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

Parametric insurance has emerged as a practical way to cover risks that may be difficult to assess. By introducing a parameter that triggers compensation and allows the insurer to determine a payment without estimating the actual loss, these products simplify the compensation process, and provide easily traceable indicators to perform risk management. On the other hand, this parameter may sometimes deviate from its intended purpose, and may not always accurately represent the basic risk. In this paper, we provide theoretical results that investigate the behavior of parametric insurance products when faced with large claims. In particular, these results measure the difference between the actual loss and the parameter in a generic situation, with a particular focus on heavy-tailed losses. These results may help to anticipate, in presence of heavy-tail phenomena, how parametric products should be supplemented by additional compensation mechanisms in case of large claims. Simulation studies, that complement the analysis, show the importance of nonlinear dependence measures in providing a good protection over the whole distribution.