GARCH-LSTM hybrid models have become increasingly popular in the volatility forecasting literature. To date, these models have almost exclusively focused on point estimation and accuracy measures such as RMSE and MAPE, while failing to assess the uncertainty of these point estimates. We approach this gap in two ways. First, we extend the existing GARCH-LSTM model by modeling the conditional mean with an ARMA structure. Second, we develop a forward bootstrap algorithm to build multi-step-ahead prediction intervals for future realized volatility. In order to address the notorious undercoverage of prediction intervals, we implement two solutions. One draws bootstrap innovations from the empirical residual distribution to mimic the fat-tail property of financial series. The other utilizes principles from conformal prediction to systematically extend the prediction interval length. We evaluate the methods in simulations with heavy-tailed and time-varying GARCH processes and in rolling-window forecasts of four U.S. stock indices from 2020 to 2025. The ARMA-based hybrid gives the lowest point-forecast errors in most settings, and combining both remedies with the mean-based hybrid yields intervals closest to the nominal level among competing methods.

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