Paper: arXiv 2504.19953

Authors: Jinghui Chen, Edward Furman, X. Sheldon Lin

Abstract

Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007–2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and best-case bounds for the marginal expected shortfall (MES) – a key measure of systemic risk contribution – under the assumption that individual firms’ risk distributions are known but their dependence structure is not. We further derive tighter MES bounds when partial information on companies’ risk exposures, and thus their dependence, is available. To represent this partial information, we employ three standard factor models: additive, minimum-based, and multiplicative background risk models. Additionally, we propose an alternative set of improved MES bounds based on a linear relationship between firm-specific and market-wide risks, consistent with the Capital Asset Pricing Model in finance and the Weighted Insurance Pricing Model in insurance. Finally, empirical analyses demonstrate the practical relevance of the theoretical bounds for industry practitioners and policymakers.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides rigorous mathematical derivations for sharp upper and lower bounds of Marginal Expected Shortfall (MES) under dependence uncertainty, using factor models and CAPM/WIPM assumptions. It complements the strong theoretical groundwork with an empirical application on S&P 500 stock data using the Fama-French five-factor model and proposes a novel Systemic Risk Criticality Index.

Research Flowchart

  flowchart TD
    A["Research Goal: Bounds for Marginal Expected Shortfall (MES) Under Dependence Uncertainty"] --> B["Inputs: Individual Risk Distributions & Market Data"]
    B --> C["Derive Unconstrained Worst/Best-Case MES Bounds"]
    B --> D["Incorporate Partial Dependence Info<br>(Factor Models & Linear CAPM/WIPM)"]
    C & D --> E["Empirical Validation on Equity Data"]
    E --> F["Key Outcomes: Robust MES Risk Bounds for Practitioners & Policymakers"]