We investigate the valuation of catastrophe insurance derivatives that are traded at the Chicago Board of Trade. By modeling the underlying index as a compound Poisson process we give a representation of no-arbitrage price processes using Fourier analysis. This characterization enables us to derive the inverse Fourier transform of prices in closed form for every fixed equivalent martingale measure. It is shown that the set of equivalent measures, the set of no-arbitrage prices, and the market prices of frequency and jump size risk are in one-to-one connection. Following a representative agent approach we determine the unique equivalent martingale under which prices in the insurance market are calculated.