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Derivatives pricing in energy markets: an infinite dimensional approach

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  • Fred Espen Benth
  • Paul Kruhner

Abstract

Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions on a Hilbert space, and options can thus be viewed as derivatives on the whole curve. The value of these options are computed under various specifications, in addition to their deltas. In a second part, cross-commodity models are investigated, leading to a study of square integrable random variables with values in a "two-dimensional" Hilbert space. We analyse the covariance operator and representations of such variables, as well as presenting applications to pricing of spread and energy quanto options.

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  • Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    • Handle: RePEc:arx:papers:1412.7943
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    References listed on IDEAS

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    1. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    2. Caporin, Massimiliano & Preś, Juliusz & Torro, Hipolit, 2012. "Model based Monte Carlo pricing of energy and temperature Quanto options," Energy Economics, Elsevier, vol. 34(5), pages 1700-1712.
    3. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling electricity forward markets by ambit fields," CREATES Research Papers 2010-41, Department of Economics and Business Economics, Aarhus University.
    4. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    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.
    6. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, Department of Economics and Business Economics, Aarhus University.
    7. Fred Benth & Jukka Lempa, 2014. "Optimal portfolios in commodity futures markets," Finance and Stochastics, Springer, vol. 18(2), pages 407-430, April.
    8. 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.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    10. Helyette Geman, 2005. "Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy," Post-Print halshs-00144182, HAL.
    11. Frestad, Dennis, 2008. "Common and unique factors influencing daily swap returns in the Nordic electricity market, 1997-2005," Energy Economics, Elsevier, vol. 30(3), pages 1081-1097, May.
    12. Dennis Frestad & Fred Espen Benth & Steen Koekebakker, 2010. "Modeling Term Structure Dynamics in the Nordic Electricity Swap Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 53-86.
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