Accurately assessing collision risk in dynamic traffic scenarios is a crucial requirement for trajectory planning in autonomous vehicles~(AVs) and enables a comprehensive safety evaluation of automated driving systems. To that end, this paper presents a novel probabilistic occupancy risk assessment~(PORA) metric. It uses spatiotemporal heatmaps as probabilistic occupancy predictions of surrounding traffic participants and estimates the risk of a collision along an AV's planned trajectory based on potential vehicle interactions. The use of probabilistic occupancy allows PORA to account for the uncertainty in future trajectories and velocities of traffic participants in the risk estimates. The risk from potential vehicle interactions is then further adjusted through a Cox model\edit{,} which considers the relative \edit{motion} between the AV and surrounding traffic participants. We demonstrate that the proposed approach enhances the accuracy of collision risk assessment in dynamic traffic scenarios, resulting in safer vehicle controllers, and provides a robust framework for real-time decision-making in autonomous driving systems. From evaluation in Monte Carlo simulations, PORA is shown to be more effective at accurately characterizing collision risk compared to other safety surrogate measures. Keywords: Dynamic Risk Assessment, Autonomous Vehicle, Probabilistic Occupancy, Driving Safety