Pricing and Hedging Asian-Style Options in Energy

Abstract

We solve the problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted. Liquid trading in the future is only possible up to the start of a so-called delivery period. After the start of the delivery period, the hedge positions can not be adjusted anymore until maturity. This reflects the trading situation at the Nordic energy market Nord Pool for example. We show that there exists a unique solution to this combined continuous-discrete quadratic hedging problem if the future price process is a special semimartingale with bounded mean-variance tradeoff. Additionally, under the assumption that the future price process is a local martingale, the hedge positions before the averaging period are inherited from the market specification without trading restriction. As an application we consider three models and derive their quadratic hedge positions in explicit form, a simple Black Scholes model with time-dependent volatility, the stochastic volatility model of Barndorff-Nielsen and Shephard and an exponential additive model. Based on an exponential spot price model driven by two NIG \levy processes, we determine an exponential additive model for the future price by moment matching techniques. We calculate hedge positions and determine the quadratic hedge error in a simulation study.