A structural risk-neutral model for pricing and hedging power derivatives

René Aïd (1, 2) , Luciano Campi (1, 3) , Nicolas Langrené (1, 4)

1 FiME Lab - Laboratoire de Finance des Marchés d'Energie
2 EDF - EDF
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We develop a structural risk-neutral model for energy market modifying along several directions the approach introduced in Aid et al. (2009). In particular a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities and electricity demand makes such a market incomplete. We follow a local risk minimization approach to price and hedge energy derivatives. Despite the richness of information included in the spot model, we obtain closed-form formulae for futures prices and semi-explicit formulae for spread options and European options on electricity forward contracts. An analysis of the electricity price risk premium is provided showing the contribution of demand and capacity to the futures prices. We show that when far from delivery, electricity futures behave like a basket of futures on fuels.

Mots clés: Electricity spot and forward prices; Fuels; Capacity; Electricity demand; Scarcity function; Local risk minimization; Minimal martingale measure; Power derivatives; Spread options; Extended incomplete Goodwin-Staton integral

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

René Aïd, Luciano Campi, Nicolas Langrené. A structural risk-neutral model for pricing and hedging power derivatives. 2010. ⟨hal-00525800⟩