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Parametric insurance has emerged as a practical way to cover risks that maybe difficult to assess. By introducing a parameter that triggers compensationand allows the insurer to determine a payment without estimating the actualloss, these products simplify the compensation process, and provide easilytraceable indicators to perform risk management. On the other hand, thisparameter may sometimes deviate from its intended purpose, and may not alwaysaccurately represent the basic risk. In this paper, we provide theoreticalresults that investigate the behavior of parametric insurance products whenfaced with large claims. In particular, these results measure the differencebetween the actual loss and the parameter in a generic situation, with aparticular focus on heavy-tailed losses. These results may help to anticipate,in presence of heavy-tail phenomena, how parametric products should besupplemented by additional compensation mechanisms in case of large claims.Simulation studies, that complement the analysis, show the importance ofnonlinear dependence measures in providing a good protection over the wholedistribution.

Parametric insurance for extreme risks: the challenge of properly covering severe claims