Electricity Option Pricing with Capped Lévy-Driven Prices

Summary

The paper proposes a model for electricity prices under a price-cap principle, representing the asset price as an exponential functional of a jump Lévy process. The chosen process is intended to capture both mean reversion and jumps, features associated with electricity markets. The study focuses on pricing European options written on this modeled asset.

The option value is characterized as the unique viscosity solution of a partial integro-differential equation. The authors approximate that solution with a finite-difference scheme and provide consistency, stability, and convergence results. Numerical simulations are reported for a smooth initial condition. The document does not give specific simulation outcomes, calibration details, or comparison with market prices, so it establishes a mathematical and numerical pricing framework rather than empirical pricing accuracy or a trading advantage.

Key ideas

• Electricity prices are modeled using an exponential functional of a jump Lévy process under a price-cap principle.
• The process is designed to represent both mean reversion and price jumps.
• European option values are characterized by a partial integro-differential equation.
• A finite-difference method is analyzed for consistency, stability, and convergence.
• The numerical evidence is limited to simulations with a smooth initial condition.

Tags

# European Option Pricing of electricity under exponential functional of Lévy processes with Price-Cap principle


# European Option Pricing of electricity under exponential functional of Lévy processes with Price-Cap principle









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 Lévy 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.

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