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.

翻译：本文构建了一个连续框架来分析金融传染，该框架同时纳入了地理邻近性与银行间网络关联。该框架通过主方程刻画压力传播过程，其解具有Feynman-Kac表示形式，可表述为空间-网络空间中随机路径上的预期累积压力。基于此表示，我推导出一般均衡放大因子——一种衡量系统重要性的结构性指标，用于捕捉局部冲击后系统整体效应与直接效应的比值。该放大因子可自然分解为空间、网络及交互作用分量，从而揭示各机构的系统重要性主要源于何种传导渠道。当违约阈值之上的跳跃强度趋于无穷时，该框架将离散级联模型作为极限情况嵌套其中，表明连续与离散方法描述的是同一现象的不同状态域。基于2008年金融危机与COVID-19疫情期间38家全球银行的实证检验表明：放大因子能准确识别系统重要性机构（放大因子与危机期间股价跌幅的Pearson相关系数$ρ= -0.450$，$p = 0.080$），并具备样本外危机预测能力（COVID-19期间$ρ= -0.352$）。采用与Feynman-Kac积分更直接关联的累计异常收益率进行稳健性分析，进一步强化了上述结论（$ρ= -0.512$，$p = 0.042$）。时序分析证实银行间平均配对相关性可追踪宏观经济压力指标（与VIX指数的相关系数$ρ= 0.265$，$p < 0.001$）。对比两次危机发现，尽管COVID-19期间权益损失较小，但其引发的相关性峰值更为陡峭（+93%），这反映了外生冲击与内生冲击下不同的传染动力学特征。