Market-Informed Networks for Modeling and Forecast Evaluation of Financial Extremes

Paper: arXiv 2609.11575

Authors: Ayla Jungbluth, Johannes Lederer, Simon Trimborn

Abstract

Modeling the joint distribution of extreme values in high-dimensional financial time series is challenging because extremes are sparse and locally extreme observations are not necessarily extreme relative to their full marginal distribution. To address this, we introduce a time-dependent network Hüsler-Reiss model in which market-informed adjacency matrices determine how strongly observations contribute to the estimation. We propose binary and weighted specifications, including the Joint Extremes Adjacency Matrix (JEAM) which combines information about individual extremeness with historical patterns of joint extreme movements. In the forecasting evaluation part, covering one-minute stock returns from three sectors of the S&P 100, JEAM achieves the best out-of-sample log scores for both tail directions; improving scores by 12.5-13.6% in the lower tail and 11.4-14.9% in the upper tail. The results show that incorporating market-informed network structures in the estimation, improves forecast evaluation of extremes across time series.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel time-dependent network Hüsler-Reiss model with market-informed adjacency matrices, demonstrating strong empirical performance in forecasting financial extremes. The mathematical framework is sophisticated, extending existing extreme value theory with network regularization. The empirical validation on high-frequency stock data shows significant improvements in forecast accuracy.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Modeling and Forecast of Financial Extremes] --> B{Key Challenge: Sparse & Locally Extreme Observations};
    B --> C[Methodology: Time-Dependent Network Hüsler-Reiss Model];
    C --> D{Key Innovations: Market-Informed Adjacency Matrices};
    D --> D1(Binary & Weighted Specifications: JEAM);
    D1 --> E[Data Input: One-minute Stock Returns (S&P 100, 3 sectors)];
    E --> F[Computational Process: Out-of-Sample Log Score Evaluation];
    F --> G[Key Outcome: JEAM achieves best out-of-sample log scores];
    G --> G1(Improvements: 12.5-13.6% lower tail, 11.4-14.9% upper tail);
    G1 --> H[Conclusion: Market-informed networks improve forecast evaluation of extremes].

Cited References (93)

1. Statistical Inference for H "u sler-Reiss Graphical Models Through Matrix Completions (2025)
2. Estimation of H "u sler–Reiss distributions and Brown–Resnick processes (2015)
3. Graphical Models for Extremes (2020)
4. Extreme value copula estimation based on block maxima of a multivariate stationary time series (2014)
5. Statistical Analysis of Extreme Values: with Applications to Insurance, Finance, Hydrology and Other Fields (2007)
6. Laws of Small Numbers: Extremes and Rare Events (2011)
7. Maxima of normal random vectors: between independence and complete dependence (1989)
8. The extremes of a triangular array of normal random variables (1996)

0 of 93 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.