13-05-2014, 12:13 PM
The use of weather forecasts in the pricing of weather derivatives
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ABSTRACT
We discuss how weather forecasts can be used in the pricing of weather derivatives and derive results for
the most important types of weather index and contract. We show that calculating the expected payoff of
linear contracts on linear indices requires only forecasts of the mean temperature over the contract
period. Calculating the expected payoff of linear contracts on non-linear indices requires forecasts of
both the mean and the distribution of temperatures, but not of the dependence between temperature
distributions on different days. Calculating the expected payoff of non-linear contracts requires forecasts
of the full multivariate distribution of temperature over the whole contract. For contracts that extend
beyond the end of available forecasts, correlations between the forecast and post-forecast periods must
be taken into account when estimating this distribution. We present two methods by which this can be
achieved, both of which combine information from climatological models of daily temperature with
information from probabilistic forecasts.
Introduction
There is little doubt that weather and climate forecasts
are of value to society, but there is growing awareness
that the full potential economic value of forecasts has yet
to be realised (Palmer 2002; Freebairn & Zillman 2002).
One way to enhance the economic value of forecasts
is to incorporate them into risk assessment tools that
allow economic actors, be they public or private, to
directly assess the financial loss or gain to them from
future weather or climate events. Here, we explore the
possibilities for doing this in a specific context, that of
weather derivatives. These are financial contracts that
allow companies (or other entities) to insure themselves
against the adverse effects of fluctuations in weather
(Zeng 2000). The classic example is that of a gas supply
company, which will lose money in warm winters. The
company may enter into a weather derivative contract
with, say, a bank. The contract stipulates that, at a
certain date, one party will pay the other an amount
which is entirely determined by measurements of the
weather.
Types of weather derivatives
Weather derivatives can be based on any meteorological
index, but cumulative heating and cooling degree days,
cumulative temperatures and average temperatures are
particularly common. We will focus the discussion
in this article on cumulative heating degree days and
cumulative temperatures. The methodologies we will
describe for heating degree days can equally well be
applied to cooling degree days, and those for cumulative
temperatures can equally well be applied to average
temperatures.
Pricing non-linear contracts
We now consider the general situation in which the
weather contract structure is non-linear. Of the contract
types mentioned in the Introduction, this is relevant
for capped swap contracts and option contracts. There
are also many other non-linear contract structures, and
indeed any shape is, in theory, possible.
For capped swap contracts, the first task is to estimate
the fair strike, defined as the strike which gives an
expected payoff of zero. In the special case in which
the index distribution is close to normal and the caps
are close to symmetrical with respect to the index
distribution, the fair strike can be approximated as the
expected value for the index, which can be calculated
using the methods described for linear swaps using
only conditional mean single track forecasts. When
calculating the par value for the fair swap strike on
standard indices, these approximations are often fairly
good.
Summary
A number of studies have looked at quantitative
applications of meteorological forecasts, such as Taylor
& Buizza (2003), Smith et al.(2001) and Jewson &
Ziehmann (2002). Taylor & Buizza (2003) and Smith
et al. (2001) both describe ‘end-to-end’ application of
ensemble forecasts, in which each ensemble member
is converted directly into a variable of user interest.
For Taylor & Buizza (2003) the variable of interest is
electricity demand, while for Smith et al. (2001) it is
bagel sales, electricity demand and wind power pro-
duction.
In this paper we have discussed how weather forecasts
can be used to estimate the fair prices and distributions
of outcomes of weather derivatives contracts. This is
important for contracts that have already started or that
will start in the next 11 days. We have illustrated how
both single and ensemble forecasts contain information
that can be used in the pricing of different types
of contract. We have argued that, in general, both
single and ensemble forecasts should be converted into
probabilistic forecasts to be most useful.