Optimal Static Hedging of Energy Price and Volume Risk: Closed-Form Results

As an extension of the VaR-constrained hedging, we propose a closed-form solution to the problem of optimizing portfolios, based on price and weather. For electric power companies, price and quantity are volatile, and in hydro-electricity generation quantity can be related to weather conditions. An optimum portfolio is derived from expected utility maximization problem, including weather indices to minimize losses. Due to electric power features, agents in this market are facing price and volume risks, the difficulty to storage efficiently electric power cannot permit to mitigate volumetric risk and alternatively weather instruments can be used in order to hedge unexpected changes in weather; the purpose of weather derivatives is to smooth out the temporal fluctuations in the company´s revenues. For electric power companies price and quantity are volatile, and quantity is correlated to the weather conditions. Moreover, exposures to price and volume risks make necessary the inclusion of the weather pay-off. Thus, we derive the optimal portfolio from the expected utility maximization problem including electric power and weather derivatives whose payoffs will minimize losses.