The study of natural catastrophe models plays an important role inthe prevention and mitigation of disasters. After the occurrence of a naturaldisaster, the reconstruction can be financed with catastrophe bonds(CAT bonds) or reinsurance. This paper examines the calibration of a realparametric CAT bond for earthquakes that was sponsored by the Mexicangovernment. The calibration of the CAT bond is based on the estimation ofthe intensity rate that describes the earthquake process from the two sidesof the contract, the reinsurance and the capital markets, and from the historicaldata. The results demonstrate that, under specific conditions, thefinancial strategy of the government, a mix of reinsurance and CAT bond, isoptimal in the sense that it provides coverage of USD 450 million for a lowercost than the reinsurance itself. Since other variables can affect the valueof the losses caused by earthquakes, e.g. magnitude, depth, city impact,etc., we also derive the price of a hypothetical modeled-index loss (zero)coupon CAT bond for earthquakes, which is based on the compound doublystochastic Poisson pricing methodology from BARYSHNIKOV, MAYOand TAYLOR (2001) and BURNECKI and KUKLA (2003). In essence,this hybrid trigger combines modeled loss and index trigger types, tryingto reduce basis risk borne by the sponsor while still preserving a nonindemnitytrigger mechanism. Our results indicate that the (zero) couponCAT bond price increases as the threshold level increases, but decreasesas the expiration time increases. Due to the quality of the data, the resultsshow that the expected loss is considerably more important for thevaluation of the CAT bond than the entire distribution of losses.The study of natural catastrophe models plays an important role inthe prevention and mitigation of disasters. After the occurrence of a naturaldisaster, the reconstruction can be financed with catastrophe bonds(CAT bonds) or reinsurance. This paper examines the calibration of a realparametric CAT bond for earthquakes that was sponsored by the Mexicangovernment. The calibration of the CAT bond is based on the estimation ofthe intensity rate that describes the earthquake process from the two sidesof the contract, the reinsurance and the capital markets, and from the historicaldata. The results demonstrate that, under specific conditions, thefinancial strategy of the government, a mix of reinsurance and CAT bond, isoptimal in the sense that it provides coverage of USD 450 million for a lowercost than the reinsurance itself. Since other variables can affect the valueof the losses caused by earthquakes, e.g. magnitude, depth, city impact,etc., we also derive the price of a hypothetical modeled-index loss (zero)coupon CAT bond for earthquakes, which is based on the compound doublystochastic Poisson pricing methodology from BARYSHNIKOV, MAYOand TAYLOR (2001) and BURNECKI and KUKLA (2003). In essence,this hybrid trigger combines modeled loss and index trigger types, tryingto reduce basis risk borne by the sponsor while still preserving a nonindemnitytrigger mechanism. Our results indicate that the (zero) couponCAT bond price increases as the threshold level increases, but decreasesas the expiration time increases. Due to the quality of the data, the resultsshow that the expected loss is considerably more important for thevaluation of the CAT bond than the entire distribution of losses.
