The use of advanced driver assistance systems and the transition towards semi-autonomous vehicles are expected to contribute to a lower frequency of motor accidents and to have a significant impact for the automobile insurance industry, as rating methods must be revised to ensure that risks are correctly measured. We analyze telematics information and usage-based insurance research to identify the effect of driving patterns on the risk of accident. This is used as a starting point for addressing risk quantification and safety for vehicles than can control speed. Here we estimate the effect of excess speed on the risk of accidents with a real telematics data set. We show scenarios for a reduction of speed limit violations and the consequent decrease in the expected number of accident claims. If excess speed could be eliminated, then the expected number of accident claims could be reduced to half of its initial value, applying the average conditions of our data. As a consequence, insurance premiums also diminish