| 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. |