Catastrophic risk management: Stochastic hybrid model to calculate the loss index trigger for catastrophe bonds (cat bonds). Adjustment using evolutionary strategies

Purpose: This paper develops a stochastic model to calculate the loss index trigger for catastrophe bonds as alternative instruments for the management of major insured risks, such as natural catastrophe. Methodology: The underlying loss index of catastrophe bonds is the aggregate catastrophe losses reported before the end of certain period. The catastrophe severity is defined as the sum of two random variable: the reported loss amount and incurred-but-not-yet-reported loss amount, and the central hypothesis is that the latter decreases proportionally to a linearly increasing function up to a certain time and constant thereafter, called the hybrid claim reporting rate. Randomness in the reporting process is represented by a geometric Brownian motion in the claim reporting rate. The validity of the proposed model is evaluated by estimating its parameters using machine learning techniques (specifically, evolutionary strategies, ES). Findings: The results shows that the model accurately captures the uneven behavior of the claim reporting process over time and therefore correctly describes the catastrophic claims reporting process. Originality: The model proposed allows for an easy calculation of catastrophic loss indexes, thus facilitating the pricing of loss index-triggered Cat bonds. This translates into better catastrophe risk management for both insurance and reinsurance companies, as well as for those companies that diversify their portfolios with this type of financial instruments. The simplicity of the presented model facilitates parameter estimation and simulation.