IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2101.02917.html
   My bibliography  Save this paper

Valuation of electricity storage contracts using the COS method

Author

Listed:
  • Boris C. Boonstra
  • Cornelis W. Oosterlee

Abstract

Storage of electricity has become increasingly important, due to the gradual replacement of fossil fuels by more variable and uncertain renewable energy sources. In this paper, we provide details on how to mathematically formalize a corresponding electricity storage contract, taking into account the physical limitations of a storage facility and the operational constraints of the electricity grid. We give details of a valuation technique to price these contracts, where the electricity prices follow a structural model based on a stochastic polynomial process. In particular, we show that the Fourier-based COS method can be used to price the contracts accurately and efficiently.

Suggested Citation

  • Boris C. Boonstra & Cornelis W. Oosterlee, 2021. "Valuation of electricity storage contracts using the COS method," Papers 2101.02917, arXiv.org.
    • Handle: RePEc:arx:papers:2101.02917
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2101.02917
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    3. 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.
    4. Damir Filipovic & Martin Larsson & Tony Ware, 2017. "Polynomial processes for power prices," Papers 1710.10293, arXiv.org, revised Apr 2018.
    5. Poullikkas, Andreas, 2013. "A comparative overview of large-scale battery systems for electricity storage," Renewable and Sustainable Energy Reviews, Elsevier, vol. 27(C), pages 778-788.
    6. Rafal Weron, 2014. "A review of electricity price forecasting: The past, the present and the future," HSC Research Reports HSC/14/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    7. Kempton, Willett & Tomic, Jasna & Letendre, Steven & Brooks, Alec & Lipman, Timothy, 2001. "Vehicle-to-Grid Power: Battery, Hybrid, and Fuel Cell Vehicles as Resources for Distributed Electric Power in California," Institute of Transportation Studies, Working Paper Series qt0qp6s4mb, Institute of Transportation Studies, UC Davis.
    8. Graves, Frank & Jenkin, Thomas & Murphy, Dean, 1999. "Opportunities for Electricity Storage in Deregulating Markets," The Electricity Journal, Elsevier, vol. 12(8), pages 46-56, October.
    9. Evans, Annette & Strezov, Vladimir & Evans, Tim J., 2012. "Assessment of utility energy storage options for increased renewable energy penetration," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(6), pages 4141-4147.
    10. Ahmadian, Ali & Sedghi, Mahdi & Elkamel, Ali & Fowler, Michael & Aliakbar Golkar, Masoud, 2018. "Plug-in electric vehicle batteries degradation modeling for smart grid studies: Review, assessment and conceptual framework," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P2), pages 2609-2624.
    11. Lund, Henrik & Kempton, Willett, 2008. "Integration of renewable energy into the transport and electricity sectors through V2G," Energy Policy, Elsevier, vol. 36(9), pages 3578-3587, September.
    12. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    13. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    14. Damir Filipović & Martin Larsson & Tony Ware, 2018. "Polynomial Processes for Power Prices," Swiss Finance Institute Research Paper Series 18-34, Swiss Finance Institute.
    15. 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, January.
    16. Connolly, D. & Lund, H. & Finn, P. & Mathiesen, B.V. & Leahy, M., 2011. "Practical operation strategies for pumped hydroelectric energy storage (PHES) utilising electricity price arbitrage," Energy Policy, Elsevier, vol. 39(7), pages 4189-4196, July.
    17. Kempton, Willett & Tomic, Jasna & Letendre, Steven & Brooks, Alec & Lipman, Timothy, 2001. "Vehicle-to-Grid Power: Battery, Hybrid, and Fuel Cell Vehicles as Resources for Distributed Electric Power in California," Institute of Transportation Studies, Working Paper Series qt5cc9g0jp, Institute of Transportation Studies, UC Davis.
    18. Lunz, Benedikt & Yan, Zexiong & Gerschler, Jochen Bernhard & Sauer, Dirk Uwe, 2012. "Influence of plug-in hybrid electric vehicle charging strategies on charging and battery degradation costs," Energy Policy, Elsevier, vol. 46(C), pages 511-519.
    19. Luo, Xing & Wang, Jihong & Dooner, Mark & Clarke, Jonathan, 2015. "Overview of current development in electrical energy storage technologies and the application potential in power system operation," Applied Energy, Elsevier, vol. 137(C), pages 511-536.
    20. M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298, October.
    21. Kyriakopoulos, Grigorios L. & Arabatzis, Garyfallos, 2016. "Electrical energy storage systems in electricity generation: Energy policies, innovative technologies, and regulatory regimes," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 1044-1067.
    22. 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.
    23. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    24. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
    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. Fei Gao & Shuaiqiang Liu & Cornelis W. Oosterlee & Nico M. Temme, 2022. "Solution of integrals with fractional Brownian motion for different Hurst indices," Papers 2203.02323, arXiv.org, revised Mar 2022.

