Among these variables, bonus-malus coefficient presents a particular interest for auto
insurance pricing, having a specific meaning according to the insurance system of each
country. Within the French bonus-malus system, this coefficient indicates an increase or a
decrease of the insurance premium depending on the number of claims declared by a
policyholder. Therefore, if the policyholder does not cause any responsible accident, he
receives a bonus, meaning that the insurance premium will be reduced. Contrary, if the
policyholder is responsible for the accident, he is penalized by applying a malus, which will
have the consequence of a premium increase. These increases and decreases are based on a
standard tariff defined by the insurer, depending on which the premium is multiplied by a
coefficient. The basic coefficient is 1 and it corresponds to the reference premium of the
insurance company. If the bonus-malus coefficient is lower than this value, a bonus is applied,
and if it is higher, a malus is considered. More specifically, the French bonus-malus system
involves a malus of 25% for a claim declared and a bonus of 5% for the non-declaration of any
claims in the reference period, usually a year. In this way, the system aims the encouragement
of prudent insured drivers and the discouragement of those who, for various reasons, register
severe losses. In the studied portfolio, the calculations corresponding to the bonus-malus
coefficient are already generated, registering negative and positive values, which indicate a
decrease or an increase of the insurance premium, respectively.