Interbank network reconstruction enforcing density and reciprocity

Paper: arXiv 2402.11136

Authors: Valentina Macchiati, Piero Mazzarisi, Diego Garlaschelli

Abstract

Networks of financial exposures are the key propagators of risk and distress among banks, but their empirical structure is not publicly available because of confidentiality. This limitation has triggered the development of methods of network reconstruction from partial, aggregate information. Unfortunately, even the best methods available fail in replicating the number of directed cycles, which on the other hand play a crucial role in determining graph spectra and hence the degree of network stability and systemic risk. Here we address this challenge by exploiting the hypothesis that the statistics of higher-order cycles is strongly constrained by that of the shortest ones, i.e. by the amount of dyads with reciprocated links. First, we provide a detailed analysis of link reciprocity on the e-MID dataset of Italian banks, finding that correlations between reciprocal links systematically increase with the temporal resolution, typically changing from negative to positive around a timescale of up to 50 days. Then, we propose a new network reconstruction method capable of enforcing, only from the knowledge of aggregate interbank assets and liabilities, both a desired sparsity and a desired link reciprocity. We confirm that the addition of reciprocity dramatically improves the prediction of several structural and spectral network properties, including the largest real eigenvalue and the eccentricity of the elliptical distribution of the other eigenvalues in the complex plane. These results illustrate the importance of correctly addressing the temporal resolution and the resulting level of reciprocity in the reconstruction of financial networks.

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 maximum-entropy network reconstruction framework that incorporates link reciprocity and sparsity constraints, significantly improving spectral properties crucial for systemic risk modeling. Empirical validation using the granular e-MID interbank dataset across multiple temporal resolutions provides strong empirical rigor to back the mathematical formulation.

Research Flowchart

  flowchart TD
    A["Research Goal: Reconstruct interbank networks using aggregate data while preserving stability metrics"] --> B["Data Inputs: e-MID dataset & aggregate assets/liabilities"]
    B --> C["Analyze Link Reciprocity: Measure temporal correlations in e-MID interbank exposures"]
    C --> D["Propose Reconstruction Method: Maximize entropy enforcing total density & link reciprocity"]
    D --> E["Spectral & Structural Evaluation: Calculate eigenvalues, cycle counts, and systemic risk metrics"]
    E --> F["Key Outcomes: Temporal scale >50d shows positive reciprocity; matching reciprocity vastly improves graph spectra & risk prediction"]

Cited References (67)

1. A spectral signature of breaking of ensemble equivalence for constrained random graphs (2021)
2. The eigenvalues of random symmetric matrices (1981)
3. Eigenvalue outliers of non-hermitian random matrices with a local tree structure (2016)
4. Linear stability analysis of large dynamical systems on random directed graphs (2020)
5. Spectral theory of sparse non-Hermitian random matrices (2019)
6. Approximating the largest eigenvalue of network adjacency matrices (2007)
7. The organization of the interbank network and how ECB unconventional measures affected the e-MID overnight market (2018)
8. Network analysis of the e-MID overnight money market: the informational value of different aggregation levels for intrinsic dynamic processes (2013)

1 of 67 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.