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Model based Monte Carlo pricing of energy and temperature quanto options


  • Caporin, Massimiliano
  • Pres, Juliusz
  • Torro, Hipolit


Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the Black-Scholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.

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  • Caporin, Massimiliano & Pres, Juliusz & Torro, Hipolit, 2010. "Model based Monte Carlo pricing of energy and temperature quanto options," MPRA Paper 25538, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:25538

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    1. Lunina, Veronika, 2016. "Joint Modelling of Power Price, Temperature, and Hydrological Balance with a View towards Scenario Analysis," Working Papers 2016:30, Lund University, Department of Economics.
    2. Thakur, Jagruti & Hesamzadeh, Mohammad Reza & Date, Paresh & Bunn, Derek, 2023. "Pricing and hedging wind power prediction risk with binary option contracts," Energy Economics, Elsevier, vol. 126(C).
    3. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, June.
    4. Fred Espen Benth, 2021. "Pricing of Commodity and Energy Derivatives for Polynomial Processes," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    5. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943,
    6. Massimiliano Caporin & Fulvio Fontini & Paolo Santucci De Magistris, 2017. "Price convergence within and between the Italian electricity day-ahead and dispatching services markets," "Marco Fanno" Working Papers 0215, Dipartimento di Scienze Economiche "Marco Fanno".
    7. Khalifa, Ahmed & Caporin, Massimiliano & Hammoudeh, Shawkat, 2015. "Spillovers between energy and FX markets: The importance of asymmetry, uncertainty and business cycle," Energy Policy, Elsevier, vol. 87(C), pages 72-82.
    8. Angelica Gianfreda & Derek Bunn, 2018. "A Stochastic Latent Moment Model for Electricity Price Formation," BEMPS - Bozen Economics & Management Paper Series BEMPS46, Faculty of Economics and Management at the Free University of Bozen.
    9. Cui, Hairong & Zhou, Ying & Dzandu, Michael D. & Tang, Yinshan & Lu, Xunfa, 2019. "Is temperature-index derivative suitable for China?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    10. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    11. Baltuttis, Dennik & Töppel, Jannick & Tränkler, Timm & Wiethe, Christian, 2020. "Managing the risks of energy efficiency insurances in a portfolio context: An actuarial diversification approach," International Review of Financial Analysis, Elsevier, vol. 68(C).
    12. Laura Casula & Guglielmo D’Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of photovoltaic energy production," Letters in Spatial and Resource Sciences, Springer, vol. 13(3), pages 267-285, December.
    13. Giovanni Masala & Marco Micocci & Andrea Rizk, 2022. "Hedging Wind Power Risk Exposure through Weather Derivatives," Energies, MDPI, vol. 15(4), pages 1-30, February.
    14. Aur'elien Alfonsi & Nerea Vadillo, 2023. "Risk valuation of quanto derivatives on temperature and electricity," Papers 2310.07692,, revised Apr 2024.
    15. Rodwell Kufakunesu & Farai Mhlanga, 2018. "On the sensitivity analysis of energy quanto options," Papers 1810.06335,
    16. Mosquera-López, Stephania & Uribe, Jorge M., 2022. "Pricing the risk due to weather conditions in small variable renewable energy projects," Applied Energy, Elsevier, vol. 322(C).

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    More about this item


    weather derivatives; Quanto options pricing; derivative pricing; model simulation; forecast;
    All these keywords.

    JEL classification:

    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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