Affiliations: Pacific Gas and Electric, San Francisco, CA, USA | Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA, USA
Abstract: Load serving entities providing electricity to regulated customers have an obligation to serve load that is subject to systematic and random fluctuations at fixed prices. In some jurisdictions like New Jersey, such obligations are auctioned off annually to third parties that commit to serve a fixed percentage of the fluctuating load at a fixed energy price. In either case the entity holding the load following obligation is exposed to the load variation and to a volatile wholesale spot market price which is correlated with the load level. Such double exposure to price and volume results in a net revenue exposure that is quadratic in price and cannot be adequately hedged with simple forward contracts whose payoff is linear in price. A fixed quantity forward contract cover, is likely to be short when the spot price is high and long when the spot price is low. In this paper we develop a self-financed hedging portfolio consisting of a risk free bond, a forward contract and a spectrum of call and put options with different strike prices. A popular portfolio design criterion is the maximization of expected hedged profits subject to a value at risk (VaR) constraint. Unfortunately, that criteria is difficult to implement directly due to the complicated form of the VaR constraint. We show, however, that under plausible distributional assumptions, the optimal VaR constrained portfolio is on the efficient mean–variance frontier. Hence, we propose an approximation method that restricts the search for the optimal VaR constrained portfolio to that efficient frontier. The proposed approach is particularly attractive when the mean–variance efficient frontier can be represented analytically, as is the case, when the load and logarithm of price follow a bivariate normal distribution. We illustrate the results with a numerical example.
Keywords: Energy risk, competitive electricity markets, volumetric hedging, incomplete markets
