Catastrophe bond pricing under the renewal process

This paper presents a novel approach to catastrophe (CAT) bond pricing, addressing the limitations of existing methodologies that often neglect crucial aspects of catastrophe data characteristics or fail to adequately analyze the impact of both loss and inter-arrival time distributions on CAT bond prices. Our proposed method combines the compound renewal process with the Cox-Ingersoll-Ross (CIR) process to model insurance and financial risks separately. Valuation is conducted in two steps, integrating risk-neutral measures for financial risks with a broader class of measures for insurance risks, thereby preserving the structural integrity of the compound renewal process. Leveraging Bayesian inference and historical data, we demonstrate effective calibration of the pricing model. Notably, our framework allows for the assessment of the influence of varying inter-arrival time distributions on CAT bond prices, a dimension previously unexplored in the literature. Empirical analysis highlights the significant impact of inter-arrival time distribution on CAT bond pricing.