Spatial Aggregation and Weather Risk Management

such that the expected pay-off is zero, that is KF = E(ACDD), where KF is known as the
“fair strike”. Pricing of a swap thus entails determining the fair strike. Pricing a zero-
cost linear swap using BA simply involves setting the fair strike equal to the historical
average of the index.¹¹

The pay-off, p, from a long call option is given by

(11)                 p(ACDD,K)=Max(0,D(ACDD-K))

and the profit, π, is given by

(12)              π (ACDD,K)=Max(0,D(ACDD-K))-P(K)

where P is the option price, or premium. For options, pricing entails simply determining
the fair premium, or fair price which is defined so that the expected profit on the contract
is zero. The fair price is equal to the expected pay-off of the contract, or P = E(p), and
pricing using BA simply consists of calculating the mean of the historical pay-offs, p,
given a strike, K.

Hedging Analysis and Risk Measures

Following VB, the hedge ratio is determined by minimizing the semi-variance (SV) of a
portfolio consisting of yields and a WD. SV only measures deviations below the mean
and thus is a measure of downside risk. Formally, for swaps the weight, or hedge ratio
(contracts/acre), w, is chosen by solving

(¹³)                   min   ∑{m^axK ^- (Ytⁱk ⁺ wkftk k ^),0]}2

w_{k          t}

where w is the hedge ratio measured in contracts/acre, Y_t,^d_k^et is detrended yield in bu/acre,

Y_k is the long-run average detrended yield, and f_t,k is the return on the swap contract

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