STEPHEN JEWSON 157look beyond these basic methods and discuss a number of more complex
issues: how simulations should be set up to account for sampling error;
how estimates of the correlation matrix can be improved; how index non-
normality can be accounted for; how the magnitude of model error can
be estimated; how simulations can be re-engineered to incorporate hedg-
ing constraints between contracts; how consistency between single contract
pricing and portfolio analysis can be achieved; how to calculate a simple
linear approximation to the sampling error; and finally, how VaR can be
estimated efficiently over short time horizons.
8.2 WHAT ARE WEATHER DERIVATIVES?
Weather derivatives are contracts between two parties that have a finan-
cial payoff that depends on some measured aspect of the weather. Since the
future weather can be considered as random, the payoff of a weather deriva-
tive is also random. The economic purpose of weather derivatives is to allow
companies that have profits that are affected by the weather to hedge some
or all of that risk. This can be illustrated by a simple example, adapted from
Jewson and Jones (2005):
A weather derivative example
ABC gas company doesn’t like warm winters because they sell less natural gas to
their domestic customers, who use the gas for heating their homes. ABC can lose
up to £10 million in a warm winter relative to an average year. They decide to use
weather derivatives to help hedge this warm winter risk. They analyse their his-
torical revenues against historical weather data and conclude that there is a high
correlation between their revenues and the total number of heating degree days
measured in London between November and March (note that heating degree
days, or HDDs, are a measure of the extent to which the temperature falls below
18 degrees Centrigrade, and, in this case, can be taken as a proxy for tempera-
ture on an inverted scale). Because of this high correlation they decide to base
their weather derivative on a London November to March HDD index. This has
the advantage that there is a well-traded market on this index, which makes it
more likely that they will get a good price in the market because of the price-
transparency brought about by such trading. In the first year of hedging they buy
a put option, which will pay them if the number of HDDs is low (correspond-
ing to a warm winter). A reasonable estimate of the average number of HDDs
at this location and over this period is 1670 HDDs, with a standard deviation of
120HDDs, and the distribution of possible numbers of HDDs is close to normal.
ABC decide to hedge themselves from 1650 HDDs downwards. They buy a put
option with a strike of 1650HDDs, a tick of £50,000/HDD and a limit of £10,000,000
(this limit corresponds to 200HDDs below the strike, or 1450 HDDs). They com-
pare quotes from a number of banks, and end up paying a premium of £2,000,000
for this contract. When the actual weather comes in at 1500 HDD they receive a
payout of £7,500,000, and hence make an overall profit on the weather derivative of