After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. For insurers, reinsurers and other corporations CAT bonds are hedging instruments that offer multi year pro- tection without the credit risk present in reinsurance by providing full collateral for the risk limits offered throught the transaction. For investors CAT bonds offer attractive returns and reduction of portfolio risk, since CAT bonds defaults are uncorrelated with defaults of other securities. Baryshnikov et al. (2001) present an arbitrage free solution to the pricing of CAT bonds under conditions of continous trading and according to the statistical char- acteristics of the dominant underlying.