This article introduces a regime-switching jump diffusion model to capture the arrival and loss process for the catastrophic loss index. Based on this model, we price catastrophe insurance derivatives—the Property Claim Services (PCS) futures call option, the PCS futures call spread and the default-free catastrophe bond. Under a framework of incomplete markets, and using non-traded CAT (catastrophe) loss indices, the existence of a well-defined arbitrage-free price is shown, and the analytic closed-form pricing formulas can be implemented via the fast Fourier transform. We derive the hedging parameters, Delta, Gamma and Rho, from these formulas. Further, the sensitivity analysis of the parameters are conducted to study the effect of these contingent claims valuation.

Property-liability insurance companies traditionally limit their liabilities or hedge catastrophic exposure by purchasing catastrophic reinsurance contracts to cover high-loss-severity catastrophe (CAT). However, larger and frequent CAT losses, as shown in Table 1, have impacted the profitability and capital bases of reinsurance companies in the recent years. These phenomena have had a marked effect on the reinsurance market, such that some reinsurance companies have given up or have reduced the CAT reinsurance contracts. How can the ability of the insurance industry to support CAT protection, be strengthened? This has become a very important issue. Some scholars propose the solution of transferring the insurance risk to the capital market (Swiss Re, 1996; Doherty, 1997; Froot, 1997; Croson and Kunreuther, 2000; and The Economist, 2001). The reason is that a severe CAT loss of $100 would be less than 1% of the US market portfolio, and be no more than a normal day’s movement in asset value of these capital markets (Laurenzano, 1998). It is believed that the capital markets can bear the impact of the CAT losses. Thus, insurance derivatives and securitization can offer alternative possibilities to transform the catastrophic risks. Four popular securitized insurance products for CAT losses are introduced.

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