It is a challenge for investors to forecast the option prices, invest in it and earn fruitful profits. The derivative markets such as option market give some flexibility in decision making, however, pricing option poses many challenges due to complexity of pricing models. In this work, I compare and discuss the limitations of the existing option pricing models. Then, I propose a novel Data-Driven Neuro-volatility ARCH (DDNA) model that alleviates the common limitation of assuming constant volatility of underlying asset(s) that allows better forecasts of volatility of the stock prices when compared to the existing models and hence compute better option price(s). I used Monte Carlo (MC) method to compute the option prices with the DDNA volatility forecast computed in the first part. The MC option pricing method requires a large number of simulations for better precision. For this, I implemented my proposed model in parallel on two easily accessible Cloud resources using the MapReduce. The MC strategy being dependent on uncertainties and random numbers is prone to errors, I propose to generate a fuzzified range of option prices instead of a single crisp option value to minimize these errors. The proposed DDNA model for forecasting volatility together with MC option pricing model implemented on MapReduce outperforms the existing option pricing models in terms of efficiency and accuracy. This proposed DDNA model could be used by investors for computing option prices precisely with relative ease, allowing them to value the numerous available option contracts for their investment decisions.