High levels of trust have been linked to a variety of benefits including the well-functioning of markets and political institutions or the ability of societies to solve public goods problems endogenously. While there is extensive literature on the macro-level determinants of trust, the micro-level processes underlying the emergence and stability of trust are not yet sufficiently understood. We address this lacuna by means of a computer simulation. With this model, conditions under which trust is likely to emerge and be sustained are identified. We focus our analysis mainly on the individual characteristics of agents: their social or geographical mobility, their attitude towards others or their general uncertainty about the environment. Contrary to predictions from previous literature, it turns out that a low geographical or social mobility is detrimental to both, the emergence and robustness of trust. The model also helps to reveal a hidden link between trusting others and being trustworthy.