systems like financial markets.

Findings

Effective separation of collective effects and idiosyncratic features.

Accurate tail shape estimation for high-frequency stock returns.

Framework accommodates nonstationarity and sectoral analysis.

Abstract

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of correlated time series. We develop our approach for finance as a concrete example but emphasize its generality. We study the extremal behavior of high-frequency stock returns after rotating them into the eigenbasis of the correlation matrix. This separates and extracts various collective effects, including information on the correlated market as a whole and on correlated sectoral behavior from idiosyncratic features, while allowing us to use univariate tools of extreme value analysis. This holds even for high-frequency data where discretization effects normally complicate analysis. We employ a peaks-over-threshold approach and thereby fully avoid the analysis of block maxima. We estimate the tail shape of the rotated returns while explicitly accounting for nonstationarity, a key feature in finance and many other complex systems. Our framework facilitates tail risk estimation relative to larger trends and intraday seasonalities at both market and sectoral levels.