Numerical hedging of electricity swaptions with a portfolio of swaps

The basic contracts traded on energy exchanges are swaps. They involve fixed-rate payments for the delivery of electricity over a certain period of time. It has been shown that options on these swaps (called electricity swaptions) can be priced efficiently using a Hilbert space-valued timeinhomogeneous jump-diffusion model for the forward curve. We consider the mean-variance hedging problem for European swaptions under this model. We use portfolios containing only traded swaps. The computation of hedging strategies leads to quadratic optimization problems whose parameters depend on the solution of an infinite-dimensional partial integrodifferential 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.