Numerical Hedging of Electricity Contracts Using Dimension Reduction

The basic contracts traded on energy exchanges involve fixed-rate payments for the delivery of electricity over a certain period of time. It has been shown that options on these electricity swaps can be priced efficiently using a Hilbert space-valued time-inhomogeneous jump-diffusion model for the forward curve. We consider the mean-variance hedging problem for European options under this model. We use portfolios containing only traded contracts. The computation of hedging strategies leads to quadratic optimization problems whose parameters depend on the solution of an infinite-dimensional partial integro-differential equation. The main objective of this article is to find an efficient numerical algorithm for this task. Using proper orthogonal decomposition (a dimension reduction method), approximately optimal strategies are computed. We prove convergence of the corresponding hedging error to the minimal achievable error in the incomplete electricity market. Numerical experiments are performed to analyze the resulting hedging strategies.