Paper: arXiv 2504.01969

Authors: Ana I. C. Pereda

Abstract

This study pioneers the application of the Gai-Kapadia framework, originally developed for interbank contagion, to global equity markets. It offers a novel approach to assess systemic risk and default cascades. Using a 20-asset network (13 Brazilian and 7 developed market assets) from 2015 to 2025, we construct exposure-based networks from price co-movements, applying thresholds theta = 0.3 and theta = 0.5 to capture significant interconnections. Cascade dynamics are evaluated through Monte Carlo simulations (n = 1000) with shocks ranging from 10 to 50 percent, complemented by deterministic propagation analysis. Results show that high clustering among Brazilian assets (Ci approx 1.0) leads to localized contagion, with an average of 2.0 failed assets per simulation. In contrast, developed markets with lower connectivity (Ci approx 0.2 to 0.4) show resilience, with zero failures beyond Brazil in all scenarios. Network visualizations highlight structural vulnerabilities: deterministic cascades reach up to 20 assets at theta = 0.3, but only 3 to 4 at theta = 0.5. Risk measures such as VaR and CVaR at 95 percent confidence confirm higher tail risks in emerging markets. This adaptation of the Gai-Kapadia model provides a robust framework for systemic risk assessment. The findings suggest that regulators should target high-clustering nodes in emerging markets, while portfolio managers may benefit from the resilience of developed markets to enhance diversification.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a interesting application of the Gai-Kapadia interbank network contagion framework to equity markets using daily return correlations, exposures, and stochastic simulations. While the mathematical formulations are straightforward network and risk metrics, the empirical methodology comparing emerging (Brazilian) and developed markets is cleanly structured and well-explained.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess Systemic Risk & Default Cascades in Equity Markets via Gai-Kapadia Model] --> B[Data Input: 20 Global Assets <br/>13 Brazilian & 7 Developed, 2015-2025]
    B --> C[Network Construction: Price Co-movements <br/>Thresholds θ = 0.3 & θ = 0.5]
    C --> D[Simulations & Stress Testing: <br/>Deterministic Cascades & Monte Carlo Shocks 10%-50%]
    D --> E[Risk & Structural Analysis: <br/>Clustering Coefficients, VaR, CVaR at 95%]
    E --> F[Key Outcomes: High EM Contagion Ci≈1.0 vs DM Resilience Ci 0.2-0.4 <br/>Cascade Reach: Up to 20 Assets at θ=0.3 vs 3-4 at θ=0.5]