This paper proposes a data-driven method, using Artificial Neural Networks, to price financial options and compute volatilities, which speeds up the corresponding numerical methods. Prospects of the Stock Market are priced by the Black Scholes model, with the difference that the volatility is considered stochastic. So, we propose an innovative hybrid method to forecast the volatility and returns in Stock Market indices, which declare a model with a generalized autoregressive conditional heteroscedasticity framework. In addition, this research analyzes the impact of COVID-19 on the option, return, and volatility of the stock market indices. It also incorporates the long short-term memory network with a traditional artificial neural network and COVID-19 to generate better volatility and option pricing forecasts. We appraise the models' performance using the root second-order quadratic function means of the out-of-sample returns powers. The results illustrate that the autoregressive conditional heteroscedasticity forecasts can serve as informative features to significantly increase the predictive power of the neural network model. Integrating the long short-term memory and COVID-19 is an effective approach to construct proper neural network structures to boost prediction performance. Finally, we interpret the sensitivity of option prices concerning the market or model parameters, which are essential in practice.