Modeling Loss Index Triggers for Catastrophe (Cat) Bonds: An Alternative Continuous Approach

Abstract

This paper proposes a method for continuous-time random modeling of loss index- triggered catastrophe bonds (cat bonds) that simplifies both rating and pricing throughout their maturity period. This index is based on the amount of declared losses calculated as the difference between the total amount of the catastrophe and that of incurred-but-not-yet- reported losses, which is modeled by means of a geometric Wiener process. The fundamental assumption of this model lies in considering that this amount decreases proportionally to a function, hereby called the mixed-rate of claims statement, which represents the pace of claim statements as growing linearly up to a certain moment, after which it becomes constant until the bond reaches maturity.