IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v9y2021i5p100-d557359.html

The Effect of Mean-Reverting Processes in the Pricing of Options in the Energy Market: An Arithmetic Approach

Author

Listed:
  • Maren Diane Schmeck

    (Center for Mathematical Economics, Bielefeld University, 33615 Bielefeld, Germany
    These authors contributed equally to this work.)

  • Stefan Schwerin

    (Independent Researcher, 51065 Cologne, Germany
    These authors contributed equally to this work.)

Abstract

In this paper we study the effect that mean-reverting components in the arithmetic dynamics of electricity spot price have on the price of a call option on a swap. Our model allows for seasonal effects, spikes, and negative values of the price of electricity. We show that for sufficiently large delivery periods of the swap contract, the error that one makes by neglecting some of the mean-reverting processes affecting the spot price evolution converges to zero. The decay rate is explicitly calculated. This is achieved by exploiting the additive structure of the electricity price process in order to determine an explicit closed-form formula for the price of the call on a swap. The theoretical analysis is then illustrated via a numerical example.

Suggested Citation

  • Maren Diane Schmeck & Stefan Schwerin, 2021. "The Effect of Mean-Reverting Processes in the Pricing of Options in the Energy Market: An Arithmetic Approach," Risks, MDPI, vol. 9(5), pages 1-19, May.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:5:p:100-:d:557359
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/9/5/100/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/9/5/100/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Piccirilli, Marco & Schmeck, Maren Diane & Vargiolu, Tiziano, 2021. "Capturing the power options smile by an additive two-factor model for overlapping futures prices," Energy Economics, Elsevier, vol. 95(C).
    2. Nomikos, Nikos K. & Soldatos, Orestes A., 2010. "Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market," Energy Economics, Elsevier, vol. 32(2), pages 302-312, March.
    3. 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.
    4. Thilo Meyer-Brandis & Peter Tankov, 2008. "Multi-Factor Jump-Diffusion Models Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 503-528.
    5. Al-Sunaidy, A. & Green, R., 2006. "Electricity deregulation in OECD (Organization for Economic Cooperation and Development) countries," Energy, Elsevier, vol. 31(6), pages 769-787.
    6. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    7. 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.
    8. Hinderks, W.J. & Wagner, A., 2020. "Factor models in the German electricity market: Stylized facts, seasonality, and calibration," Energy Economics, Elsevier, vol. 85(C).
    9. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(1), pages 53-65, March.
    10. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    11. 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.
    12. Maren Diane Schmeck, 2016. "Pricing options on forwards in energy markets: the role of mean reversion's speed," Papers 1602.03402, arXiv.org.
    13. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    14. Fanone, Enzo & Gamba, Andrea & Prokopczuk, Marcel, 2013. "The case of negative day-ahead electricity prices," Energy Economics, Elsevier, vol. 35(C), pages 22-34.
    15. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    16. repec:dau:papers:123456789/1433 is not listed on IDEAS
    17. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    18. 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.
    19. 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.
    20. 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.
    21. Thomas Deschatre & Olivier F'eron & Pierre Gruet, 2021. "A survey of electricity spot and futures price models for risk management applications," Papers 2103.16918, arXiv.org, revised Jul 2021.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Samuel Tabot Enow, 2023. "Investigating mean reversion in financial markets using Hurst Model," International Journal of Research in Business and Social Science (2147-4478), Center for the Strategic Studies in Business and Finance, vol. 12(6), pages 197-201, September.
    2. Chi Yong & Mu Tong & Zhongyi Yang & Jixian Zhou, 2023. "Conventional Natural Gas Project Investment and Decision Making under Multiple Uncertainties," Energies, MDPI, vol. 16(5), pages 1-30, February.
    3. Eduardo Abi Jaber & Soukaina Bruneau & Nathan De Carvalho & Dimitri Sotnikov & Laurent Tur, 2025. "Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration," Papers 2501.05975, arXiv.org, revised Apr 2026.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    2. Piccirilli, Marco & Schmeck, Maren Diane & Vargiolu, Tiziano, 2021. "Capturing the power options smile by an additive two-factor model for overlapping futures prices," Energy Economics, Elsevier, vol. 95(C).
    3. Thomas Deschatre & Olivier F'eron & Pierre Gruet, 2021. "A survey of electricity spot and futures price models for risk management applications," Papers 2103.16918, arXiv.org, revised Jul 2021.
    4. Albani, V.V.L. & Marcavillaca, R.T. & Moreira, P.S.E. & Avila, S.L. & Geremia, M. & Piovezan, R.P.B. & Sica, E.T. & Santos, E., 2025. "Short-term forecasting of forward prices in the Brazilian electricity market with a hybrid stochastic-neural network model," Energy Economics, Elsevier, vol. 148(C).
    5. 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.
    6. 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.
    7. Bégin, Jean-François & Gómez, Fabio & Ignatieva, Katja & Li, Han, 2025. "The stochastic behavior of electricity prices under scrutiny: Evidence from spot and futures markets," Energy Economics, Elsevier, vol. 144(C).
    8. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    9. Gonzalez, Jhonny & Moriarty, John & Palczewski, Jan, 2017. "Bayesian calibration and number of jump components in electricity spot price models," Energy Economics, Elsevier, vol. 65(C), pages 375-388.
    10. Gavronski, Pedro & De Genaro, Alan, 2026. "Jumps and jolts: A continuous-time model for electricity future contract pricing," Journal of Commodity Markets, Elsevier, vol. 41(C).
    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. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    13. Christian Laudag'e & Florian Aichinger & Sascha Desmettre, 2023. "A Comparative Study of Factor Models for Different Periods of the Electricity Spot Price Market," Papers 2306.07731, arXiv.org, revised Apr 2024.
    14. 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.
    15. 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.
    16. 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, June.
    17. Laudagé, Christian & Aichinger, Florian & Desmettre, Sascha, 2024. "A comparative study of factor models for different periods of the electricity spot price market," Journal of Commodity Markets, Elsevier, vol. 36(C).
    18. Mikkel Bennedsen, 2015. "Rough electricity: a new fractal multi-factor model of electricity spot prices," CREATES Research Papers 2015-42, Department of Economics and Business Economics, Aarhus University.
    19. Piergiacomo Sabino, 2021. "Normal Tempered Stable Processes and the Pricing of Energy Derivatives," Papers 2105.03071, arXiv.org.
    20. Carlo Mari & Emiliano Mari, 2021. "Gaussian clustering and jump-diffusion models of electricity prices: a deep learning analysis," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1039-1062, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:9:y:2021:i:5:p:100-:d:557359. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.