Paper: arXiv 2603.02357

Authors: Xiaochun Liu, Richard Luger

Abstract

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted quantile regression. Focusing on downside risk, VaR is derived from the left-tail quantile of rescaled returns, and ES is approximated by averaging quantiles below the VaR level. The method delivers robust, distribution-free estimates of extreme losses and captures skewness, heavy tails, and leverage effects. Simulation experiments and empirical analysis show that it often outperforms established models, including GARCH and joint VaR-ES conditional-quantile approaches. An application to daily returns on major international stock indices, spanning the COVID-19 period, highlights its effectiveness in capturing risk dynamics.

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 semiparametric approach (QbSD) for forecasting VaR and ES using restricted quantile regression to model scale dynamics without parametric assumptions. It demonstrates exceptional empirical rigor through extensive simulations and backtesting on international stock indices, including the high-volatility COVID-19 period.

Research Flowchart

  flowchart TD
    A[Goal: Robust VaR & ES Forecasting for Financial Risk] --> B[Inputs: Daily Returns on Major Stock Indices & Simulated Data]
    B --> C[Methodology: Semiparametric Conditional Scale Modeling via Restricted Quantile Regression]
    C --> D[Compute Downside Risk Metrics: VaR from Left-Tail Quantile & ES via Sub-VaR Averaging]
    D --> E[Backtesting & Comparative Analysis vs. GARCH & Joint VaR-ES Models]
    E --> F[Outcomes: Superior Performance Capturing Heavy Tails, Leverage, & COVID-19 Volatility]

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