Modelling, mathematical analysis and numerical simulation to value derivatives related to renewable energy certificates

Abstract

The main objective of this thesis concerns to the modelling, mathematical analysis and numerical solution of partial differential equations (PDEs) models for pricing renewable energy certificates (RECs) and associated derivatives products. In the modelling, the price of the REC plays a relevant role. A non-linear PDE model with two stochastic factors is proposed. The stochastic factors are the accumulated green certificates and the renewable electricity generation rate. One novelty of this thesis comes from the numerical treatment of the non-linear convective term in the PDE. In order to solve the obtained linearized problem, semi-Lagrangian schemes in time combined with finite differences discretizations, or alternative Lagrange-Galerkin methods are proposed. An equivalent methodology has been used for the valuation of the REC derivatives to obtain a linear PDE model once the REC price is known. Existence of solution is obtained in this setting. The application to the pricing of European options and futures on RECs is addressed. Finally, we show illustrative results of the performance of the models and numerical methods that have been implemented.