Pricing and simulations of catastrophe bonds

The increasing number of natural catastrophes like floods, hurricanes, and earthquakes not only causes many victims, but also leads to severe production, infrastructure, and individual property losses. Classic insurance mechanisms may be inadequate for dealing with such losses because of the dependencies that exist, inter alia, between the sources of the losses, the huge values of claims, and problems with adverse selection and moral hazard. To cope with the dramatic consequences of extreme events, new financial and insurance instruments are required. One example of a catastrophe-linked security is the catastrophe bond (cat bond), also known as the Act-of-God bond. In this paper we price some catastrophe bonds. We apply models of the risk-free spot interest rate under the assumption that the occurrence of the catastrophe is independent of financial market behavior. We then use Monte Carlo simulations to analyze the numerical properties of the pricing formulas thus obtained. We make a twofold contribution to the literature of catastrophe bond pricing. First, we prove a general pricing formula, which can be applied to cat bonds with different payoff functions under the assumption of different models of the risk-free spot interest rate. Second, we price some new types of cat bonds with interest rate dynamics described by the CIR and the Hull–White model.