CHAPTER 8
The Modeling of
Weather Derivative
Portfolio Risk
Stephen Jewson
8.1 INTRODUCTION
The companies that trade weather derivatives typically hold portfolios of
between 100 and 1,000 weather derivative contracts. Different contracts have
payoffs that may depend on different weather variables measured at dif-
ferent locations over different time periods. The payoffs between any two
contracts may be highly correlated or anticorrelated (if they are based on
the same or similar variables, locations or time periods), or they may be
uncorrelated (if the weather variables, locations or time periods are very
different). How, then, should the total financial risk in such portfolios be
estimated?
In this chapter we present a number of methods for estimating this total
portfolio risk and discuss some of the issues and trade-offs that arise when
deciding which method to use. Several of the issues we discuss and the
solutions we propose are novel in that, to our knowledge, they have not
previously appeared in the literature on weather derivatives.
The chapter is structured as follows. We start with a brief description of
what weather derivatives are.^1 We then explain how risk is usually defined
for portfolios of weather derivatives, and follow that with a discussion of
the two simplest methods for the evaluation of the risk of a weather deriva-
tive portfolio: burn analysis, and the application of the multivariate normal
distribution to contract indices. In the main part of the chapter we then
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