Pricing Loss Index Triggered Cat Bonds. An Ornstein-Uhlenbeck Process-Based Model
DOI:
https://doi.org/10.46661/revmetodoscuanteconempresa.2891Keywords:
bonos sobre catástrofes, cuantía de siniestros pendiente de declarar, cuantía declarada de siniestros, tasa de declaración de siniestros, índice de pérdidas por catástrofes, proceso de Ornstein-UhlenbeckAbstract
This paper develops a continuous-time random model of loss index triggers for cat bonds on the basis of the loss amount incurred until their maturity. Assuming that total loss amount due to a catastrophe is defined as the sum of the incurred loss amount plus the incurred-but-not-yet reported loss amount, we model the decreasing linear dynamics of the latter amount by means of an additive Brownian process (or Ornstein Uhlenbeck process); and get the former by the difference between the total loss amount and the incurred-but-not-yet-reported loss amount. Finally, we test the validity of the model by estimating its core parameters and by contrasting the goodness of fit through a data series of six floods occurred in several Spanish cities prone to suffer such kind of catastrophes.
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