Reciprocity in Interbank Markets

ArXiv ID: 2412.10329 “View on arXiv”

Authors: Unknown

Abstract

Weighted reciprocity between two agents can be defined as the minimum of sending and receiving value in their bilateral relationship. In financial networks, such reciprocity characterizes the importance of individual banks as both liquidity absorber and provider, a feature typically attributed to large, intermediating dealer banks. In this paper we develop an exponential random graph model that can account for reciprocal links of each node simultaneously on the topological as well as on the weighted level. We provide an exact expression for the normalizing constant and thus a closed-form solution for the graph probability distribution. Applying this statistical null model to Italian interbank data, we find that before the great financial crisis (i) banks displayed significantly more weighted reciprocity compared to what the lower-order network features (size and volume distributions) would predict (ii) with a disappearance of this deviation once the early periods of the crisis set in, (iii) a trend which can be attributed in particular to smaller banks (dis)engaging in bilateral high-value trading relationships. Moreover, we show that neglecting reciprocal links and weights can lead to spurious findings of triadic relationships. As the hierarchical structure in the network is found to be compatible with its transitive but not with its intransitive triadic sub-graphs, the interbank market seems to be well-characterized by a hierarchical core-periphery structure enhanced by non-hierarchical reciprocal trading relationships.

Keywords: Exponential Random Graph Model, Interbank Networks, Weighted Reciprocity, Network Topology, Systemic Risk, Interbank Lending

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper develops a closed-form exponential random graph model with exact normalizing constants, representing advanced statistical mechanics and graph theory, while applying it to real-world Italian interbank data with detailed empirical analysis.

  flowchart TD
    A["Research Goal<br>Model weighted reciprocity in interbank networks<br>and identify its structural role"] --> B["Methodology<br>Exponential Random Graph Model with weighted reciprocity<br>Exact expression for the normalizing constant"]
    B --> C["Data Input<br>Italian interbank data pre- and during<br>the Great Financial Crisis"]
    C --> D["Computational Process<br>Apply statistical null model to network topology,<br>weights, and triadic structures"]
    D --> E["Key Findings & Outcomes"]
    
    subgraph E [" "]
        F["Pre-crisis: Significantly higher weighted reciprocity<br>than predicted by size/volume"]
        G["Crisis onset: Reciprocity deviation disappears,<br>driven by smaller banks disengaging"]
        H["Hierarchical core-periphery structure<br>enhanced by non-hierarchical reciprocal links"]
    end
    
    E --> I["Implication<br>Neglecting reciprocity/weights<br>leads to spurious triadic findings"]
    
    style A fill:#e1f5e1
    style B fill:#fff3e0
    style C fill:#e3f2fd
    style D fill:#f3e5f5
    style E fill:#fce4ec
    style I fill:#fff9c4