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Putting a price tag on temperature

Author

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  • Heng Xiong

    (University of Western Ontario)

  • Rogemar Mamon

    (University of Western Ontario
    University of the Philippines Visayas)

Abstract

A model for the evolution of daily average temperatures (DATs) is put forward to support the analysis of weather derivatives. The goal is to capture simultaneously the stochasticity, mean-reversion, and seasonality patterns of the DATs process. An Ornstein–Uhlenbeck (OU) process modulated by a hidden Markov chain (HMC) is proposed to model both the mean-reversion and stochasticity of a deseasonalised component. The seasonality part is modelled by a combination of linear and sinusoidal functions. Modified and more efficient OU–HMM filtering algorithms relative to the current ones in the literature are presented for the evolution of adaptive and switching model parameter estimates. Numerical implementation of the estimation technique using a 4-year Toronto temperature data set compiled by the National Climatic Data Center was conducted. A sensitivity analysis of the option prices with respect to model parameters is included.

Suggested Citation

  • Heng Xiong & Rogemar Mamon, 2018. "Putting a price tag on temperature," Computational Management Science, Springer, vol. 15(2), pages 259-296, June.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:2:d:10.1007_s10287-017-0291-8
    DOI: 10.1007/s10287-017-0291-8
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    References listed on IDEAS

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    1. Fred Espen Benth & Jurate Saltyte-Benth, 2005. "Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 53-85.
    2. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
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    5. Xi, Xiaojing & Mamon, Rogemar, 2011. "Parameter estimation of an asset price model driven by a weak hidden Markov chain," Economic Modelling, Elsevier, vol. 28(1-2), pages 36-46, January.
    6. Dorfleitner, Gregor & Wimmer, Maximilian, 2010. "The pricing of temperature futures at the Chicago Mercantile Exchange," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1360-1370, June.
    7. Tak Kuen Siu & Christina Erlwein & Rogemar Mamon, 2008. "The Pricing of Credit Default Swaps under a Markov-Modulated Merton’s Structural Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 18-46.
    8. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    9. Xi, Xiaojing & Mamon, Rogemar, 2011. "Parameter estimation of an asset price model driven by a weak hidden Markov chain," Economic Modelling, Elsevier, vol. 28(1), pages 36-46.
    10. Oliver Musshoff, 2008. "Indifference Pricing of Weather Derivatives," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 90(4), pages 979-993.
    11. Erlwein, Christina & Benth, Fred Espen & Mamon, Rogemar, 2010. "HMM filtering and parameter estimation of an electricity spot price model," Energy Economics, Elsevier, vol. 32(5), pages 1034-1043, September.
    12. Melanie Cao & Jason Wei, 2004. "Weather derivatives valuation and market price of weather risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(11), pages 1065-1089, November.
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    14. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming, 2017. "Risk measurement of a guaranteed annuity option under a stochastic modelling framework," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 100-119.
    15. Fred Benth & Wolfgang Karl Härdle & Brenda López Cabrera, 2009. "Pricing of Asian temperature risk," SFB 649 Discussion Papers SFB649DP2009-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
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    18. Helyette Geman & M. Leonardi, 2005. "Alternative Approaches to Weather Derivatives Pricing," Post-Print halshs-00144304, HAL.
    19. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 87-107, March.
    20. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
    21. repec:dau:papers:123456789/1386 is not listed on IDEAS
    22. Elias, R.S. & Wahab, M.I.M. & Fang, L., 2014. "A comparison of regime-switching temperature modeling approaches for applications in weather derivatives," European Journal of Operational Research, Elsevier, vol. 232(3), pages 549-560.
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    Cited by:

    1. Xiong, Heng & Mamon, Rogemar, 2019. "A higher-order Markov chain-modulated model for electricity spot-price dynamics," Applied Energy, Elsevier, vol. 233, pages 495-515.

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