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Seasonal Stochastic Volatility: Implications for the Pricing of Commodity Options

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  • Janis Back

    (WHU - Otto Beisheim School of Management)

  • Marcel Prokopczuk

    (ICMA Centre, Henley Business School, University of Reading)

  • Markus Rudolf

    (WHU - Otto Beisheim School of Management)

Abstract

Many commodity markets contain a strong seasonal component in volatility. In this paper, the importance of this seasonal behavior for the pricing of commodity options is analyzed. We propose a stochastic volatility model where the drift term of the variance process captures the observed seasonal pattern in volatility. This framework allows us to derive semi-closed-form pricing formulas for the valuation of options on commodity futures. In the main part of the paper, we empirically study the impact of the proposed seasonal stochastic volatility model on the pricing accuracy of natural gas futures options traded at the New York Mercantile Exchange (NYMEX). Our results demonstrate that allowing stochastic volatility to fluctuate seasonally significantly reduces pricing errors for these contracts.

Suggested Citation

  • Janis Back & Marcel Prokopczuk & Markus Rudolf, 2011. "Seasonal Stochastic Volatility: Implications for the Pricing of Commodity Options," ICMA Centre Discussion Papers in Finance icma-dp2011-16, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2011-16
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    3. 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.
    4. Lorenz Schneider & Bertrand Tavin, 2015. "Seasonal Stochastic Volatility and Correlation together with the Samuelson Effect in Commodity Futures Markets," Papers 1506.05911, arXiv.org.
    5. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    6. 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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    10. 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).
    11. Lorenz Schneider & Bertrand Tavin, 2018. "Seasonal Stochastic Volatility and the Samuelson Effect in Agricultural Futures Markets," Papers 1802.01393, arXiv.org, revised Nov 2018.
    12. Roncoroni, Andrea & Prokopczuk, Marcel & Ronn, Ehud I., 2018. "Introduction—special issue on commodity and energy markets in the Journal of Banking and Finance," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 1-4.
    13. Cagatay Basarir & Mehmet Fatih Bayramoglu, 2018. "Global Macroeconomic Determinants of the Domestic Commodity Derivatives," Contributions to Economics, in: Hasan Dincer & Ümit Hacioglu & Serhat Yüksel (ed.), Global Approaches in Financial Economics, Banking, and Finance, chapter 0, pages 331-349, Springer.
    14. Proelss, Juliane & Schweizer, Denis & Seiler, Volker, 2020. "The economic importance of rare earth elements volatility forecasts," International Review of Financial Analysis, Elsevier, vol. 71(C).
    15. 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.
    16. Chen, Yu-Fu & Mu, Xiaoyi, 2021. "Asymmetric volatility in commodity markets," Journal of Commodity Markets, Elsevier, vol. 22(C).
    17. Chih-Chen Hsu & An-Sing Chen & Shih-Kuei Lin & Ting-Fu Chen, 2017. "The affine styled-facts price dynamics for the natural gas: evidence from daily returns and option prices," Review of Quantitative Finance and Accounting, Springer, vol. 48(3), pages 819-848, April.
    18. Alfeus, Mesias & Nikitopoulos, Christina Sklibosios, 2022. "Forecasting volatility in commodity markets with long-memory models," Journal of Commodity Markets, Elsevier, vol. 28(C).
    19. Ignatieva, Katja & Wong, Patrick, 2022. "Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models," Energy Economics, Elsevier, vol. 108(C).
    20. Branger, Nicole & Herold, Michael & Muck, Matthias, 2021. "International stochastic discount factors and covariance risk," Journal of Banking & Finance, Elsevier, vol. 123(C).
    21. 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).
    22. Janis Back & Marcel Prokopczuk, 2013. "Commodity Price Dynamics And Derivative Valuation: A Review," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-30.

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    More about this item

    Keywords

    Commodities; Seasonality; Stochastic volatility; Options pricing; Natural gas;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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