TITLE:
A Closed-Form Approximation for Pricing Temperature-Based Weather Derivatives
AUTHORS:
A. E. Clements, A. S. Hurn, K. A. Lindsay
KEYWORDS:
Weather Derivatives; Temperature Models; Cooling-Degree Days; Distributions for Correlated Variables
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.9,
September
20,
2013
ABSTRACT: 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.