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We propose a new model for electricity pricing based on the price capprinciple. The particularity of the model is that the asset price is anexponential functional of a jump L\'evy process. This model can capture bothmean reversion and jumps which are observed in electricity market. It is shownthat the value of an European option of this asset is the unique viscositysolution of a partial integro-differential equation (PIDE). A numericalapproximation 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.

European Option Pricing of electricity under exponential functional of L\'evy processes with Price-Cap principle