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Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing

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  • A. Zapranis
  • A. Alexandridis

Abstract

In this paper, in the context of an Ornstein-Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non-parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent.

Suggested Citation

  • A. Zapranis & A. Alexandridis, 2008. "Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 355-386.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:355-386
    DOI: 10.1080/13504860802006065
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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.
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    3. Jewson,Stephen & Brix,Anders With contributions by-Name:Ziehmann,Christine, 2005. "Weather Derivative Valuation," Cambridge Books, Cambridge University Press, number 9780521843713, October.
    4. 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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    6. Fred ESPEN Benth & Jurate saltyte Benth, 2007. "The volatility of temperature and pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 553-561.
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    Cited by:

    1. Hainaut, Donatien, 2018. "Hedging of crop harvest with derivatives on temperature," LIDAM Discussion Papers ISBA 2018012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Gunther Leobacher & Philip Ngare, 2011. "On Modelling and Pricing Rainfall Derivatives with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 71-91.
    3. Ahmet Göncü, 2013. "Comparison of temperature models using heating and cooling degree days futures," Journal of Risk Finance, Emerald Group Publishing, vol. 14(2), pages 159-178, February.
    4. Rui Zhou & Johnny Siu-Hang Li & Jeffrey Pai, 2019. "Pricing temperature derivatives with a filtered historical simulation approach," The European Journal of Finance, Taylor & Francis Journals, vol. 25(15), pages 1462-1484, October.
    5. Andrea Barth & Fred Espen Benth & Jurgen Potthoff, 2011. "Hedging of Spatial Temperature Risk with Market-Traded Futures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(2), pages 93-117.
    6. 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).
    7. 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.
    8. Wei Yuan & Ahmet Göncü & Giray Ökten, 2015. "Estimating sensitivities of temperature-based weather derivatives," Applied Economics, Taylor & Francis Journals, vol. 47(19), pages 1942-1955, April.
    9. 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, October.
    10. Šaltytė Benth, Jūratė & Benth, Fred Espen, 2012. "A critical view on temperature modelling for application in weather derivatives markets," Energy Economics, Elsevier, vol. 34(2), pages 592-602.
    11. Tellez Gaytán, Jesús Cuauhtémoc & Serrano Acevedo, María Eugenia & Rico Arias, Jaime Ángel, 2014. "Modelación del clima bajo un proceso estocástico de reversión a la media estacional / Modeling weather under a seasonal mean reversion stochastic process," Estocástica: finanzas y riesgo, Departamento de Administración de la Universidad Autónoma Metropolitana Unidad Azcapotzalco, vol. 4(1), pages 9-32, enero-jun.
    12. Eirini Konstantinidi & Gkaren Papazian & George Skiadopoulos, 2015. "Modeling the Dynamics of Temperature with a View to Weather Derivatives," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 17, pages 511-544, World Scientific Publishing Co. Pte. Ltd..
    13. Alexandridis, Antonis K. & Kampouridis, Michael & Cramer, Sam, 2017. "A comparison of wavelet networks and genetic programming in the context of temperature derivatives," International Journal of Forecasting, Elsevier, vol. 33(1), pages 21-47.
    14. Beyazıt, Mehmet Fuat & Koc, Erdogan, 2010. "An analysis of snow options for ski resort establishments," Tourism Management, Elsevier, vol. 31(5), pages 676-683.
    15. Hainaut, Donatien, 2019. "Hedging of crop harvest with derivatives on temperature," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 98-114.

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