We present a theoretical methodology for the pricing of catastrophe (CAT) derivatives with event‐dependent and non‐convex payoffs given the price of a CAT indexed futures contract. We do not assume a fully diversifiable CAT event risk, nor do we assume knowledge of the martingale probability measure beyond the futures price. We derive tight bounds on the contract value and present trading strategies exploiting the mispricing whenever the bounds are violated. We estimate the bounds of the reinsurance contract with data from hurricane landings in Florida. Our method is also applicable when there is no futures market but the price of a CAT‐indexed bond is available.