Paper: arXiv 2309.15511

Authors: Bikramjit Das, Vicky Fasen-Hartmann

Abstract

The stability of a complex financial system may be assessed by measuring risk contagion between various financial institutions with relatively high exposure. We consider a financial network model using a bipartite graph of financial institutions (e.g., banks, investment companies, insurance firms) on one side and financial assets on the other. Following empirical evidence, returns from such risky assets are modeled by heavy-tailed distributions, whereas their joint dependence is characterized by copula models exhibiting a variety of tail dependence behavior. We consider CoVaR, a popular measure of risk contagion and study its asymptotic behavior under broad model assumptions. We further propose the Extreme CoVaR Index (ECI) for capturing the strength of risk contagion between risk entities in such networks, which is particularly useful for models exhibiting asymptotic independence. The results are illustrated by providing precise expressions of CoVaR and ECI when the dependence of the assets is modeled using two well-known multivariate dependence structures: the Gaussian copula and the Marshall-Olkin copula.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents strong theoretical innovation by deriving asymptotic behavior for CoVaR and introducing the Extreme CoVaR Index (ECI) using complex copulas and heavy-tailed network models. However, it relies primarily on analytical derivations and synthetic illustrations rather than robust empirical backtesting on live market data.

Research Flowchart

  flowchart TD
    A[Goal: Measure Risk Contagion in Financial Networks] --> B[Data/Inputs: Bipartite Graph of Institutions & Assets]
    B --> C[Methodology: Model Returns with Heavy Tails & Copula Dependence]
    C --> D[Computational Process: Analyze Asymptotic Behavior of CoVaR]
    D --> E[Outcome 1: Propose Extreme CoVaR Index ECI for Tail Independence]
    D --> F[Outcome 2: Derive Closed-Form Expressions for Gaussian & Marshall-Olkin Copulas]