Financial networks: reconstruction and stability

The study of complex systems aims to uncover how intricate interactions among components lead to unpredictable emergent phenomena. Stability refers to the system’s ability to maintain functionality and structure despite internal and external disruptions. Such systems are characterized by complex and nonlinear interactions among components, which means that small changes can have amplified effects, making prediction and management of systemic risks challenging. Networks, often represented as graphs, are important tools for depicting and analyzing interactions within complex systems. This PhD thesis focuses on the reconstruction and stability of financial networks, particularly within the interbank market network. Understanding the structure and dynamics of these networks is essential for assessing systemic risks, identifying vulnerabilities, and implementing effective regulatory measures to enhance financial stability. However, network reconstruction is necessary since data on exposures between the financial entities are often unavailable due to confidentiality. To analyze network stability and systemic risk, it is necessary to reconstruct them from the available partial information. Between the reconstruction methods, this PhD thesis is focused on the maximum entropy approach that provides the least biased probability distribution of network configurations compatible with the empirical data. In the case of interbank networks, the so-called Fitness-induced Directed Configuration Model (F-DCM) in interbank networks is state-of-the-art between the probabilistic approaches, requiring only link density and aggregated exposures. Two novel contributions are proposed to better capture the stability properties of empirical networks than F-DCM. The first contribution integrates data from the Bank for International Settlements (BIS) on inter- and intra-country exposure volumes into F-DCM. This integration allows for the replication of country-specific blocks within the network, reflecting intra-country preferential lending in the European interbank network. Building on these networks, an effective contagion model is proposed to simulate liquidity shortages through an epidemic-like mechanism on the interbank network. This model exploits country- and bank-specific risk features to account for heterogeneity in financial institutions. Results indicate that this contagion model can estimate systemic liquidity risk across multiple years and countries. The second contribution aims to improve the reconstruction of spectral properties in empirical networks. Current methods often overlook reciprocity, which affects the reconstructed network’s properties, particularly the adjacency matrix’s spectrum. Given that eigenvalues of adjacency matrices in financial networks significantly impact network stability under financial distress propagation, a new method, the so-called Fitness-induced Global Reciprocity Model (F-GRM), is proposed. This method enforces not only link density but also reciprocity. Results confirm that networks reconstructed with F-GRM closely resemble empirical networks, especially in spectral properties, enhancing the reliability of predicting network stability compared to methods ignoring reciprocity. Additionally, two novel contributions are proposed to advance the assessment of systemic stability, which is essential for managing risk and ensuring the resilience of financial systems. The first contribution involves reconstructability; this concept is introduced and analyzed in the context of homogeneous and heterogeneous nodes’ exposures. Reconstructability occurs when the imposed constraints are, on average, reproduced and remain close to the empirical values in individual realizations. This is because the maximum entropy approach generates an ensemble of possible networks that, on average, fit the imposed empirical data, though individual realizations may differ. Discrepancies between realized and empirical marginals can lead to inaccurate systemic risk estimates, making their assessment essential. Theoretical and empirical results reveal regimes influenced by factors such as the number of nodes and specific characteristics of strength distributions. The second contribution aims to determine the spectral signature of structural changes by analyzing closed walks of any length. Existing methods have been developed to assess whether an empirical network is stationary by analyzing the consistency of its structural evolution with maximum entropy ensembles of graphs. While these analyses have provided valuable early-warning signals of critical events, they focused on dyadic and triadic ’debt loops’ with varying levels of reciprocity, overlooking higher-order structures such as longer cycles. This new approach aims to address this limitation by examining the ensemble properties of the spectral radius in random network models through the analysis of closed walks of any length, thus providing a more comprehensive representation of the spectral signature of structural changes. This PhD thesis aims to enhance reconstruction methodologies by integrating additional public information and addressing crucial network properties, thereby advancing our understanding and management of systemic risks in financial networks.