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The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets

Author

Listed:
  • Kemper, Annika

    (Center for Mathematical Economics, Bielefeld University)

  • Schmeck, Maren Diane

    (Center for Mathematical Economics, Bielefeld University)

  • Khripunova Balci, Anna

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an arbitrage-free pricing framework for derivatives based on these contracts. Furthermore, we use a weighted geometric averaging of an artificial geometric futures price over the corresponding delivery period. Without any need for approximations, this averaging results in geometric swap price dynamics. Our framework allows for including typical features as the Samuelson effect, seasonalities, and stochastic volatility. In particular, we investigate the pricing procedures for electricity swaps and options in line with Arismendi et al. (2016), Schneider and Tavin (2018), and Fanelli and Schmeck (2019). A numerical study highlights the differences between these models depending on the delivery period.

Suggested Citation

  • Kemper, Annika & Schmeck, Maren Diane & Khripunova Balci, Anna, 2020. "The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets," Center for Mathematical Economics Working Papers 635, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:635
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    File URL: https://pub.uni-bielefeld.de/download/2943342/2943343
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    References listed on IDEAS

    as
    1. Bertrand Tavin & Lorenz Schneider, 2018. "From the Samuelson volatility effect to a Samuelson correlation effect : An analysis of crude oil calendar spread options," Post-Print hal-02311970, HAL.
    2. Bertram During & Michel Fourni'e & Christof Heuer, 2014. "High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids," Papers 1404.5138, arXiv.org.
    3. Maren Diane Schmeck, 2016. "Pricing options on forwards in energy markets: the role of mean reversion's speed," Papers 1602.03402, arXiv.org.
    4. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    5. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    6. Viviana Fanelli & Maren Diane Schmeck, 2019. "On the seasonality in the implied volatility of electricity options," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1321-1337, August.
    7. Rudiger Kiesel & Gero Schindlmayr & Reik Borger, 2009. "A two-factor model for the electricity forward market," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 279-287.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Arismendi, Juan C. & Back, Janis & Prokopczuk, Marcel & Paschke, Raphael & Rudolf, Markus, 2016. "Seasonal Stochastic Volatility: Implications for the pricing of commodity options," Journal of Banking & Finance, Elsevier, vol. 66(C), pages 53-65.
    10. Schneider, Lorenz & Tavin, Bertrand, 2018. "From the Samuelson volatility effect to a Samuelson correlation effect: An analysis of crude oil calendar spread options," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 185-202.
    11. Maren Diane Schmeck, 2016. "Pricing Options On Forwards In Energy Markets: The Role Of Mean Reversion'S Speed," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-26, December.
    12. Fred Espen Benth & Marco Piccirilli & Tiziano Vargiolu, 2017. "Additive energy forward curves in a Heath-Jarrow-Morton framework," Papers 1709.03310, arXiv.org, revised Jun 2018.
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