We report the results of Monte Carlo simulations with the aim to clarify the microscopic origin of exchange bias in the magnetization hysteresis loops of a model of individual core/shell nanoparticles. Increase of the exchange coupling across the core/shell interface leads to an enhancement of exchange bias and to an increasing asymmetry between the two branches of the loops which is due to different reversal mechanisms. A detailed study of the magnetic order of the interfacial spins shows compelling evidence that the existence of a net magnetization due to uncompensated spins at the shell interface is responsible for both phenomena and allows to quantify the loop shifts directly in terms of microscopic parameters with striking agreement with the macroscopic observed values.