With the advancements in social robotics and virtual avatars, it becomes increasingly important that these agents adapt their behavior to the mood, feelings and personality of their users. One such aspect of the user is empathy. Whereas many studies measure empathy through offline measures that are collected after empathic stimulation (e.g. post-hoc questionnaires), the current study aimed to measure empathy online, using brain activity collected during the experience. Participants watched an affective 360 video of a child experiencing domestic violence in a virtual reality headset while their EEG signals were recorded. Results showed a significant attenuation of alpha, theta and delta asymmetry in the frontal and central areas of the brain. Moreover, a significant relationship between participants' empathy scores and their frontal alpha asymmetry at baseline was found. These results demonstrate specific brain activity alterations when participants are exposed to an affective virtual reality environment, with the level of empathy as a personality trait being visible in brain activity during a baseline measurement. These findings suggest the potential of EEG measurements for development of passive brain-computer interfaces that assess the user's affective responses in real-time and consequently adapt the behavior of socially intelligent agents for a personalized interaction.