Numerical Solution of a Nonlinear PDE Model for Pricing Renewable Energy Certificates (RECs)

Abstract

[Abstract] In this article we present a valuation method for Renewable Energy Certificates (RECs) or green certificates. For this purpose, we propose a non-linear PDE model with two stochastic factors: the accumulated green certificates sold by an authorized generator and the natural logarithm of the renewable electricity generation rate. One novelty of the work comes from the numerical treatment of the non-linear convective term in the PDE. Thus, we use the Bermdez-Moreno algorithm to deal with this non-linear term. This duality algorithm is based on the Yosida regularization of non-linear maximal monotone operators. In order to solve the obtained linearized problem, we use numerical methods based on semi-Lagrangian schemes in the direction without diffusion while we consider an implicit second order finite differences scheme in the direction with diffusion term. Finally, we show illustrative results of the performance of the proposed model and numerical methods that have been implemented.