Indifference prices of structured catastrophe (CAT) bonds

We present a method for pricing structured CAT bonds based on utility indifference pricing. The CAT bond considered here is issued in two distinct notes called tranches, specifically senior and junior tranches each with its own payment schedule. Our contributions to the literature of CAT bond pricing are two-fold. First, we apply indifference pricing to structured CAT bonds. We find a price for the senior tranche as a relative indifference price, that is, relative to the price of the junior tranche. Alternatively, one could take the approach that the senior tranche is priced first and the price of the junior tranche is relative to that. Second, instead of simply supposing that the “not-issue-a-CAT-bond” strategy of the reinsurer is to do nothing, we suppose that the reinsurer reduces its risk by reinsuring proportionally less claims. We assume that the reinsurance claims follow a (Poisson) jump-diffusion process.