In this talk, some new pricing methods for Renewable Energy Certificates (RECs) or green certificates and associated derivatives products are presented.

For this purpose, starting from a system of FBSDEs and using Ito lemma, we first propose a mathematical model based on a semilinear PDE arising from the consideration of two stochastic factors: the accumulated green certificates sold by an authorized generator and the natural logarithm of the renewable electricity generation rate. One main novelty of the work comes from the numerical treatment of the nonlinerity that appears in the term containing first order derivative in the PDE. Thus, mainly a couple of numerical strategies are proposed.

Moreover, we state the mathematical model that governs the valuation of derivatives whose underlying is a REC, in particular we study European options and futures contracts. Thus, we derive the PDE model to price these derivatives, study the existence of solution and propose how to solve the models by using appropriate numerical techniques. Finally, we show some numerical results that illustrate the performance of the proposed model and the numerical methods.

This is a joint work with María Baamonde and M. Carmen Calvo-Garrido, both from Department of Mathematics and CITIC, University of a Coruña (Spain).