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 indextriggeredcatastrophe bonds (cat bonds) that simplifies both rating and pricing throughouttheir maturity period. This index is based on the amount of declared losses calculated as thedifference between the total amount of the catastrophe and that of incurred-but-not-yetreportedlosses, which is modeled by means of a geometric Wiener process. Thefundamental assumption of this model lies in considering that this amount decreasesproportionally to a function, hereby called the mixed-rate of claims statement, whichrepresents the pace of claim statements as growing linearly up to a certain moment, afterwhich it becomes constant until the bond reaches maturity.