In this course a vast number of derivatives models is presented by implementing a standardized, uniform pricing approach. The first part is devoted to the development of a very general pricing representation that includes the major classes of equity derivatives models developed in literature (from Black-Scholes-Merton, CEV, local volatility to AJD and Pure Jump models). Generally these models are presented with heterogeneous techniques, notations and a plethora of various pricing representation; by starting from the simplest examples, the course bring back all the models in a uniform, formalized approach. In the second part the standardized analytical environment allows the regular deployment of powerful numerical techniques (i.e. adaptive quadrature schemes) that can solve in a flexible way the pricing and hedging problems regardless of the model’s theoretical complexity: the course aims to end up with the building of the code of an efficient, modular “all-purpose pricing and calibration engine.