Calibrating CAT bonds for Mexican earthquakes

The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government. The calibration of the CAT bond is based on the estimation of the intensity rate that describes the earthquake process from the two sides of the contract, the reinsurance and the capital markets, and from the historical data. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. Since other variables can affect the value of the losses caused by earthquakes, e.g. magnitude, depth, city impact, etc., we also derive the price of a hypothetical modeled-index (zero) coupon CAT bond for earthquakes, which is based on a compound doubly stochastic Poisson pricing methodology. In essence, this hybrid trigger combines modeled loss and index trigger types, trying to reduce basis risk borne by the sponsor while still preserving a non-indemnity trigger mechanism. Our results indicate that the (zero) coupon CAT bond price increases as the threshold level increases, but decreases as the expiration time increases. Due to the quality of the data, the results show that the expected loss is considerably more important for the valuation of the CAT bond than the entire distribution of losses.