Recently, parametric insurance has emerged as a convenient way to cover risks that may be difficult to evaluate. Through the introduction of a parameter that triggers compensation and allows the insurer to determine a payment without evaluating the true loss, these products simplify the compensation process, and provide easily tractable indicators to perform risk management. On the other hand, this parameter may sometimes deviate from its purpose, and may not always correctly represent the basis risk. In this paper, we provide theoretical results that investigate the behavior of parametric insurance products when they are confronted to large claims. These results, in particular, measure the difference between the true loss and the parameter in a generic situation, with a particular focus on heavy-tailed losses. Simulation studies that complete the analysis show the importance of nonlinear dependence measures to ensure a good protection over the whole distribution.