A jump-diffusion model for pricing electricity under price cap regulation and parameters estimation

Abstract

One of the major developments in the electricity sector is the functional separation of the industry into three main phases, namely: the generation, transmission and distribution phases. This reform has leat to the openness of the electricity industry to competition, with the progressive replacement of state monopoly in favour of independent producers, and recently to the opening of deregulated or free electricity markets. Markets regulated by economic principles such as "price cap" or "revenue cap" to cap the fluctuation of the electricity prices were also introduced . In this thesis, we propose a new model for pricing electricity based on the price cap principle and derive some financial derivatives. To achieve the goal we divided the work into three parts. In the first part, we modelling the dynamics of spot electricity prices under price cap regulated market.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. In the second part, we derive the forward contract and the European option using two approaches. The first is based on the use of Fourier transforms, while the other uses the price of the option as a solution of an integro-differential equation (PIDE). It is shown that the value of an European option of this asset is the unique viscosity solution of a partial integro-differential equation. 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. In the last part we propose a maximum likelihood approach for estimating the parameters of the model via estimating the transition density by the saddlepoint method.