Financial Networks

A Heterogeneous Spatiotemporal GARCH Model: A Predictive Framework for Volatility in Financial Networks ArXiv ID: 2508.20101 “View on arXiv” Authors: Atika Aouri, Philipp Otto Abstract We introduce a heterogeneous spatiotemporal GARCH model for geostatistical data or processes on networks, e.g., for modelling and predicting financial return volatility across firms in a latent spatial framework. The model combines classical GARCH(p, q) dynamics with spatially correlated innovations and spatially varying parameters, estimated using local likelihood methods. Spatial dependence is introduced through a geostatistical covariance structure on the innovation process, capturing contemporaneous cross-sectional correlation. This dependence propagates into the volatility dynamics via the recursive GARCH structure, allowing the model to reflect spatial spillovers and contagion effects in a parsimonious and interpretable way. In addition, this modelling framework allows for spatial volatility predictions at unobserved locations. In an empirical application, we demonstrate how the model can be applied to financial stock networks. Unlike other spatial GARCH models, our framework does not rely on a fixed adjacency matrix; instead, spatial proximity is defined in a proxy space constructed from balance sheet characteristics. Using daily log returns of 50 publicly listed firms over a one-year period, we evaluate the model’s predictive performance in a cross-validation study. ...

Detecting Fraud in Financial Networks: A Semi-Supervised GNN Approach with Granger-Causal Explanations ArXiv ID: 2507.01980 “View on arXiv” Authors: Linh Nguyen, Marcel Boersma, Erman Acar Abstract Fraudulent activity in the financial industry costs billions annually. Detecting fraud, therefore, is an essential yet technically challenging task that requires carefully analyzing large volumes of data. While machine learning (ML) approaches seem like a viable solution, applying them successfully is not so easy due to two main challenges: (1) the sparsely labeled data, which makes the training of such approaches challenging (with inherent labeling costs), and (2) lack of explainability for the flagged items posed by the opacity of ML models, that is often required by business regulations. This article proposes SAGE-FIN, a semi-supervised graph neural network (GNN) based approach with Granger causal explanations for Financial Interaction Networks. SAGE-FIN learns to flag fraudulent items based on weakly labeled (or unlabelled) data points. To adhere to regulatory requirements, the flagged items are explained by highlighting related items in the network using Granger causality. We empirically validate the favorable performance of SAGE-FIN on a real-world dataset, Bipartite Edge-And-Node Attributed financial network (Elliptic++), with Granger-causal explanations for the identified fraudulent items without any prior assumption on the network structure. ...

Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks ArXiv ID: 2503.15534 “View on arXiv” Authors: Unknown Abstract The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies. ...

Analyzing Communicability and Connectivity in the Indian Stock Market During Crises ArXiv ID: 2502.08242 “View on arXiv” Authors: Unknown Abstract Understanding how information flows through the financial networks is important, especially during times of market turbulence. Unlike traditional assumptions where information travels along the shortest paths, real-world diffusion processes often follow multiple routes. To capture this complexity, we apply communicability, a network measure that quantifies the ease of information flow between nodes, even beyond the shortest path. In this study, we aim to examine how communicability responds to structural disruptions in financial networks during periods of high volatility. We compute communicability-based metrics on correlation-derived networks constructed from financial market data, and apply statistical testing through permutation methods to identify significant shifts in network structure. Our results show that approximately 70% and 80% of stock pairs exhibit statistically significant changes in communicability during the global financial crisis and the unprecedented COVID-19 crisis, respectively, at a significance level of 0.001. The observed shifts in shortest communicability path lengths offer directional cues about the nature and depth of each crisis. Furthermore, when used as features in machine learning classification models, communicability measures outperform the shortest-path-based measures in distinguishing between market stability and volatility periods. The performance of geometric measures was also comparable to that of topology-based measures. These findings offer valuable insights into the dynamic behavior of financial markets during times of crises and underscore the practical relevance of communicability in modeling systemic risk and information diffusion in complex networks. ...

Graph Neural Networks for Financial Fraud Detection: A Review ArXiv ID: 2411.05815 “View on arXiv” Authors: Unknown Abstract The landscape of financial transactions has grown increasingly complex due to the expansion of global economic integration and advancements in information technology. This complexity poses greater challenges in detecting and managing financial fraud. This review explores the role of Graph Neural Networks (GNNs) in addressing these challenges by proposing a unified framework that categorizes existing GNN methodologies applied to financial fraud detection. Specifically, by examining a series of detailed research questions, this review delves into the suitability of GNNs for financial fraud detection, their deployment in real-world scenarios, and the design considerations that enhance their effectiveness. This review reveals that GNNs are exceptionally adept at capturing complex relational patterns and dynamics within financial networks, significantly outperforming traditional fraud detection methods. Unlike previous surveys that often overlook the specific potentials of GNNs or address them only superficially, our review provides a comprehensive, structured analysis, distinctly focusing on the multifaceted applications and deployments of GNNs in financial fraud detection. This review not only highlights the potential of GNNs to improve fraud detection mechanisms but also identifies current gaps and outlines future research directions to enhance their deployment in financial systems. Through a structured review of over 100 studies, this review paper contributes to the understanding of GNN applications in financial fraud detection, offering insights into their adaptability and potential integration strategies. ...

