A STRUCTURAL RISK‐NEUTRAL MODEL FOR PRICING AND HEDGING POWER DERIVATIVES

René Aïd · Luciano Campi · Nicolas Langrené

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Stochastic processes and financial applications Market Dynamics and Volatility Energy Load and Power Forecasting

Abstract

We develop a structural risk‐neutral model for energy market modifying along several directions the approach introduced in Aïd et al. 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 semiexplicit 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.

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References

2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 1997The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging 1998Brownian Motion and Stochastic Calculus 1991Continuous Martingales and Brownian Motion 1976Stochastic Differential Equations and Applications 1990Hedging of contingent claims under incomplete information 2010A Guided Tour through Quadratic Hedging Approaches

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2013Quantitative Energy Finance 2014A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension 2013Electricity Derivatives Pricing with Forward-Looking Information 2021A survey of electricity spot and futures price models for risk management applications 2012The valuation of clean spread options: linking electricity, emissions and fuels 2016Modelling electricity futures prices using seasonal path-dependent volatility

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