Pricing Swing Options in Electricity Markets with Two Stochastic Factors Using a Partial Differential Equation Approach

Abstract

In this paper, we consider the numerical valuation of swing options in electricity markets based on a two-factor model. These kinds of contracts are modeled as path dependent options with multiple exercise rights. From a mathematical point of view, the valuation of these products is posed as a sequence of free boundary problems, where two exercise rights are separated by a time period. In order to solve the pricing problem, we propose appropriate numerical methods based on a Crank-Nicolson semi-Lagrangian method combined with biquadratic Lagrange finite elements for the discretization of the partial differential equation. In addition, we use an augmented Lagrangian active set method to cope with the early exercise feature when it appears. Moreover, we derive appropriate artificial boundary conditions to treat the unbounded domain numerically. Finally, we present some numerical results to illustrate the proper behavior of the numerical schemes.