The MAPK (mitogen-activated protein kinase) or its synonymous ERK (extracellular signal regulated kinase) pathway whose components are Ras, Raf, and MEK proteins with many biochemical links, is one of the major signalling systems involved in cellular growth control of eukaryotes including cell proliferation, transformation, differentiation, and apoptosis. In this study we describe the MAPK/ERK pathway via (quasi) biochemical reactions and then implement the pathway by a stochastic Markov process. A novelty of our approach is to use multiple parametrizations in order to deal with molecules for which localization in the cell is an intricate part of the dynamic process and to describe the protein using different binding sites and various phosphorylations. We simulate the system by exact and different approximate simulations, e.g. via the Poisson τ-leap, the Binomial τ-leap and the diffusion methods, in which we introduce a new updating plan for dependent columns of the diffusion matrix. Finally we compare the results of different algorithms by the current biological knowledge and find out new relations about this complex system.