IDEAS home Printed from https://ideas.repec.org/a/eee/eneeco/v149y2025ics014098832500564x.html

Pricing energy futures options: The role of seasonality and liquidity

Author

Listed:
  • Chen, Wenting
  • Yang, Zhao
  • He, Xin-Jiang

Abstract

In this paper, we propose an enhanced pricing framework for energy derivatives by incorporating seasonal effects and liquidity risks into the traditional two-factor model. The main theoretical challenge lies in deriving a tractable semi-analytical solution for the price of energy futures options under this enhanced model specification, which we have successfully achieved through advanced analytical techniques. Our solution demonstrates superior computational efficiency compared to the Monte-Carlo method, and greatly facilitates the model calibration process. Empirical results reveal that the proposed model outperforms both the standard two-factor model and the model with a seasonal-only specification, validating the importance of jointly modeling seasonal factors and liquidity risks for pricing energy futures options.

Suggested Citation

  • Chen, Wenting & Yang, Zhao & He, Xin-Jiang, 2025. "Pricing energy futures options: The role of seasonality and liquidity," Energy Economics, Elsevier, vol. 149(C).
  • Handle: RePEc:eee:eneeco:v:149:y:2025:i:c:s014098832500564x
    DOI: 10.1016/j.eneco.2025.108737
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S014098832500564X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.eneco.2025.108737?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Kun Peng & Zhepeng Hu & Michel A. Robe, 2024. "Maximum order size and market quality: Evidence from a natural experiment in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(5), pages 803-825, May.
    2. Puneet Pasricha & Song-Ping Zhu & Xin-Jiang He, 2022. "A closed-form pricing formula for European options in an illiquid asset market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-18, December.
    3. Mellios, Constantin & Six, Pierre & Lai, Anh Ngoc, 2016. "Dynamic speculation and hedging in commodity futures markets with a stochastic convenience yield," European Journal of Operational Research, Elsevier, vol. 250(2), pages 493-504.
    4. Yongmin Zhang & Shusheng Ding, 2018. "Return and volatility co-movement in commodity futures markets: the effects of liquidity risk," Quantitative Finance, Taylor & Francis Journals, vol. 18(9), pages 1471-1486, September.
    5. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    6. Ugochi C. Okoroafor & Thomas Leirvik, 2024. "Dynamic link between liquidity and return in the crude oil market," Cogent Economics & Finance, Taylor & Francis Journals, vol. 12(1), pages 2302636-230, December.
    7. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    8. Iordanis Angelos Kalaitzoglou & Boulis Maher Ibrahim, 2015. "Liquidity and resolution of uncertainty in the European carbon futures market," Post-Print hal-01107956, HAL.
    9. Christian-Oliver Ewald & Ruolan Ouyang, 2017. "An Analysis of the Fish Pool Market in the Context of Seasonality and Stochastic Convenience Yield," Marine Resource Economics, University of Chicago Press, vol. 32(4), pages 431-449.
    10. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    11. Carme Frau & Viviana Fanelli, 2024. "Correction to: Seasonality in commodity prices: new approaches for pricing plain vanilla options," Annals of Operations Research, Springer, vol. 332(1), pages 1297-1297, January.
    12. He, Xin-Jiang & Wei, Wenting & Lin, Sha, 2025. "A closed-form formula for pricing exchange options with regime switching stochastic volatility and stochastic liquidity," International Review of Financial Analysis, Elsevier, vol. 103(C).
    13. Riccardo Brignone & Luca Gonzato & Carlo Sgarra, 2024. "Commodity Asian option pricing and simulation in a 4-factor model with jump clusters," Annals of Operations Research, Springer, vol. 336(1), pages 275-306, May.
    14. Kalaitzoglou, Iordanis Angelos & Ibrahim, Boulis Maher, 2015. "Liquidity and resolution of uncertainty in the European carbon futures market," International Review of Financial Analysis, Elsevier, vol. 37(C), pages 89-102.
    15. 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.
    16. Feng, Shih-Ping & Hung, Mao-Wei & Wang, Yaw-Huei, 2014. "Option pricing with stochastic liquidity risk: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 18(C), pages 77-95.
    17. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    18. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    19. Xin‐Jiang He & Hang Chen & Sha Lin, 2025. "A Closed‐Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(5), pages 429-440, May.
    20. Ewald, Christian-Oliver & Haugom, Erik & Lien, Gudbrand & Størdal, Ståle & Wu, Yuexiang, 2022. "Trading time seasonality in commodity futures: An opportunity for arbitrage in the natural gas and crude oil markets?," Energy Economics, Elsevier, vol. 115(C).
    21. Carme Frau & Viviana Fanelli, 2024. "Seasonality in commodity prices: new approaches for pricing plain vanilla options," Annals of Operations Research, Springer, vol. 336(1), pages 1089-1131, May.
    22. repec:dau:papers:123456789/607 is not listed on IDEAS
    23. Sheng-Hung Chen & Song-Zan Chiou-Wei & Zhen Zhu, 2022. "Stochastic seasonality in commodity prices: the case of US natural gas," Empirical Economics, Springer, vol. 62(5), pages 2263-2284, May.
    24. Lin, Sha & Chen, Meiling & He, Xin-Jiang, 2025. "Analytically pricing crude oil options under a jump-diffusion model with stochastic liquidity risk and convenience yield," The North American Journal of Economics and Finance, Elsevier, vol. 78(C).
    25. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    26. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    27. Kian Guan Lim & Da Zhi, 2002. "Pricing options using implied trees: Evidence from FTSE‐100 options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(7), pages 601-626, July.
    28. Pankaj K. Jain & Ayla Kayhan & Esen Onur, 2024. "Determinants of commodity market liquidity," The Financial Review, Eastern Finance Association, vol. 59(1), pages 9-30, February.
    29. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
    30. Conghui Hu & Zhibing Li & Xiaoyu Liu, 2020. "Liquidity shocks, commodity financialization, and market comovements," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(9), pages 1315-1336, September.
    31. Helyette Geman, 2005. "Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy," Post-Print halshs-00144182, HAL.
    32. Ma, Zonggang & Ma, Chaoqun & Wu, Zhijian, 2020. "Closed-form analytical solutions for options on agricultural futures with seasonality and stochastic convenience yield," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    Full references (including those not matched with items on IDEAS)

