  We propose a new model for electricity pricing based on the price cap
principle. The particularity of the model is that the asset price is an
exponential functional of a jump L\'evy process. This model can capture both
mean reversion and jumps which are observed in electricity market. It is shown
that the value of an European option of this asset is the unique viscosity
solution of a partial integro-differential equation (PIDE). A numerical
approximation of this solution by the finite differences method is provided.
The consistency, stability and convergence results of the scheme are given.
Numerical simulations are performed under a smooth initial condition.
