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Developing analytical distributions for temperature indices for the purposes of pricing temperature-based weather derivatives

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Author Info

  • Adam Clements

    ()
    (QUT)

  • A S Hurn

    ()
    (QUT)

  • K A Lindsay

    ()
    (University of Glasgow)

Abstract

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If deviations of daily temperature from its expected value is modelled as an Ornstein-Uhlenbeck process with time-varying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records is a particulary poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.

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File URL: http://www.ncer.edu.au/papers/documents/NCER_WpNo34Sep08.pdf
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Bibliographic Info

Paper provided by National Centre for Econometric Research in its series NCER Working Paper Series with number 34.

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Length: 25
Date of creation: 15 Sep 2008
Date of revision:
Handle: RePEc:qut:auncer:2008-23

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Related research

Keywords: Weather Derivatives; Temperature Models; Cooling Degree Days; Maximum Likelihood Estimation; Distribution for Correlated Variables;

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. 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.
  3. Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series 2004/10, Center for Financial Studies (CFS).
  4. 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.
  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 637-54, May-June.
  6. Eckhard Platen & Jason West, 2003. "Fair Pricing of Weather Derivatives," Research Paper Series 106, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. 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.
  8. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308.
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