    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. Lin, Sha & Chen, Meiling & He, Xin-Jiang, 2025. "Analytically pricing crude oil options under a jump-diffusion model with stochastic liquidity risk and convenience yield," The North American Journal of Economics and Finance, Elsevier, vol. 78(C).
    2. Chen, Wenting & Huo, Zhongyao & He, Xin-Jiang, 2025. "Analytically pricing commodity futures options in a regime-switching financialization framework," Finance Research Letters, Elsevier, vol. 85(PE).
    3. Dong Yan & Xin-Jie Huang & Guiyuan Ma & Xin-Jiang He, 2025. "Pricing American options with exogenous and endogenous transaction costs," Papers 2509.00485, arXiv.org, revised Sep 2025.
    4. Shao, Chengwu & Bhar, Ramaprasad & Colwell, David B. & Sheng, Ni & Wei, Xinyang, 2024. "Variance dynamics and term structure of the natural gas market," Energy Economics, Elsevier, vol. 137(C).
    5. Cheng, Benjamin & Nikitopoulos, Christina Sklibosios & Schlögl, Erik, 2018. "Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 148-166.
    6. Ma, Zonggang & Ma, Chaoqun & Wu, Zhijian, 2020. "Closed-form analytical solutions for options on agricultural futures with seasonality and stochastic convenience yield," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    8. He, Xin-Jiang & Pasricha, Puneet & Lu, Tuantuan & Lin, Sha, 2024. "Vulnerable options with regime switching and stochastic liquidity," The Quarterly Review of Economics and Finance, Elsevier, vol. 98(C).
    9. Zhang, Hongyu & Guo, Xunxiang & Wang, Ke & Huang, Shoude, 2024. "The valuation of American options with the stochastic liquidity risk and jump risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    10. Xin‐Jiang He & Hang Chen & Sha Lin, 2025. "A Closed‐Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(5), pages 429-440, May.
    11. 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.
    12. He, Xin-Jiang & Lin, Sha, 2025. "Foreign exchange option pricing with a three-factor Heston model with regime switching and stochastic interest rate," The North American Journal of Economics and Finance, Elsevier, vol. 80(C).
    13. Sha Lin & Xin‐Jiang He, 2024. "Closed‐Form Formulae for Variance and Volatility Swaps Under Stochastic Volatility With Stochastic Liquidity Risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1447-1461, August.
    14. He, Xin-Jiang & Wei, Wenting & Lin, Sha, 2025. "A closed-form formula for pricing exchange options with regime switching stochastic volatility and stochastic liquidity," International Review of Financial Analysis, Elsevier, vol. 103(C).
    15. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    16. He, Xin-Jiang & Pasricha, Puneet & Lin, Sha, 2024. "Analytically pricing European options in dynamic markets: Incorporating liquidity variations and economic cycles," Economic Modelling, Elsevier, vol. 139(C).
    17. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    18. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, March.
    19. 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.
    20. Chris Brooks & Marcel Prokopczuk, 2013. "The dynamics of commodity prices," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 527-542, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:eee:eneeco:v:149:y:2025:i:c:s014098832500564x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eneco .

    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.