Bridging Econometrics and AI: VaR Estimation via Reinforcement Learning and GARCH Models

ArXiv ID: 2504.16635 “View on arXiv”

Authors: Fredy Pokou, Jules Sadefo Kamdem, François Benhmad

Abstract

In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the current market dynamics. To overcome these limitations, we propose a hybrid framework for Value-at-Risk (VaR) estimation, combining GARCH volatility models with deep reinforcement learning. Our approach incorporates directional market forecasting using the Double Deep Q-Network (DDQN) model, treating the task as an imbalanced classification problem. This architecture enables the dynamic adjustment of risk-level forecasts according to market conditions. Empirical validation on daily Eurostoxx 50 data covering periods of crisis and high volatility shows a significant improvement in the accuracy of VaR estimates, as well as a reduction in the number of breaches and also in capital requirements, while respecting regulatory risk thresholds. The ability of the model to adjust risk levels in real time reinforces its relevance to modern and proactive risk management.

Keywords: Value-at-Risk (VaR), Deep Reinforcement Learning, GARCH, Double Deep Q-Network (DDQN), Volatility Modeling, Equities

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematical concepts including GARCH formulations, quantile theory, and a complex Deep Reinforcement Learning (DDQN) architecture, indicating high math complexity. It also demonstrates strong empirical rigor through rigorous backtesting on 16 years of Eurostoxx 50 data, using statistical tests like Kupiec and Christoffersen, and reporting specific metrics like 79.4% test accuracy and capital requirement reductions.
  flowchart TD
    A["Research Goal: Hybrid VaR Estimation<br/>GARCH + Deep RL"] --> B["Data Input<br/>Eurostoxx 50 Daily Data"]
    B --> C["Methodology 1: GARCH Model<br/>Baseline Volatility Estimation"]
    B --> D["Methodology 2: DDQN Agent<br/>Directional Market Forecasting"]
    C --> E["Computational Process<br/>Dynamic Integration &amp; Risk Adjustment"]
    D --> E
    E --> F["Outcome 1: Improved VaR Accuracy<br/>Reduced Breaches"]
    E --> G["Outcome 2: Lowered Capital Requirements<br/>Regulatory Compliance"]