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The price of power: The valuation of power and weather derivatives

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  • Pirrong, Craig
  • Jermakyan, Martin
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    Abstract

    Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999-2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.

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    File URL: http://www.sciencedirect.com/science/article/B6VCY-4SFXK6D-1/2/fb177d74c07c0668bff09e851fad5b15
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 32 (2008)
    Issue (Month): 12 (December)
    Pages: 2520-2529

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    Handle: RePEc:eee:jbfina:v:32:y:2008:i:12:p:2520-2529

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Electricity markets Derivatives pricing Market price of risk Inverse techniques;

    References

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    Citations

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    Cited by:
    1. Caporin, Massimiliano & Pres, Juliusz & Torro, Hipolit, 2010. "Model based Monte Carlo pricing of energy and temperature quanto options," MPRA Paper 25538, University Library of Munich, Germany.
    2. Rene Carmona & Michael Coulon & Daniel Schwarz, 2012. "The Valuation of Clean Spread Options: Linking Electricity, Emissions and Fuels," Papers 1205.2302, arXiv.org.
    3. Giuseppe Benedetti & Luciano Campi, 2013. "Utility indifference valuation for non-smooth payoffs with an application to power derivatives," Papers 1307.4591, arXiv.org.
    4. Kanamura, Takashi, 2009. "A supply and demand based volatility model for energy prices," Energy Economics, Elsevier, vol. 31(5), pages 736-747, September.
    5. Furió, Dolores & Meneu, Vicente, 2010. "Expectations and forward risk premium in the Spanish deregulated power market," Energy Policy, Elsevier, vol. 38(2), pages 784-793, February.
    6. René Aid & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.
    7. Rubin, Ofir D. & Babcock, Bruce A., 2011. "A novel approach for modeling deregulated electricity markets," Energy Policy, Elsevier, vol. 39(5), pages 2711-2721, May.
    8. Viehmann, Johannes, 2011. "Risk premiums in the German day-ahead Electricity Market," Energy Policy, Elsevier, vol. 39(1), pages 386-394, January.
    9. Álvaro Cartea & Carlos González-Pedraz, 2010. "How much should we pay for interconnecting electricity markets? A real options approach," Business Economics Working Papers wb103206, Universidad Carlos III, Departamento de Economía de la Empresa.
    10. Ullrich, Carl J., 2012. "Realized volatility and price spikes in electricity markets: The importance of observation frequency," Energy Economics, Elsevier, vol. 34(6), pages 1809-1818.
    11. Lyle, Matthew R. & Elliott, Robert J., 2009. "A 'simple' hybrid model for power derivatives," Energy Economics, Elsevier, vol. 31(5), pages 757-767, September.
    12. 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.
    13. Dorfleitner, Gregor & Wimmer, Maximilian, 2010. "The pricing of temperature futures at the Chicago Mercantile Exchange," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1360-1370, June.
    14. Coulon, Michael & Powell, Warren B. & Sircar, Ronnie, 2013. "A model for hedging load and price risk in the Texas electricity market," Energy Economics, Elsevier, vol. 40(C), pages 976-988.
    15. Parpas, Panos & Webster, Mort, 2014. "A stochastic multiscale model for electricity generation capacity expansion," European Journal of Operational Research, Elsevier, vol. 232(2), pages 359-374.
    16. Rene Carmona & Michael Coulon & Daniel Schwarz, 2012. "Electricity price modeling and asset valuation: a multi-fuel structural approach," Papers 1205.2299, arXiv.org.
    17. Elliott, Robert J. & Lyle, Matthew R. & Miao, Hong, 2010. "A model for energy pricing with stochastic emission costs," Energy Economics, Elsevier, vol. 32(4), pages 838-847, July.

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