Pricing renewable energy certificates with a Crank–Nicolson Lagrange–Galerkin numerical method

Abstract

The valuation problem of renewable energy certificates can be formulated in terms of a nonlinear PDE model where the underlying stochastic factors are the accumulated green certificates sold by an authorized producer and the natural logarithm of the renewable generation rate. In the present paper, the nonlinear convective term is treated with the Bermúdez–Moreno duality method for maximal monotone operators as in Baamonde-Seoane et al. (2021). The main novelty of this article comes from the proposed techniques for the numerical solution of the resulting linear problem. In this case, we propose a Lagrange–Galerkin method which mainly consists of Crank–Nicolson characteristics for time discretization combined with finite elements for the discretization in the accumulated green certificates and the natural logarithm of the renewable generation rate directions. Finally, several numerical examples are presented to illustrate the good performance of the method and model, and its comparison with other numerical schemes employed to solve the same problem.