Paper: arXiv 2405.07549

Authors: Tong Pu, Yifei Zhang, Yiying Zhang

Abstract

Systemic risk is the risk that a company- or industry-level risk could trigger a huge collapse of another or even the whole institution. Various systemic risk measures have been proposed in the literature to quantify the domino and (relative) spillover effects induced by systemic risks such as the well-known CoVaR, CoES, MES and CoD risk measures, and associated contribution measures. This paper proposes another new type of systemic risk measure, called the joint marginal expected shortfall (JMES), to measure whether the MES of one entity’s risk-taking adds to another one or the overall risk conditioned on the event that the entity is already in some specified distress level. We further introduce two useful systemic risk contribution measures based on the difference function or relative ratio function of the JMES and the conventional ES, respectively. Some basic properties of these proposed measures are studied such as monotonicity, comonotonic additivity, non-identifiability and non-elicitability. For both risk measures and two different vectors of bivariate risks, we establish sufficient conditions imposed on copula structure, stress levels, and stochastic orders to compare these new measures. We further provide some numerical examples to illustrate our main findings. A real application in analyzing the risk contagion among several stock market indices is implemented to show the performances of our proposed measures compared with other commonly used measures including CoVaR, CoES, MES, and their associated contribution measures.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sound systemic risk measure (JMES) with detailed theoretical properties, copula dependency analyses, and stochastic ordering proofs. It includes both numerical simulations and an empirical application comparing the measure to CoVaR and MES on stock index data.

Research Flowchart

  flowchart TD
    A["Research Goal: Propose Joint Marginal Expected Shortfall (JMES) & Contribution Measures"] --> B["Theoretical Framework: Formulate JMES using Copulas & Stochastic Orders"]
    B --> C["Property Analysis: Prove Monotonicity, Non-elicitability & Non-identifiability"]
    C --> D["Empirical Inputs: Financial Stock Market Indices & Bivariate Risk Vectors"]
    D --> E["Comparative Analysis: Evaluate JMES vs. CoVaR, CoES, and MES"]
    E --> F["Key Outcomes: Proven efficacy in capturing risk contagion & systemic spillover effects"]

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