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Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives

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  • Fred Espen Benth
  • Jurate Saltyte-Benth

Abstract

Daily average temperature variations are modelled with a mean-reverting Ornstein-Uhlenbeck process driven by a generalized hyperbolic Levy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean-reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME).

Suggested Citation

  • 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.
  • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:53-85
    DOI: 10.1080/1350486042000271638
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    References listed on IDEAS

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    1. 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.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    4. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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    Citations

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    Cited by:

    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. Romain Biard & Christophette Blanchet-Scalliet & Anne Eyraud-Loisel & Stéphane Loisel, 2013. "Impact of Climate Change on Heat Wave Risk," Risks, MDPI, Open Access Journal, vol. 1(3), pages 1-16, December.
    3. Wolfgang Karl Härdle & Brenda López-Cabrera & Matthias Ritter, 2012. "Forecast based Pricing of Weather Derivatives," SFB 649 Discussion Papers SFB649DP2012-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Markus Hess, 2016. "Modeling And Pricing Precipitation Derivatives Under Weather Forecasts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-29, November.
    5. Benth, Fred Espen & Taib, Che Mohd Imran Che, 2013. "On the speed towards the mean for continuous time autoregressive moving average processes with applications to energy markets," Energy Economics, Elsevier, vol. 40(C), pages 259-268.
    6. 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.
    7. Christos Floros, 2011. "On the relationship between weather and stock market returns," Studies in Economics and Finance, Emerald Group Publishing, vol. 28(1), pages 5-13, March.
    8. Adam Clements & A S Hurn & K A Lindsay, 2008. "Estimating the Payoffs of Temperature-based Weather Derivatives," NCER Working Paper Series 33, National Centre for Econometric Research.
    9. 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.
    10. Adam Clements & A S Hurn & K A Lindsay, 2008. "Developing analytical distributions for temperature indices for the purposes of pricing temperature-based weather derivatives," NCER Working Paper Series 34, National Centre for Econometric Research.
    11. Song Song & Wolfgang K. Härdle & Ya'acov Ritov, 2010. "High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model," SFB 649 Discussion Papers SFB649DP2010-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Dupuis, Debbie J., 2011. "Forecasting temperature to price CME temperature derivatives," International Journal of Forecasting, Elsevier, vol. 27(2), pages 602-618, April.
    13. 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.
    14. Xiaofeng Cao & Ostap Okhrin & Martin Odening & Matthias Ritter, 2015. "Modelling spatio-temporal variability of temperature," Computational Statistics, Springer, vol. 30(3), pages 745-766, September.
    15. Ahčan, Aleš, 2012. "Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 131-138.
    16. 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.
    17. FRED ESPEN BENTH & JŪRATĖ SALTYTĖ BENTH & STEEN KOEKEBAKKER, 2007. "Putting a Price on Temperature," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 746-767.
    18. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856, HAL.
    19. Dupuis, Debbie J., 2011. "Forecasting temperature to price CME temperature derivatives," International Journal of Forecasting, Elsevier, vol. 27(2), pages 602-618.
    20. 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.
    21. Gülpınar, Nalân & Çanakoḡlu, Ethem, 2017. "Robust portfolio selection problem under temperature uncertainty," European Journal of Operational Research, Elsevier, vol. 256(2), pages 500-523.
    22. Hélène Hamisultane, 2008. "Sunshine-Factor Model with Treshold GARCH for Predicting Temperature of Weather Contracts," Working Papers halshs-00355857, HAL.
    23. Benth, Fred Espen & Saltyte Benth, Jurate, 2009. "Dynamic pricing of wind futures," Energy Economics, Elsevier, vol. 31(1), pages 16-24, January.

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