In this study we discuss various methods to assess the statistics of extreme response of a floating structure subjected to random waves. This issue is of great importance in the case of low frequency motion of floating bodies in shallow water. Those methods are based on the evaluation of the level crossing rate, which is easily related to the extreme value statistics for stationary random processes and large levels. Four main methods are considered, namely the Rice formula with either a Gaussian assumption or an approximation of the joint distribution of the response and its first derivative by a projection method; the Breitung's formula; the Hagberg's approaches using either an asymptotic expansion or a Monte-Carlo integration and finally the time domain simulation which serves as the reference solution. All these methods are applied to the surge motion of a floating body subjected to unidirectional waves. In that case, the Rice formula under the Gaussian assumption strongly underestimates the level crossing rate. The other methods are more or less accurate compared to the time domain simulation, but Hagberg's Monte-Carlo integration is shown to give the best approximation.