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The market price of jump risk for delivery periods: pricing of electricity swaps with geometric averaging

Author

Listed:
  • Annika Kemper

    (Center for Mathematical Economics (IMW) at Bielefeld University)

  • Maren Diane Schmeck

    (Center for Mathematical Economics (IMW) at Bielefeld University)

Abstract

In this paper, we extend the market price of risk for delivery periods (MPDP) of electricity swap contracts by introducing a dimension for jump risk. As introduced by Kemper et al. [30], the MPDP arises through the use of geometric averaging while pricing electricity swaps in a geometric framework. We adjust the work by Kemper et al. [30] in two directions: First, we examine a Merton type model taking jumps into account. Second, we transfer the model to the physical measure by implementing mean-reverting behavior. We compare swap prices resulting from the arithmetic (approximated) average to the geometric weighted average. Under the physical measure, we discover a decomposition of the swap’s market price of risk into the instantaneous market price of risk and the MPDP.

Suggested Citation

  • Annika Kemper & Maren Diane Schmeck, 2025. "The market price of jump risk for delivery periods: pricing of electricity swaps with geometric averaging," Mathematics and Financial Economics, Springer, volume 19, number 3, December.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:2:d:10.1007_s11579-025-00383-5
    DOI: 10.1007/s11579-025-00383-5
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    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. Xi Kleisinger-Yu & Vlatka Komaric & Martin Larsson & Markus Regez, 2019. "A multi-factor polynomial framework for long-term electricity forwards with delivery period," Papers 1908.08954, arXiv.org, revised Jun 2020.
    3. Markus Burger & Bernhard Klar & Alfred Muller & Gero Schindlmayr, 2004. "A spot market model for pricing derivatives in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 109-122.
    4. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    5. 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.
    6. Hinderks, W.J. & Wagner, A., 2020. "Factor models in the German electricity market: Stylized facts, seasonality, and calibration," Energy Economics, Elsevier, vol. 85(C).
    7. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, April.
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Jaeck, Edouard & Lautier, Delphine, 2016. "Volatility in electricity derivative markets: The Samuelson effect revisited," Energy Economics, Elsevier, vol. 59(C), pages 300-313.
    10. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    11. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
    12. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    13. Claudia Kluppelberg & Thilo Meyer-Brandis & Andrea Schmidt, 2010. "Electricity spot price modelling with a view towards extreme spike risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 963-974.
    14. repec:eme:mfppss:03074350510769703 is not listed on IDEAS
    15. 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.
    16. 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.
    17. W.J. Hinderks & R. Korn & A. Wagner, 2020. "A structural Heath–Jarrow–Morton framework for consistent intraday spot and futures electricity prices," Quantitative Finance, Taylor & Francis Journals, vol. 20(3), pages 347-357, March.
    18. Annika Kemper & Maren D. Schmeck & Anna Kh. Balci, 2020. "The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets," Papers 2002.07561, arXiv.org, revised Jun 2022.
    19. Les Clewlow & Chris Strickland, 1999. "Valuing Energy Options in a One Factor Model Fitted to Forward Prices," Research Paper Series 10, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. 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.
    21. Latini, Luca & Piccirilli, Marco & Vargiolu, Tiziano, 2019. "Mean-reverting no-arbitrage additive models for forward curves in energy markets," Energy Economics, Elsevier, vol. 79(C), pages 157-170.
    22. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.
    23. Edouard Jaeck & Delphine Lautier, 2016. "Volatility in electricity derivative markets: the Samuelson effect revisited," Post-Print hal-01488127, HAL.
    24. Antonis Papapantoleon, 2008. "An introduction to L\'{e}vy processes with applications in finance," Papers 0804.0482, arXiv.org, revised Nov 2008.
    25. Christa Cuchiero & Luca Di Persio & Francesco Guida & Sara Svaluto-Ferro, 2022. "Measure-valued processes for energy markets," Papers 2210.09331, arXiv.org.
    26. Paraschiv, Florentina & Erni, David & Pietsch, Ralf, 2014. "The impact of renewable energies on EEX day-ahead electricity prices," Energy Policy, Elsevier, vol. 73(C), pages 196-210.
    27. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    28. Kemper, Annika & Schmeck, Maren Diane & Kh.Balci, Anna, 2022. "The market price of risk for delivery periods: Pricing swaps and options in electricity markets," Energy Economics, Elsevier, vol. 113(C).
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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