MODELO CONTINUO BASADO EN DOS PROCESOS DE WIENER PARA CALCULAR UN ÍNDICE DE PÉRDIDAS POR CATÁSTROFES SUBYACENTE DE LOS DERIVADOS SOBRE SEGUROS (INSURANCE-LINKED SECURITIES, ILS).

Resumen

This paper develops a random continuous-time model that simplifies calculation of insurance linked securities’ (ILS) underlying catastrophic loss index and allows us to price them with the traditional option valuation methodology. Under the hypothesis that the total amount of the catastrophe is defined as the sum of two random variables, the incurred claims amount and the incurred-but-not-yet reported claims amount, we model the decreasing dynamics of the latter through a geometric Brownian process characterized by two Wiener processes that introduce a greater volatility to the model which increases its accuracy. The difference between the incurred-but-not-yet-reported claims amount and the total amount of the catastrophe results in the reported claims amount, which is the numerator of the loss ratio that we intend to determine.
In order to verify the validity of the proposed hereby, its parameters are estimated using the maximum likelihood method and a Ji-square normality test is performed on a sample of six floods occurred in several Spanish locations prone to such events.
KEYWORDS: Insurance-linked securities, Wiener process, incurred-but-not-yet-reported loss amount, reported loss amount
MSC: 60G15, 91G20