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This paper proposes a continuous random modeling of catastrophic loss indexes underlying insurance-linked securities (ILS), by convolution of each catastrophic events amount of reported claims. This variable is calculated, in turn, as the difference between the catastrophes total severity, on one hand, and its amount of incurred-but-not-yet-reported claims, which is considered to be driven by a geometric Brownian motion, on the other hand. Parameters estimation and verification of the goodness-of-fit to a sample of data series on floods in Spain have subsequently been conducted in order to test the models validity.

Elaborating a Catastrophic Loss Index for Insurance-linked Securities (ILS): A Continuous Model