Tarificación de derivados sobre catástrofes con desencadenantes de índices de pérdidas: Modelo asintótico basado en un proceso geométrico de Wiener

Abstract

This paper proposes a valutaion model for insurance-linked derivatives written on a catastrophic loss index. To this aim, we consider that the total amount of the thus covered catastrophe results from the sum of two random variables, the reported claims amount and the reported-but-not-yet-reported claims amount. The central hypothesis of our model assumes a temporary decrease of the latter, proportional to an exponential function that we call asymptotic reporting claims rate. We represent the dynamics of this decrease through a geometric Brownian motion, wheras the reported claims amount, numerator of the loss ratio intended to be determined, is obtained by the difference between the incurred-but-not-yet-reported claims amount and the catastrophe’s total amount. Finally, we test the validity of the model by estimating its parameters and contrasting the goodness-of-fit with a sample of six floods in different Spanish cities prone to suffer this type of events.