Paper: arXiv 2509.21904

Authors: Yuhong Xu, Xinyao Zhao

Abstract

We propose a general CoVaR framework that extends the traditional CoVaR by incorporating diverse expert views and information, such as asset moment characteristics, quantile insights, and perspectives on the relative loss distribution between two assets. To integrate these expert views effectively while minimizing deviations from the prior distribution, we employ the entropy pooling method to derive the posterior distribution, which in turn enables us to compute the general CoVaR. Assuming bivariate normal distributions, we derive its analytical expressions under various perspectives. Sensitivity analysis reveals that CoVaR exhibits a linear relationship with both the expectations of the variables in the views and the differences in expectations between them. In contrast, CoVaR shows nonlinear dependencies with respect to the variance, quantiles, and correlation within these views. Empirical analysis of the US banking system during the Federal Reserve’s interest rate hikes demonstrates the effectiveness of the general CoVaR when expert views are appropriately specified. Furthermore, we extend this framework to a general $Δ$CoVaR, which allows for the assessment of risk spillover effects from various perspectives.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative extension of the CoVaR systemic risk metric by integrating Meucci’s Entropy Pooling to incorporate general expert views. It strikes a good balance between analytical derivations (under bivariate normal assumptions) and an empirical application to the US banking sector during interest rate hike cycles.

Research Flowchart

  flowchart TD
    A["Research Goal: Develop a General CoVaR Framework<br>incorporating diverse expert views for systemic risk"] --> B["Inputs: Prior Distributions & Expert Views<br>(Asset moments, quantiles, relative loss views)"]
    B --> C["Methodology: Entropy Pooling"]
    C --> D["Derive Posterior Distribution &<br>Analytical CoVar / ΔCoVaR"]
    D --> E["Empirical Analysis & Sensitivity Analysis<br>(US Banking System during Fed Rate Hikes)"]
    E --> F["Key Outcomes:<br>1. Linear dependence on view expectations<br>2. Nonlinear dependence on variance/quantiles/correlation<br>3. Effective assessment of risk spillover effects"]