Advances in Risk Management

160 THE MODELING OF WEATHER DERIVATIVE PORTFOLIO RISK

it considers the outcome of contracts at expiry. Then in section 8.12 we
briefly come back to the question of how to estimate risk over shorter time
horizons.

8.4 BASIC METHODS FOR ESTIMATING THE RISK IN

WEATHER DERIVATIVE PORTFOLIOS

We now present the two most basic methods that one might use to estimate
the risk in a weather derivative portfolio, as a starting point for our subse-
quent discussion. These methods are (a) burn analysis, and (b) use of the
multivariate normal distribution to model weather indices.

8.4.1 Burn analysis

Burn analysis, which is the simplest method for analysing risk in a weather
derivative portfolio, typically works as follows:

1 For each contract in the portfolio, 10 years of cleaned historical weather

data is purchased.

2 For each of these 10 years, the historical settlement indices for each

contract in the portfolio are calculated.

3 Trends (such as the global warming trend) may be removed from these

historical settlement indices, if appropriate.

4 The detrended historical settlement indices are converted into historical

payoffs for each contract and each historical year.

5 The historical payoffs are aggregated over the portfolio, giving a portfolio

historical payoff for each of the 10 years.

6 The 10 portfolio historical payoffs thus obtained are taken as an empirical

estimate for the distribution of possible payoffs for the portfolio. Quan-

tities such as the expected payoff, the variance of payoffs or the risk of

extreme losses can then be estimated.

This method is sufficiently simple that it could be implemented in a
spreadsheet. However, it has two major shortcomings. First, since the esti-
mate of the distribution of payoffs is based on only 10 points, the highest
level of risk than can be estimated is 1 in 10 year risk. More years of historical
data could be used in order to estimate risk at higher levels, but even in the
best cases the maximum number of years of reliable data typically available
is only around 50. This is not particularly satisfactory for risk managers, who
often like to see estimates of the 1 in 100 or 1 in 1,000 year risk. One might