An Analytic Hedging Model of Energy Quanto Contracts

Abstract

Earnings of energy firms are exposed to a joint risk of energy price and energy consumption. The correlated fluctuations in both price and consumption present a joint risk of price and volume for a load-serving entity (LSE). In order to manage such a joint risk, LSEs take positions in a variety of hedging contracts. Among these financial instruments, we analyze the use of electricity-temperature quantity-adjusting (quanto) contracts. In this paper, we consider an LSE that has access to electricity price derivatives, temperature derivatives, and energy quanto contracts. We derive the closed-form optimal hedging positions in these contracts and the optimal mean-variance tradeoff, from an analytic model that we develop within the Constant Absolute Risk Aversion (CARA)-normal setting. We mathematically prove that the use of quanto contracts allows an LSE to lower its revenue volatility. Furthermore, our model offers novel economic insights into the application of energy quanto contracts to hedging practice. First, we document and quantify the “dirty hedge” of standardized price and temperature derivatives in the absence of tailor-made energy quanto contracts. Second, we derive a threshold price of energy quanto contracts. If an energy quanto contract is quoted above this threshold price, an LSE shall not trade such a contract for risk management purposes. Third, this paper investigates a questionable, yet commonly adopted practice of using temperature as a perfect proxy for power consumption.