Combining Deep Learning and GARCH Models for Financial Volatility and
  Risk Forecasting
Jakub Michańków Łukasz Kwiatkowski Janusz Morajda
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.