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

## TL;DR

This paper introduces a novel electricity pricing model using exponential functionals of jump Lévy processes, capturing market features like mean reversion and jumps, and provides a numerical scheme for option valuation.

## Contribution

The paper develops a new Lévy process-based model for electricity prices incorporating the price cap principle and offers a finite difference method for option valuation.

## Key findings

- The option price is characterized as a viscosity solution of a PIDE.
- A finite difference scheme is proposed with proven stability and convergence.
- Numerical simulations demonstrate the model's applicability.

## Abstract

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.