Paper: arXiv 2406.06235

Authors: Alessandra Amendola, Vincenzo Candila, Antonio Naimoli, Giuseppe Storti

Abstract

To comply with increasingly stringent international standards in risk management and regulation, several approaches have been developed in the literature for forecasting tail-risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). However, the accuracy of these measures can be significantly affected by multiple sources of uncertainty, including model misspecification, data limitations and estimation procedures. To address these challenges and enhance the predictive performance of individual models, this study introduces novel forecast combination strategies based on the Model Confidence Set (MCS) methodology. Specifically, a strictly consistent joint VaR-ES loss function is employed to identify the best-performing models, which constitute the Set of Superior Models (SSM). Subsequently, the VaR and ES forecasts of the models included in the SSM are combined using various weighting schemes. An empirical analysis based on nine stock market indices at the 2.5% and 1% risk levels provides evidence that the proposed combined predictors are a robust alternative for forecasting tail-risk measures, successfully passing standard backtests and consistently entering the SSM of the MCS.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel framework for combining VaR and ES predictions by integrating the Model Confidence Set (MCS) trimming mechanism with consistent joint FZ loss functions. It features a highly rigorous empirical evaluation across nine global equity indices using 32 baseline forecasting models and extensive backtesting procedures.

Research Flowchart

  flowchart TD
    A[Goal: Enhance VaR & ES Forecast Accuracy via Combination] --> B[Input: Financial Data 9 Stock Market Indices @ 1% & 2.5% Risk Levels]
    B --> C[Generate Individual VaR & ES Model Forecasts]
    C --> D[Apply MCS Procedure with Joint VaR-ES Loss Function]
    D --> E[Identify Superior Set of Models & Apply Weighting Schemes]
    E --> F[Outcomes: Combined Predictors Pass Backtests & Consistently Enter SSM]

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