Model and numerical methods for pricing renewable energy certificate derivatives

Abstract

[Abstract]: Assuming that the price of the renewable energy certificate (REC) is known, we formulate the valuation problem of a European REC derivative in terms of a linear 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. Next, a result of existence of solution is obtained for this PDE problem. In order to solve numerically the PDE problem, we propose two different methods: a semi-Lagrangian scheme in time combined with finite differences discretizations in the spatial-like variables, or alternative Lagrange–Galerkin methods. The application to the pricing of European options and futures on renewable energy certificates is addressed. Finally, we show illustrative results about the performance of the models and numerical methods that have been implemented.