Robust Graph Neural Networks for Stability Analysis in Dynamic Networks ArXiv ID: 2411.11848 “View on arXiv” Authors: Unknown Abstract In the current context of accelerated globalization and digitalization, the complexity and uncertainty of financial markets are increasing, and the identification and prevention of economic risks have become a key link in maintaining the stability of the financial system. Traditional risk identification methods often have limitations because they are difficult to cope with the multi-level and dynamically changing complex relationships in financial networks. With the rapid development of financial technology, graph neural network (GNN) technology, as an emerging deep learning method, has gradually shown great potential in the field of financial risk management. GNN can map transaction behaviors, financial institutions, individuals, and their interactive relationships in financial networks into graph structures, and effectively capture potential patterns and abnormal signals in financial data through embedded representation learning. Using this technology, financial institutions can extract valuable information from complex transaction networks, identify hidden dangers or abnormal behaviors that may cause systemic risks in a timely manner, optimize decision-making processes, and improve the accuracy of risk warnings. This paper explores the economic risk identification algorithm based on the GNN algorithm, aiming to provide financial institutions and regulators with more intelligent technical tools to help maintain the security and stability of the financial market. Improving the efficiency of economic risk identification through innovative technical means is expected to further enhance the risk resistance of the financial system and lay the foundation for building a robust global financial system. ...

Computing Systemic Risk Measures with Graph Neural Networks ArXiv ID: 2410.07222 “View on arXiv” Authors: Unknown Abstract This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph structured data. In particular, we focus on an aggregation function that is derived from a market clearing algorithm proposed by Eisenberg and Noe (2001). In this setting, we show the existence of an optimal random allocation that distributes the overall minimal bailout capital and secures the network. We study numerical methods for the approximation of systemic risk and optimal random allocations. We propose to use permutation equivariant architectures of neural networks like graph neural networks (GNNs) and a class that we name (extended) permutation equivariant neural networks ((X)PENNs). We compare their performance to several benchmark allocations. The main feature of GNNs and (X)PENNs is that they are permutation equivariant with respect to the underlying graph data. In numerical experiments we find evidence that these permutation equivariant methods are superior to other approaches. ...

Causal Hierarchy in the Financial Market Network – Uncovered by the Helmholtz-Hodge-Kodaira Decomposition ArXiv ID: 2408.12839 “View on arXiv” Authors: Unknown Abstract Granger causality can uncover the cause and effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into a rotational and gradient component which reveals the hierarchy of Granger causality flow. Using Kenneth French’s business sector return time series, it is revealed that during the Covid crisis, precious metals and pharmaceutical products are causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during crisis which means that the research presented here can be especially useful to better understand crises in the market by revealing the dominant drivers of the crisis dynamics. ...

Complex network analysis of cryptocurrency market during crashes ArXiv ID: 2405.05642 “View on arXiv” Authors: Unknown Abstract This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is carried out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation based complex network analysis is carried out to study the crashes. Degree density ($ρ_D$), average path length ($\bar{“l”}$), and average clustering coefficient ($\overline{“cc”}$) are estimated from these networks. We find that both $ρ_D$ and $\overline{“cc”}$ are smallest during the pre-crash period, and spike during the crash suggesting the network is dense during a crash. Although $ρ_D$ and $\overline{“cc”}$ decrease in the post-crash period, they remain higher than pre-crash levels for the 2017-18 and 2018-19 crashes suggesting a market attempt to return to normalcy. We get $\bar{“l”}$ is minimal during the crash period, suggesting a rapid flow of information. A dense network and rapid information flow suggest that during a crash uninformed synchronized panic sell-off happens. However, during the 2019-20 crash, the values of $ρ_D$, $\overline{“cc”}$, and $\bar{“l”}$ did not vary significantly, indicating minimal change in dynamics compared to other crashes. The findings of this study may guide investors in making decisions during market crashes. ...

A novel portfolio construction strategy based on the core-periphery profile of stocks ArXiv ID: 2405.12993 “View on arXiv” Authors: Unknown Abstract This paper highlights the significance of mesoscale structures, particularly the core-periphery structure, in financial networks for portfolio optimization. We build portfolios of stocks belonging to the periphery part of the Planar maximally filtered subgraphs of the underlying network of stocks created from Pearson correlations between pairs of stocks and compare its performance with some well-known strategies of Pozzi et. al. hinging around the local indices of centrality in terms of the Sharpe ratio, returns and standard deviation. Our findings reveal that these portfolios consistently outperform traditional strategies and further the core-periphery profile obtained is statistically significant across time periods. These empirical findings substantiate the efficacy of using the core-periphery profile of the stock market network for both inter-day and intraday trading and provide valuable insights for investors seeking better returns. ...