This paper develops analytical distributions of
temperature indices on which temperature derivatives are written. If the
deviations of daily temperatures from their expected values are modelled as an
Ornstein-Uhlenbeck process with timevarying 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 are a
particularly 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.
Cite this paper
A. Clements, A. Hurn and K. Lindsay, "A Closed-Form Approximation for Pricing Temperature-Based Weather Derivatives," Applied Mathematics
, Vol. 4 No. 9, 2013, pp. 1347-1360. doi: 10.4236/am.2013.49182
 J. Tindall, “Weather Derivatives: Pricing and Risk Management Applications,” Institute of Actuaries of Australia, Unpublished Manuscript, 2006.
 M. Garman, C. Blanco and R. Erickson, “Weather Derivatives: Instruments and Pricing Issues,” Environmental Finance, 2000.
 F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, 1973, pp. 637-659. doi:10.1086/260062
 L. Zeng, “Pricing Weather Derivatives,” Journal of Risk Finance, Vol. 81, No. 3, 2000, pp. 72-78.
 E. Platen and J. West, “Fair Pricing of Weather Derivatives,” Quantitative Finance Research Centre, University of Technology Sydney, Research Paper Series, 106, 2003.
 S. D. Campbell and F. X. Diebold, “Weather Forecasting for Weather Derivatives,” Journal of the American Statistical Society, Vol. 100, 2005, pp. 6-16.
 D. S. Wilks, “Statistical Methods in the Atmospheric Sciences,” Academic Press, New York, 1995.
 S. Jewson and R. Caballero, “The Use of Weather Forecasts in the Pricing of Weather Derivatives,” Meterological Applications, Vol. 10, No. 4, 2003, pp. 377-389.
 F. E. Benth and J. Saltyne-Benth, “Stochastic Modelling of Temperature Variations with a View Toward Weather Derivatives,” Applied Mathematical Finance, Vol. 12, No. 1, 2005, pp. 53-85.
 M. H. A. Davis, “Pricing Weather Derivatives by Marginal Value,” Quantitative Finance, Vol. 1, 2001, pp. 1-4.
 P. Alaton, B. Djehiche and D. Stillberger, “On Modelling and Pricing Weather Derivatives,” Applied Mathematical Finance, Vol. 9, No. 1, 2002, pp. 1-20.
 B. M. Bibby and M. Sorensen, “Martingale Estimation Functions for Discretely Observed Diffusion Processes,” Bernoulli, Vol. 1, No. 1/2, 1995, pp. 17-39.