Pricing Temperature Derivatives

  • Antonis K. Alexandridis
  • Achilleas D. Zapranis


In this chapter, pricing formulas for weather derivatives on various temperature indices will be derived. The model that developed in the previous chapter described the daily dynamics of the temperature. Hence, it can be applied in order to estimate the various indices. This model is used for the pricing on futures and options written on various temperature indices used in the weather market. First, the pricing formulas are derived under the assumption of normally distributed residuals. Next, since our results in the previous chapter indicate that the hyperbolic distribution provides the best fit to the residuals, the pricing formulas are derived under the assumption of a Lévy motion driven process.


Market Price Future Price Temperature Index Incomplete Market Temperature Contract 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alaton P, Djehince B, Stillberg D (2002) On modelling and pricing weather derivatives. Appl Math Finance 9:1–20CrossRefGoogle Scholar
  2. Bellini F (2005) The weather derivatives market: modelling and pricing temperature. Ph.D. Thesis, University of Lugano, LuganoGoogle Scholar
  3. Benth FE (2003) On arbitrage-free pricing of weather derivatives based on fractional Brownian motion. Appl Math Finance 10:303–324CrossRefGoogle Scholar
  4. Benth FE (2004) Option theory with stochastic analysis. Springer, BerlinCrossRefGoogle Scholar
  5. Benth FE, Hardle WK, Lopez Cabrera B (2009) Pricing of Asian temperature risk. SFB649 working paper. Humboldt-Universitat zu Berlin, BerlinGoogle Scholar
  6. Benth FE, Saltyte-Benth J (2004) The normal inverse Gaussian distribution and spot price modeling in energy markets. Int J Theor Appl Finance 7(2):177–192. doi: 10.1142/S0219024904002360 CrossRefGoogle Scholar
  7. Benth FE, Saltyte-Benth J (2005) Stochastic modelling of temperature variations with a view towards weather derivatives. Appl Math Finance 12(1):53–85CrossRefGoogle Scholar
  8. Benth FE, Saltyte-Benth J (2007) The volatility of temperature and pricing of weather derivatives. Quant Finance 7(5):553–561CrossRefGoogle Scholar
  9. Benth FE, Saltyte-Benth J, Koekebakker S (2008) Stochastic modelling of electricity and related markets, vol 11, Advance series on statistical science & applied probability. World Scientific, SingaporeGoogle Scholar
  10. Brockwell PJ, Marquardt T (2005) Levy-driven and fractionality integrated ARMA process with continuous time parameter. Statistica Sinica 15:477–494Google Scholar
  11. Brody CD, Syroka J, Zervos M (2002) Dynamical pricing of weather derivatives. Quant Finance 2:189–198CrossRefGoogle Scholar
  12. Cao M, Wei J (2004) Weather derivatives valuation and market price of weather risk. J Future Markets 24(1):1065–1089CrossRefGoogle Scholar
  13. Carr M, Madan DB (1999) Option valuation using the fast fourier transform. J Comput Finance 2(4):61–73Google Scholar
  14. Davis M (2001) Pricing weather derivatives by marginal value. Quant Finance 1:1–4Google Scholar
  15. Garman M, Blanco C, Erickson R (2000) Weather derivatives: instruments and pricing issues. Environ FinanceGoogle Scholar
  16. Geman H (1999) Insurance and weather derivatives. RISK Books, LondonGoogle Scholar
  17. Hardle WK, Lopez Cabrera B (2009) Infering the market price of weather risk. SFB649 working paper. Humboldt-Universitat zu Berlin, BerlinGoogle Scholar
  18. Huang H-H, Shiu Y-M, Lin P-S (2008) HDD and CDD option pricing with market price of weather risk for Taiwan. J Futures Markets 28(8):790–814CrossRefGoogle Scholar
  19. Ikeda N, Watanabe S (1981) Stochastic differential equations and diffusion processes. North-Holland/Kodansha, TokyoGoogle Scholar
  20. Jewson S, Brix A, Ziehmann C (2005) Weather derivative valuation: the meteorological, statistical, financial and mathematical foundations. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  21. Platen E, West J (2005) A fair pricing approach to weather derivatives. Asia-Pacific Financial Markets 11:23–53CrossRefGoogle Scholar
  22. Richards TJ, Manfredo MR, Sanders DR (2004) Pricing weather derivatives. Am J Agricul Econ 4(86):1005–1017CrossRefGoogle Scholar
  23. Turvey CG (2005) The pricing of degree-day weather options. Agricul Finance Rev 2005:59–85CrossRefGoogle Scholar
  24. Xu W, Odening M, Musshof O (2008) Indifference pricing of weather derivatives. Am J Agricul Econ 90(4):979–993CrossRefGoogle Scholar
  25. Zapranis A, Alexandridis A (2008) Modelling temperature time dependent speed of mean reversion in the context of weather derivative pricing. Appl Math Finance 15(4):355–386CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Antonis K. Alexandridis
    • 1
  • Achilleas D. Zapranis
    • 2
  1. 1.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterburyUK
  2. 2.Department of Accounting and FinanceUniversity of MacedoniaThessalonikiGreece

Personalised recommendations