VaR constrained hedging of fixed price load-following obligations in competitive electricity markets

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 ∗The work described in this paper was partially supported by the Power Systems Engineering Research Center and by the Consortium for Electric Reliability Technology Solutions (CERTS) on behalf of the Department of Energy. †Pacific Gas and Electric, San Francisco ‡Department of Industrial Engineering and Operations Research, University of California at Berkeley