Arbitrage conditions for electricity markets with production and storage

Abstract

This work analyzes the notion of arbitrage for market models with electricity production from fuel. Several generators, fuel storage, and the related fuel and storage costs are considered. Based on stochastic optimization in Banach spaces, a necessary and a sufficient no-arbitrage condition in terms of stochastic discount factors are derived and analyzed further in the context of (potentially nonlinear) vector-autoregressive price models with additive residuals. For this large class of statistical models, it is found that both the necessary and the sufficient condition can be rejected only in very rare cases. Based on these results, it is demonstrated how absence of arbitrage can be used to construct superhedging based valuation formulas for physical electricity delivery contracts, and that absence of arbitrage in tree-based stochastic programming can be ensured easier in the context of electricity production than in a purely financial context.