CAT Bond Pricing in Uncertain Environment

Abstract

Catastrophe bonds are among the essential instruments in providing a financial hedge for insurance companies and their policyholders. Catastrophic events are rare, and the shortage of data weakens the inference of using probability theory. Uncertainty theory, on the other hand, is a reliable alternative to model these kinds of indeterminacies. We model the problem of pricing catastrophe bonds as an uncertain optimization problem where the maximization of the cedent insurance company’s profit is constrained to the uncertain measure of ruin defined for the investors. Consequently, we balance the concerns of profitability and reasonable protection for the investors and the cedent of the bond, respectively. The solution of the optimization problem is considered as the spread over the LIBOR, which effectively determines the price of the bond. The results depicted the practicality of the modeling, especially the uncertainty theory, in pricing catastrophe bonds. Finally, the basic part of the methodology, on calculating the ruin index, is implemented on a real-world problem, and the results are compared with those obtained using probability theory.