Paper: arXiv 2407.14272

Authors: Paolo Bartesaghi, Fernando Diaz-Diaz, Rosanna Grassi, Pierpaolo Uberti

Abstract

The global balance index is used in the network literature to quantify how balanced a signed network is. In this paper we show that the global balance index of financial correlation networks can be used as a systemic risk measure. We define the global balance index of a network starting from a diffusive process that describes how the information spreads across nodes in a network, providing an alternative derivation to the usual combinatorial one. The steady state of this process is the solution of a linear system governed by the exponential of the replication matrix of the process. We provide a bridge between the numerical stability of this linear system, measured by the condition number in an opportune norm, and the structural predictability of the underlying signed network. The link between the condition number and related systemic risk measures, such as the market rank indicators, allows the global balance index to be interpreted as a new systemic risk measure. A comprehensive empirical application to real financial data finally confirms that the global balance index of financial correlation networks represents a valuable and effective systemic risk indicator.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by linking signed network structural balance and diffusion dynamics to condition numbers and systemic risk measures. It backs up this novel algebraic framework with an empirical evaluation on real financial market return data.

Research Flowchart

  flowchart TD
    A[Goal: Evaluate Global Balance Index as a Systemic Risk Measure] --> B[Input: Cross-Asset Financial Correlation Data]
    B --> C[Model Diffusive Process on Signed Networks]
    C --> D[Solve Linear System via Replication Matrix Exponential]
    D --> E[Link Condition Number to Structural Predictability & Market Rank]
    E --> F[Outcome: Global Balance Index Validated as Systemic Risk Indicator]

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0 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.