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


  • René Aid

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine, EDF - EDF)

  • Luciano Campi

    () (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Langrené

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)


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.

Suggested Citation

  • René Aid & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.
  • Handle: RePEc:hal:wpaper:hal-00525800
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    References listed on IDEAS

    1. Cartea, Álvaro & Villaplana, Pablo, 2008. "Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2502-2519, December.
    2. repec:wsi:ijtafx:v:12:y:2009:i:07:n:s021902490900552x is not listed on IDEAS
    3. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2009. "Variance Optimal Hedging for continuous time processes with independent increments and applications," Papers 0912.0372,
    4. Noufel Frikha & Vincent Lemaire, 2010. "Joint Modelling of Gas and Electricity spot prices," Working Papers hal-00421289, HAL.
    5. Pirrong, Craig & Jermakyan, Martin, 2008. "The price of power: The valuation of power and weather derivatives," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2520-2529, December.
    6. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    7. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    8. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    9. Bruno Bouchard & Adrien Nguyen Huu, 2013. "No marginal arbitrage of the second kind for high production regimes in discrete time production-investment models with proportional transaction costs," Post-Print hal-00487030, HAL.
    10. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    11. Kanamura, Takashi & Ohashi, Kazuhiko, 2007. "A structural model for electricity prices with spikes: Measurement of spike risk and optimal policies for hydropower plant operation," Energy Economics, Elsevier, vol. 29(5), pages 1010-1032, September.
    12. Lyle, Matthew R. & Elliott, Robert J., 2009. "A 'simple' hybrid model for power derivatives," Energy Economics, Elsevier, vol. 31(5), pages 757-767, September.
    13. Fred Espen Benth & Lars Ekeland & Ragnar Hauge & BjøRn Fredrik Nielsen, 2003. "A note on arbitrage-free pricing of forward contracts in energy markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 325-336.
    14. René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
    15. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
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