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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. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Fred Espen Benth, 2003. "On arbitrage-free pricing of weather derivatives based on fractional Brownian motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 303-324.
    3. 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.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. 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.
    6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    7. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    8. 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.
    9. Fred Espen Benth & Lars Ekeland & Ragnar Hauge & BjøRn Fredrik Nielsen, 2003. "A note on arbitrage-free pricing of forward contracts in energy markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 325-336.
    10. 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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