Optimal linear hedge under volumetric and price uncertainties in both retail and wholesale electricity markets

Abstract

Linear instruments such as forward and futures contracts have been widely used for managing hedgable price risks in electricity industry. However, an integrated utility faces both price (retail & wholesale) and volumetric (supply & demand) uncertainties in both retail and wholesale markets. This paper presents a general framework for applying utility theory to the determination of optimal linear hedges for managing hedgable price risk under both volumetric and price uncertainties and derives a general analytical formula for the optimal linear hedge. A closed-form solution can be obtained if load obligation, power supply quantity and spot market price are assumed to have joint normal distributions. It is found that the optimal linear hedge position includes four components: (a) the expected net open position at the wholesale market; (b) an adjustment term due to the correlation risk between supply quantity and price; (c) an adjustment term due to the correlation risk between load obligation and price due to the rate differential between the retail and the expected wholesale spot market prices; and (d) a speculative component due to the bias on the expected spot price. The first three components are for pure risk reduction, and are independent of management's risk aversion. The last component exploits the expected profit that can be achieved when the management has a bias on the expected spot price, and is inversely proportional to management's risk aversion.