example, large yield shortfalls may be due to other events not related to ACDD’s, such as
in 1974 when late planting and an early season-ending frost were responsible for large
yield shortfalls (Figure 2). Second, the relationship between weather and yields is likely
non-linear. In Figure 2 a trend line is obtained by plotting the fitted values from
regressing yields on ACCD’s for the highest (above 900) and lowest (below 900)
observed ACCD’s separately. For Illinois corn, it appears that yields are non-linearly
related to ACDD’s, suggesting the potential advantage in hedging applications of an
options contract which can be non-linearly related to an ACCD index. In the analysis we
include swaps as well as options in order to investigate the degree to which non-linear
weather effects exist in yields.
All derivatives are priced using burn analysis (BA). BA is the simplest method
for pricing weather derivatives, and is based on calculating what the contract would have
paid out in the past based on observed historical distributions.9 It is attractive in that it
does not require strong assumptions about the distribution of the underlying index, and it
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is simple to compute.
The pay-off, f, from a long swap contract is given by
(10) f(ACDD)=D(ACDD-K)
where ACDD is the index, D is the tick value measured in $/ACCD, and K is the strike
price of the contract (i.e. the contract pays $D per ACCD above the chosen strike price
K). The pay-off is a linear function of the index. The buyer is swapping a certain
exposure, K, to the index for an uncertain exposure, ACDD, and thus the name swap.
Most swaps are costless (i.e. there is no premium, and the pay-off equals the profit). If
the swap contract is to be traded without a premium then the strike must be set at a value
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