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Electricity price modeling and asset valuation: a multi-fuel structural approach

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  • Rene Carmona
  • Michael Coulon
  • Daniel Schwarz

Abstract

We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity spot prices. The stack structure allows for a range of generator efficiencies per fuel type and for the possibility of future changes in the merit order of the fuels. The derived spot price process captures important stylized facts of historical electricity prices, including both spikes and the complex dependence upon its underlying supply and demand drivers. Furthermore, under mild and commonly used assumptions on the distributions of the input factors, we obtain closed-form formulae for electricity forward contracts and for spark and dark spread options. As merit order dynamics and fuel forward prices are embedded into the model, we capture a much richer and more realistic dependence structure than can be achieved by classical reduced-form models. We illustrate these advantages by comparing with Margrabe's formula and a simple cointegration model, and highlight important implications for the valuation of power plants.

Suggested Citation

  • Rene Carmona & Michael Coulon & Daniel Schwarz, 2012. "Electricity price modeling and asset valuation: a multi-fuel structural approach," Papers 1205.2299, arXiv.org.
  • Handle: RePEc:arx:papers:1205.2299
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    References listed on IDEAS

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    1. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
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    5. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    9. 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.
    10. M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298.
    11. 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.
    12. repec:wsi:ijtafx:v:12:y:2009:i:07:n:s021902490900552x is not listed on IDEAS
    13. 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.
    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.
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    Citations

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    Cited by:

    1. René Carmona & Michael Coulon & Daniel Schwarz, 2012. "The valuation of clean spread options: linking electricity, emissions and fuels," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1951-1965, December.
    2. Kallabis, Thomas & Pape, Christian & Weber, Christoph, 2016. "The plunge in German electricity futures prices – Analysis using a parsimonious fundamental model," Energy Policy, Elsevier, vol. 95(C), pages 280-290.
    3. Mahringer, Steffen & Fuess, Roland & Prokopczuk, Marcel, 2015. "Electricity Market Coupling and the Pricing of Transmission Rights: An Option-based Approach," Working Papers on Finance 1512, University of St. Gallen, School of Finance.
    4. Mireille Bossy & Nadia Maizi & Odile Pourtallier, 2013. "Nash equilibrium for coupling of CO2 allowances and electricity markets," Papers 1311.1535, arXiv.org.
    5. Florian Ziel & Rick Steinert, 2015. "Electricity Price Forecasting using Sale and Purchase Curves: The X-Model," Papers 1509.00372, arXiv.org, revised Aug 2016.
    6. Damir Filipovic & Martin Larsson & Tony Ware, 2017. "Polynomial processes for power prices," Papers 1710.10293, arXiv.org, revised Apr 2018.
    7. Benedetti, Giuseppe & Campi, Luciano, 2016. "Utility indifference valuation for non-smooth payoffs with an application to power derivatives," LSE Research Online Documents on Economics 63016, London School of Economics and Political Science, LSE Library.
    8. Clemence Alasseur & Olivier Feron, 2017. "Structural price model for electricity coupled markets," Papers 1704.06027, arXiv.org.
    9. Andreas Wagner, 2014. "Residual Demand Modeling and Application to Electricity Pricing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    10. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    11. Füss, Roland & Mahringer, Steffen & Prokopczuk, Marcel, 2015. "Electricity derivatives pricing with forward-looking information," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 34-57.
    12. Mireille Bossy & Odile Pourtallier & Nadia Maïzi, 2014. "Game theory analysis for carbon auction market through electricity market coupling," Working Papers hal-00954377, HAL.
    13. Füss, Roland & Mahringer, Steffen & Prokopczuk, Marcel, 2013. "Electricity Spot and Derivatives Pricing when Markets are Interconnected," Working Papers on Finance 1323, University of St. Gallen, School of Finance.
    14. Miha Troha & Raphael Hauser, 2014. "Calculation of a power price equilibrium," Papers 1409.6645, arXiv.org.
    15. Giuseppe Benedetti & Luciano Campi, 2013. "Utility indifference valuation for non-smooth payoffs with an application to power derivatives," Papers 1307.4591, arXiv.org.
    16. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    17. Stein-Erik Fleten & Ronald Huisman & Mehtap Kilic & Enrico Pennings & Sjur Westgaard, 2014. "Electricity futures prices: time varying sensitivity to fundamentals," Working Papers 2014/21, Institut d'Economia de Barcelona (IEB).
    18. Samuel N. Cohen & Victor Fedyashov, 2014. "Ergodic BSDEs with jumps and time dependence," Papers 1406.4329, arXiv.org, revised Nov 2015.

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