Reciprocity in Interbank Markets

Paper: arXiv 2412.10329

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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

Cited References (104)

1. Too big to fail: The hazards of bank bailouts (2004)
2. Stylized facts in money markets: an empirical analysis of the eurozone data (2024) — link
3. Giant strongly connected component of directed networks (2001)
4. Relationship lending in the interbank market and the price of liquidity (2017)
5. Generalized percolation in random directed networks (2005)
6. The asymptotic number of labeled graphs with given degree sequences (1978)
7. Random graphs with arbitrary degree distributions and their applications (2001)
8. A contribution to the mathematical theory of epidemics (1927)

0 of 104 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.