We consider pricing weather derivatives for use as protection against weather extremes. The

method described utilizes results from spatial statistics and extreme value theory to first

model extremes in the weather as a max-stable process, and then use these models to simulate

payments for a general collection of weather derivatives. As the joint likelihood function

for max-stable processes is unavailable, we fit max-stable processes using two approaches: the

first is based on the composite likelihood, and the second is based on approximate Bayesian

computing (ABC). Both capture the spatial dependence of payments. To incorporate parameter

uncertainty into the pricing model, we use bootstrapping with the composite likelihood

approach, while the ABC method naturally incorporates parameter uncertainty into the

pricing model. Using ideas from catastrophe ratemaking, we show how this method can be