This article examines the task of multi-step forecasting of realized volatility. The paper introduces a modification of the loss function of the form quantile log-hyperbolic cosine (quantile log-cosh), and information extracted from options using the recovery theorem [Ross, 2015] is also used as exogenous factors in the context of predicting the realized volatility of exchange-Traded funds (ETF) SPY (SPDR S&P 500 ETF Trust) и QQQ (Invesco QQQ Trust). Two hypotheses are put forward: the first one assumes that the quantile log-cosh in neural networks will increase the accuracy of the predictive model on the test dataset compared to the same models trained on other target functions. The second hypothesis is to use information extracted from the recovery theorem. This theorem makes it possible to approximate the true distribution density of SPY and QQQ states in terms of Markov chains and get rid of the assumptions of a risk-neutral measure in financial models. Then, according to the second hypothesis, it is expected that the model with the factors extracted using the recovery theorem will show more accurate predictions on the test sample compared to the classical heterogeneous autoregression (HAR-RV) model. The following machine learning models are used to test hypotheses: LSTM, GRU, BiLSTM, BiGRU, FCNN and N-BEATS. The results show that the modification of the quantile log-cosh makes it possible to improve the accuracy of model predictions on the test dataset. Also, the inclusion of exogenous factors from the recovery theorem in the forecasting models of realized volatility makes it possible to significantly outperform the HAR-RV model, especially over the long-term horizon.