Recent developments have made autonomous vehicles (AVs) closer to hitting our roads. However, their security is still a major concern among drivers as well as manufacturers. Although some work has been done to identify threats and possible solutions, a theoretical framework is needed to measure the security of AVs. In this paper, a simple security model based on defense graphs is proposed to quantitatively assess the likelihood of threats on components of an AV in the presence of available countermeasures. A Bayesian network (BN) analysis is then applied to obtain the associated security risk. In a case study, the model and the analysis are studied for GPS spoofing attacks to demonstrate the effectiveness of the proposed approach for a highly vulnerable component.