A Markov Model for the Pricing of Catastrophe Insurance Futures and Spreads

This article presents a valuation theory of futures contracts and derivatives on such contracts when the underlying delivery value follows a stochastic process containing jumps of random claim sizes at random time points of catastrophe occurrence. Applications of the theory are made on insurance futures and options, new instruments for risk management launched by the Chicago Board of Trade. Several closed pricing formulas are derived based on a partial, competitive equilibrium assumption both for futures contracts and for futures derivatives, such as caps, call options, and spreads, assuming constant relative risk aversion for the representative agent.