Modeling Loss Index Triggers for Cat Bonds: A Continuous Approach

This paper proposes a method for the continuous random modeling of loss index triggers for cat bonds. Under the premise that the total incurred loss of the hedged catastrophe consists of the amount of reported losses plus the amount of incurred-but-not-yet-reported losses, our basic hypothesis is that the latter decreases in time proportionally to a real-value function named “claim reporting rate.” To account for randomness in the reporting process, the claim reporting rate is considered to follow a Wiener process. Within this framework, it is quite straightforward to quantify the amount of reported losses by merely subtracting the amount of incurred-but-not-yet-reported losses from the total catastrophic incurred loss, and accordingly calculating the loss index as the amount of reported losses multiplied by an indicator which varies according to the occurrence of the specified catastrophe. The estimation of parameters and the verification of the goodness-of-fit have been conducted in order to test the validity of the model.