Pricing catastrophe risk during transitions of physical and economic environments

The increasing frequency and severity of natural catastrophes call for comprehensive strategies to manage, mitigate, and transfer catastrophe (CAT) risk. In response, a variety of financial instruments—such as CAT bonds, CAT futures, CAT options, CAT swaps, and industry loss warranties—have been created. This paper investigates the pricing of CAT risk, focusing on two main challenges. First, catastrophe risk is increasingly intertwined with financial risk due to evolving physical and economic environments, driven by climate change and socioeconomic factors, respectively. Second, the cyclical nature of the two environments reshapes both catastrophe and financial risks. We model the occurrence of CAT events using a doubly stochastic Poisson process. Three underlying rate processes—a hazard rate process controlling the occurrence of CAT events, a risk-free rate process for discounting, and a floating coupon rate process determining floating coupon payments—are assumed to jointly follow an affine jump-diffusion model, governed by the regimes of the physical and economic environments. Building on these conceptualizations of a joint physical–economic environment and three rate processes, we develop a general pricing framework and derive semi-analytical expressions, which, when combined with simulation techniques, yield an efficient computational scheme. We illustrate the framework through the pricing of a standard CAT bond. Extensive numerical studies underscore the importance of accounting for the interplay between catastrophe and financial risks, as well as the cyclical nature of the physical and economic environments.