We compare global methods for solving models with jump discontinuities in the policy function. We find that differences between value function iteration (VFI) and other methods are economically significant and Euler equation errors fail to be a sufficient measure of accuracy in such models. VFI fails to accurately identify both the location and size of jump discontinuities, while the endogenous grid method (EGM) and the finite element method (FEM) are much better at approximating this class of models. We further show that combining VFI with a local interpolation step (VFI‐INT) is sufficient to obtain accurate approximations. The combination of computational speed, relatively easy implementation and adaptability make VFI‐INT especially suitable for approximating models with jump discontinuities in policy functions: while EGM is the fastest method, it is relatively complex to implement; implementation of VFI‐INT is relatively straightforward and it is much faster than FEM.