The attribution of traits plays an important role as a heuristic for how we interact with others. Many psychological models of personality are analytical in that they derive a classification from reported or hypothesised behaviour. In the work presented here, we follow the opposite approach: Our personality model generates behaviour that leads an observer to attribute personality characteristics to the actor. Concretely, the model controls all relevant aspects of non-verbal behaviour such as gaze, facial expression, gesture, and posture. The model, embodied in a virtual human, affords to realistically interact with participants in real-time. Conceptually, our model focuses on the two dimensions of extra/introversion and stability/neuroticism. In the model, personality parameters influence both, the internal affective state as well as the characteristic of the behaviour execution. Importantly, the parameters of the model are based on empirical findings in the behavioural sciences. To evaluate our model, we conducted two types of studies. Firstly, passive experiments where participants rated videos showing variants of behaviour driven by different personality parameter configurations. Secondly, presential experiments where participants interacted with the virtual human, playing rounds of the Rock-Paper-Scissors game. Our results show that the model is effective in conveying the impression of the personality of a virtual character to users. Embodying the model in an artificial social agent capable of real-time interactive behaviour is the only way to move from an analytical to a generative approach to understanding personality, and we believe that this methodology raises a host of novel research questions in the field of personality theory.