Paper: arXiv 2411.13384

Authors: Limin Wen, Junxue Li, Tong Pu, Yiying Zhang

Abstract

Conditional risk measures and their associated risk contribution measures are commonly employed in finance and actuarial science for evaluating systemic risk and quantifying the effects of risk interactions. This paper introduces various types of contribution ratio measures based on the MCoVaR, MCoES, and MMME studied in Ortega-Jiménez et al. (2021) and Das & Fasen-Hartmann (2018) to assess the relative effects of a single risk when other risks in a group are in distress. The properties of these contribution risk measures are examined, and sufficient conditions for comparing these measures between two sets of random vectors are established using univariate and multivariate stochastic orders and statistically dependent notions. Numerical examples are presented to validate these conditions. Finally, a real dataset from the cryptocurrency market is used to analyze the spillover effects through our proposed contribution measures.

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 a rigorous mathematical framework extending multivariate conditional risk measures (MCoVaR, MCoES, MMME) using stochastic ordering and copula theory. While it includes an empirical application to cryptocurrency systemic risk, the core contribution remains heavily theoretical with moderate empirical backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Quantify Systemic Risk & Spillover Effects in Cryptocurrencies"] --> B["Methodology:<br>Develop Contribution Ratio Measures based on MCoVaR, MCoES & MMME"]
    B --> C["Theoretical Framework:<br>Analyze Properties & Establish Conditions via Stochastic Orders"]
    C --> D["Validation & Application Inputs:<br>Numerical Simulations & Crypto Market Data"]
    D --> E["Computational Process:<br>Evaluate Risk Contributions & Compare Random Vector Sets"]
    E --> F["Key Outcomes:<br>Validated Risk Formulas & Empirical Insights on Crypto Market Spillover"]

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1 of 85 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.