The optimal payment reduction ratios for a catastrophe bond

Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. If there is a catastrophe, the CAT bond is triggered and the future bond payments are reduced. This projects first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal payment reduction ratios which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal payment reduction ratios help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it shows how strike price, maturity, parameters of the catastrophe loss process and different interest rate assumptions affect the optimal payment reduction ratios. Numerical examples are also given for illustrations.