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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, 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 doubly
stochastic Poisson pricing methodology from BARYSHNIKOV, MAYO
and TAYLOR (2001) and BURNECKI and KUKLA (2003). 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 nonindemnity
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.
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 loss (zero)
coupon CAT bond for earthquakes, which is based on the compound doubly
stochastic Poisson pricing methodology from BARYSHNIKOV, MAYO
and TAYLOR (2001) and BURNECKI and KUKLA (2003). 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 nonindemnity
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.