The Estimation Risk in Extreme Systemic Risk Forecasts

Paper: arXiv 2304.10349

Authors: Yannick Hoga

Abstract

Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for systemic risk as measured by the marginal expected shortfall (MES). It is based on first de-volatilizing the observations and, then, calculating systemic risk for the residuals using an estimator based on extreme value theory. We show the validity of the method by establishing the asymptotic normality of the MES forecasts. The good finite-sample coverage of the implied MES forecast intervals is confirmed in simulations. An empirical application to major US banks illustrates the significant time variation in the precision of MES forecasts, and explores the implications of this fact from a regulatory perspective.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides strong mathematical grounding by establishing the asymptotic normality of MES forecasts using extreme value theory. Its empirical framework is rigorously evaluated via both finite-sample Monte Carlo simulations and a practical application to major US bank data.

Research Flowchart

  flowchart TD
    A[Goal: Improve Forecasts & Estimate Risk<br/>of Marginal Expected Shortfall MES] --> B[Input: Major US Banks Equity Data]
    B --> C[Step 1: De-volatilize Financial Returns]
    C --> D[Step 2: Apply Extreme Value Theory EVT<br/>to Residuals]
    D --> E[Establish Asymptotic Normality<br/>of MES Forecasts]
    E --> F[Simulations: Confirm Finite-Sample<br/>Coverage of Forecast Intervals]
    F --> G[Outcome: Identify Significant Time Variation<br/>in MES Forecast Precision for Regulators]