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Putting a Price on Temperature

  • FRED ESPEN BENTH
  • JŪRATĖ SALTYTĖ BENTH
  • STEEN KOEKEBAKKER

This paper analyzes the weather derivatives traded at the Chicago Mercantile Exchange (CME), with futures and options written on different temperature indices. We propose to model the temperature dynamics as a continuous-time autoregressive process with lag "p" and seasonal variation. The choice ""p"=3" turns out to be sufficient to explain the temperature dynamics observed in Stockholm, Sweden, where we fit the model to more than 40 years of daily observations. The main finding is a clear seasonal variation in the regression residuals, where temperature shows high variability in winter, low in autumn and spring, and increasing variability towards the early summer. Our model allows for derivations of explicit prices for several futures and options. Note that the volatility term structure of futures written on the cumulative average temperature has a "modified" Samuelson effect, where the volatility prior to the measurement period increases, except for the last part, where it may decrease. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

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Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

Volume (Year): 34 (2007)
Issue (Month): 4 ()
Pages: 746-767

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Handle: RePEc:bla:scjsta:v:34:y:2007:i:4:p:746-767
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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series 2004/10, Center for Financial Studies (CFS).
  3. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
  4. Henghsiu Tsai & K. S. Chan, 2005. "A note on non-negative continuous time processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 589-597.
  5. 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.
  6. 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.
  7. 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.
  8. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308.
  9. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 23-53, March.
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