PAY-AS-YOU-DRIVE INSURANCE: THE EFFECT OF THE KILOMETERS ON THE RISK OF ACCIDENT

Pay-As-You-Drive (PAYD) motor policies are a new concept of insurance contracts which has started to be commercialized in many countries. It is also called Usage Based Insurance (UBI) because, instead of an annual premium be established, the premium is fixed according to the number of kilometers done by the car, besides other characteristics of the risk traditionally used in pricing. Therefore, those who use more the car are going to pay a higher premium because they are more exposed to the risk of accident. In this article we present a bibliographical review on the most relevant contributions about PAYD insurances, which are not still sufficiently known in Spain. An empirical application is carried out in which the influence of the number of driven kilometers in the risk of accident is investigated. Four types of claims are studied: property damages/bodily injuries, at-fault/not-at-fault claims. A generalization of the offset Poisson regression model is applied to identify the shape of the effect of driven kilometers on the risk of accident. We show that the association between the number of kilometers and claim frequency is not properly captured by a linear relationship, and alternative forms of relationship are discussed.