Paper: arXiv 2510.24775

Authors: Tatsuru Kikuchi

Abstract

This paper develops a continuous framework for analyzing financial contagion that incorporates both geographic proximity and interbank network linkages. The framework characterizes stress propagation through a master equation whose solution admits a Feynman-Kac representation as expected cumulative stress along stochastic paths through spatial-network space. From this representation, I derive the General Equilibrium Amplification Factor – a structural measure of systemic importance that captures the ratio of total system-wide effects to direct effects following a localized shock. The amplification factor decomposes naturally into spatial, network, and interaction components, revealing which transmission channels contribute most to each institution’s systemic importance. The framework nests discrete cascade models as a limiting case when jump intensity becomes infinite above default thresholds, clarifying that continuous and discrete approaches describe different regimes of the same phenomenon. Empirical validation using 38 global banks across the 2008 financial crisis and COVID-19 pandemic demonstrates that the amplification factor correctly identifies systemically important institutions (Pearson correlation $ρ= -0.450$, $p = 0.080$ between amplification factor and crisis drawdowns) and predicts crisis outcomes out-of-sample ($ρ= -0.352$ for COVID-19). Robustness analysis using cumulative abnormal returns – a measure more directly connected to the Feynman-Kac integral – strengthens these findings ($ρ= -0.512$, $p = 0.042$). Time-series analysis confirms that average pairwise bank correlations track macroeconomic stress indicators ($ρ= 0.265$ with VIX, $p < 0.001$). Comparing the two crises reveals that COVID-19 produced a sharper correlation spike (+93%) despite smaller equity losses, reflecting different contagion dynamics for exogenous versus endogenous shocks.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel continuous theoretical framework for financial contagion by mapping stress propagation to a Feynman-Kac representation and master equations. It balances this heavy mathematical machinery with empirical validation on 38 global banks across both the 2008 GFC and COVID-19 crises, though empirical reproducibility is constrained by proprietary/detailed network data access.

Research Flowchart

  flowchart TD
    A["Research Goal: Quantify systemic risk & financial contagion via GE Amplification Factor"] --> B["Inputs: Data on 38 global banks<br/>(2008 GFC & 2009 COVID-19, VIX, Equity Returns)"]
    B --> C["Methodology: Continuous framework combining spatial proximity & interbank networks"]
    C --> D["Process: Derive Master Equation & Feynman-Kac path-integral representation"]
    D --> E["Decomposition: Isolate GE Amplification Factor into Spatial, Network & Interaction channels"]
    E --> F["Validation: Predict crisis outcomes & track macro stress<br/>(CAR correlation ρ = -0.512, VIX correlation ρ = 0.265)"]
    F --> G["Key Finding: Identifies SIFIs out-of-sample & shows COVID-19 had higher correlation spike (+93%) than GFC"]