    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. Filipović, Damir & Larsson, Martin & Pulido, Sergio, 2020. "Markov cubature rules for polynomial processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1947-1971.
    2. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    3. Marcelo G. Figueroa, 2006. "Pricing Multiple Interruptible-Swing Contracts," Birkbeck Working Papers in Economics and Finance 0606, Birkbeck, Department of Economics, Mathematics & Statistics.
    4. Michel Culot & Valérie Goffin & Steve Lawford & Sébastien de Meten & Yves Smeers, 2013. "Practical stochastic modelling of electricity prices," Post-Print hal-01021603, HAL.
    5. Max F. Schöne & Stefan Spinler, 2017. "A four-factor stochastic volatility model of commodity prices," Review of Derivatives Research, Springer, vol. 20(2), pages 135-165, July.
    6. Hanfeld, Marc & Schlüter, Stephan, 2016. "Operating a swing option on today's gas markets: How least squares Monte Carlo works and why it is beneficial," FAU Discussion Papers in Economics 10/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. Lund, Henrik & Andersen, Anders N. & Østergaard, Poul Alberg & Mathiesen, Brian Vad & Connolly, David, 2012. "From electricity smart grids to smart energy systems – A market operation based approach and understanding," Energy, Elsevier, vol. 42(1), pages 96-102.
    8. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    9. Antweiler, Werner, 2021. "Microeconomic models of electricity storage: Price Forecasting, arbitrage limits, curtailment insurance, and transmission line utilization," Energy Economics, Elsevier, vol. 101(C).
    10. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    11. Nicola Cufaro Petroni & Piergiacomo Sabino, 2019. "Fast Pricing of Energy Derivatives with Mean-reverting Jump-diffusion Processes," Papers 1908.03137, arXiv.org, revised Mar 2020.
    12. Ren, Guorui & Liu, Jinfu & Wan, Jie & Guo, Yufeng & Yu, Daren, 2017. "Overview of wind power intermittency: Impacts, measurements, and mitigation solutions," Applied Energy, Elsevier, vol. 204(C), pages 47-65.
    13. Cartea, Álvaro & Williams, Thomas, 2008. "UK gas markets: The market price of risk and applications to multiple interruptible supply contracts," Energy Economics, Elsevier, vol. 30(3), pages 829-846, May.
    14. Piergiacomo Sabino, 2021. "Normal Tempered Stable Processes and the Pricing of Energy Derivatives," Papers 2105.03071, arXiv.org.
    15. Zhong, Jin & He, Lina & Li, Canbing & Cao, Yijia & Wang, Jianhui & Fang, Baling & Zeng, Long & Xiao, Guoxuan, 2014. "Coordinated control for large-scale EV charging facilities and energy storage devices participating in frequency regulation," Applied Energy, Elsevier, vol. 123(C), pages 253-262.
    16. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.
    17. 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).
    18. Zhang, Hanyu & Assereto, Martina & Byrne, Julie, 2023. "Deferring real options with solar renewable energy certificates," Global Finance Journal, Elsevier, vol. 55(C).
    19. Larsson, Karl & Nossman, Marcus, 2011. "Jumps and stochastic volatility in oil prices: Time series evidence," Energy Economics, Elsevier, vol. 33(3), pages 504-514, May.
    20. Cortazar, Gonzalo & Naranjo, Lorenzo & Sainz, Felipe, 2021. "Optimal decision policy for real options under general Markovian dynamics," European Journal of Operational Research, Elsevier, vol. 288(2), pages 634-647.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2101.02917. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.