This study estimates linear and nonlinear GARCH models to find optimal hedge ratios with futures contracts for some of the main European stock indexes. By introducing nonlinearities through a regime‐switching model, we can obtain more efficient hedge ratios and superior hedging performance in both an in‐sample and an out‐sample analysis compared to the other methodologies (constant hedge ratios and linear GARCH). Moreover, nonlinear models also reflect the different patterns followed by the dynamic relationship between the volatility of spot and futures returns during low‐ and high‐volatility periods.