Spatial Aggregation and Weather Risk Management

hedging may be more effective at larger levels of spatial aggregation.

To illustrate consider an extreme case. Suppose there are two locations and that
the ε_t,k's are perfectly negatively correlated, f_k(W_t,k)'s are perfectly positively
correlated, andCov[f_k(W_t,k),ε_{t, j}] = 0   ∀j,k . In this case the variance of aggregate

yields reduces to

(4)                             Var[∑Yt,k]=Var[∑fk(Wt,k)],

kk

and all variation in yields can be attributed to weather events. This risk can be potentially
hedged with a WD equal in size but opposite in direction to the underlying systemic
weather effect, f_k(W_t,k). This situation is depicted in Figure 1. If W can be
approximated by a temperature index the risk of the aggregated exposure can be
effectively hedged with a call option on the index W with strike price K*. This
framework supports the notion that while WDs may not be useful for individual
producers they may still prove useful in hedging systemic risks borne by aggregators of
risk such as re/insurers.

Of course, this may not always be the case. At the other extreme, consider two
locations where the ε_t,k's are perfectly positively correlated, the f_k(W_t,k)'s are perfectly
negatively correlated, andCov[f_k(W_t,k),ε_t,j]= 0   ∀j,k . In this case the variance of

aggregate yields reduces to

(5)                            Var[∑Y_t,k] = Var[∑ε_t,k],

kk

all variation in aggregate yields is attributed to idiosyncratic effects and none of the
aggregate risk can be hedged using WDs.

While both cases are unrealistic they illustrate the main point of the aggregation

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