Combining Deep Learning and GARCH Models for Financial Volatility and Risk Forecasting

ArXiv ID: 2310.01063 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets’ risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts.

Keywords: GARCH, Gated Recurrent Unit (GRU), Volatility Forecasting, Value-at-Risk (VaR), Expected Shortfall (ES), Equities, Commodities, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, featuring multiple GARCH model specifications with derivatives and nonlinear functions, and employs complex deep learning architectures (GRU) with specific activation functions. It demonstrates high empirical rigor by applying models to real-world financial data (S&P 500, gold, Bitcoin), implementing rigorous backtesting for volatility and risk forecasts (VaR, ES), and using established libraries (R’s rugarch) for estimation.

  flowchart TD
    A["Research Goal<br>Hybrid GARCH-DL Volatility &<br>Risk Forecasting"] --> B["Data & Targets"]
    B --> C["Methodology<br>GARCH Models x GRU Networks"]
    C --> D["Computational Process<br>Hybrid Forecast Generation"]
    D --> E{"Risk Metrics Evaluation<br>VaR & ES at 5% & 1%"}
    E --> F["Key Findings"]
    
    subgraph B ["Data & Inputs"]
        B1["S&P 500, Gold, Bitcoin<br>Daily Log Returns"]
        B2["Target Variable<br>Garman-Klass Volatility Estimator"]
    end

    subgraph C ["Models"]
        C1["GARCH<br>EGARCH, GJR-GARCH, APARCH"]
        C2["Deep Learning<br>GRU Networks"]
    end

    subgraph D ["Process"]
        D1["Train Models"]
        D2["Generate Hybrid Forecasts"]
    end

    subgraph F ["Outcomes"]
        F1["Superior Volatility<br>Point Forecasts"]
        F2["No Significant Improvement<br>in VaR/ES Forecasts"]
    end