Advancements in autonomous vehicle (AV) technologies necessitate precise estimation of perceived risk to enhance user comfort, acceptance and trust. This paper introduces a novel AV-Occupant Risk (AVOR) model designed for perceived risk estimation during AV cut-in scenarios. An empirical study is conducted with 18 participants with realistic cut-in scenarios. Two factors were investigated: scenario risk and scene population. 76% of subjective risk responses indicate an increase in perceived risk at cut-in initiation. The existing perceived risk model did not capture this critical phenomenon. Our AVOR model demonstrated a significant improvement in estimating perceived risk during the early stages of cut-ins, especially for the high-risk scenario, enhancing modelling accuracy by up to 54%. The concept of the AVOR model can quantify perceived risk in other diverse driving contexts characterized by dynamic uncertainties, enhancing the reliability and human-centred focus of AV systems.