Analysis of futures and spot electricity markets under risk aversion

We analyze the procurement problem in the electricity supply chain, focusing on the interaction between futures and spot prices. The supply chain network analyzed in our study includes risk-averse generators and retailers, both with the ability to use conditional value at risk (CV@R) in their decision processes. In this supply chain, the futures price is computed to clear the futures market, without imposing the constraint that the expected spot price equals the futures price. As major methodological contributions: we compute the Nash equilibrium of the problem using CV@R and considering conjectural variations; we derive analytical relationships between the futures and the spot market outcomes and study the implications of demand and marginal cost uncertainty, as well as the level of the players’ risk aversion, on market equilibrium; we introduce the concept of risk-adjusted expectation to derive the futures market price as a function of the players’ expected losses or profits in the spot market; and we use consistent spot and wholesale price derivatives to calculate the players’ reaction functions. Finally, we illustrate our model with several numerical examples in the context of the Spanish electricity market, studying how the shape of the forward curve and the relationship between spot and futures prices depend on seasonality, risk aversion, generators’ market power, and hydrological resources. Surprisingly we observed that risk aversion increases the profit and reduces firms’ risk, and that the consumer utility is higher in the scenarios in which retailers behave a la Cournot in the wholesale market.