Intelligent Transportation Systems (ITS) are utilized in car insurance policies known as Usage-Based Insurance (UBI), where driving data is collected using a telematics device to determine driving behavior. This enables offering personalized car insurance fees based on driving performance. Current research focuses on advantages, disadvantages, and privacy aspects of UBI, paying less attention to its user acceptance. In this work, we propose a UBI acceptance model based on an adaptation of the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) and test it with 585 participants by means of structural equation modeling. We find that social influence and hedonic motivation are the most important predictors of the intention to use UBI, and perceived privacy influences it indirectly. Furthermore, we refine the model with new connections, improving model fit.