tailieunhanh - SFB 649 Discussion Paper 2007-037 : 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 nat- ural 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. | SFB 649 Discussion Paper 2007-037 Calibrating CAT Bonds for Mexican Earthquakes Wolfgang Hardle Brenda Lopez Cabrera Humboldt-Universitat zu Berlin Germany This research was supported by the Deutsche Forschungsgemeinschaft through the SFB 649 Economic Risk . http ISSN 1860-5664 SFB 649 Humboldt-Universitat zu Berlin Spandauer StraBe 1 D-10178 Berlin SFB 6 4 9 E C O N O M I C R I S K B E R L I N Calibrating CAT bonds for Mexican earthquakes Wolfgang Karl Hardle Brenda Lopez Cabrera CASE - Center for Applied Statistics and Economics Humboldt-Universitat zu Berlin Abstract 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 . 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 .