The Valuation of Contingent Capital with Catastrophe Risks

Abstract

To value catastrophe insurance products, most previous studies (e.g. Louberge et al., 1999; Lee and Yu, 2002; Cox et al., 2004; Jaimungal and Wang, 2006) assume that the arrival process of catastrophe events follows a Poisson process. The IPCC (Intergovernmental Panel on Climate Change) Fourth Assessment Report published in 2007 indicates that unanticipated catastrophic events could increase through time because of global warming. Therefore, the assumption that resulting claims occur in terms of a Poisson process with a constant frequency seems inadequate for catastrophic events. To overcome this shortcoming, alternative models are proposed to address the stochastic intensity of catastrophic risks. This paper proposes a counting process and the doubly stochastic Poisson process to model the arrival process for catastrophe events. Furthermore, this paper generalizes the assumption of Jaimungal and Wang (2006) to define the general loss function expressing that different specific losses have different impacts on the drop in stock price. Based on modeling the arrival rates for catastrophe risks, the pricing formulas of contingent capital are derived by the Merton measure. Results of empirical experiments of the option prices as well as sensitivity analyses are presented.