This work explores a deep-learning approach to the problem of Parametric Option Pricing. In a first phase, neural networks are used to learn a pricing function starting from a set of prices computed by means of a suitable benchmark method. In a second phase, the method is coupled with a complexity reduction technique in order for it to be scaled up to higher dimensions. The contributions of this work are multiple. On the one hand, it shows the applicability of the neural-network approach to the parametric pricing problem. While few recent works have tackled a similar problem, this thesis shows that solutions can be found to more complex financial products, such as American and basket options.