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In this paper, we develop a hybrid approach to forecasting the volatility andrisk of financial instruments by combining common econometric GARCH time seriesmodels with deep learning neural networks. For the latter, we employ GatedRecurrent Unit (GRU) networks, whereas four different specifications are usedas the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Modelsare tested using daily logarithmic returns on the S&P 500 index as well as goldprice Bitcoin prices, with the three assets representing quite distinctvolatility dynamics. As the main volatility estimator, also underlying thetarget function of our hybrid models, we use the price-range-based Garman-Klassestimator, modified to incorporate the opening and closing prices. Volatilityforecasts resulting from the hybrid models are employed to evaluate the assets'risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two differenttolerance levels of 5% and 1%. Gains from combining the GARCH and GRUapproaches are discussed in the contexts of both the volatility and riskforecasts. In general, it can be concluded that the hybrid solutions producemore accurate point volatility forecasts, although it does not necessarilytranslate into superior VaR and ES forecasts.

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