We present a novel method to generate realistic simulations of extracellular recordings. The simulations were obtained by superimposing the activity of neurons placed randomly in a cube of brain tissue. Detailed models of individual neurons were used to reproduce the extracellular action potentials of close-by neurons. To reduce the computational load, the contributions of neurons further away were simulated using previously recorded spikes with their amplitude normalized by the distance to the recording electrode. For making the simulations more realistic, we also considered a model of a finite-size electrode by averaging the potential along the electrode surface and modeling the electrode-tissue interface with a capacitive filter. This model allowed studying the effect of the electrode diameter on the quality of the recordings and how it affects the number of identified neurons after spike sorting. Given that not all neurons are active at a time, we also generated simulations with different ratios of active neurons and estimated the ratio that matches the signal-to-noise values observed in real data. Finally, we used the model to simulate tetrode recordings.