Comments on «Bonus-Malus Scales in Segmented Tariffs with Stochastic Migrations between Segments» (JRI 2003, CAS research award 2003)

Transcription

1 Comments on «Bonus-Malus Scales in Segmented Tariffs with Stochastic Migrations between Segments» (JRI 2003, CAS research award 2003) Casualty Actuarial Society Conference, Baltimore November 15, 2005 Jean Pinquet 1

2 Coauthors of the paper Natacha Brouhns & Michel Denuit (Université Catholique de Louvain, Belgique) Montserrat Guillén (Universitat de Barcelona, Catalunya, Espana) Jean Pinquet (Ecole Polytechnique & Université Paris 10, France) 2

3 Outline of the presentation 1. Bonus-malus scales: definitions 2. Abstract of the paper 3. Bonus-malus scales in the real world and their link with market structure 4. The informational content of a bonus-malus scale, as compared with event histories (accidents, traffic violations, etc) 5. Conclusions on information sharing between competitors in motor insurance markets 3

4 - I Bonus-malus scales: definitions and comments (1) Bonus-malus: latin denomination for experience rating, i.e. Bonus: no-claim discount Malus: increase in premium after an event, with a «crime and punishment» flavor (claim at fault, moving traffic violation, etc) Bonus-malus scales: see Lemaire (1995) for a thorough presentation 4

5 Bonus-malus scales: definitions and comments (2) Usual features of a bonus-malus scale: a coefficient is attached to each level. A type of event is defined (accident, traffic violation) which triggers an upward movement in the scale. One step down (if not already at the lowest level) after an eventless year, several steps (usually between 2 and 5, which may depend on severity) up after each event. On average, drivers climb down the stairs and eventually cluster at the lowest level. 5

6 Bonus-malus scales: definitions and comments (3) The meaning of a bonus-malus scale is completely different, whether it enforces or not the rating structure. Premium paid by the policyholder: basic premium times the coefficient derived from the bonus-malus scale. If the basic premium cannot depend on the driver s experience, several flaws are expected. First, competition is hampered on the rating side. 6

7 Bonus-malus scales: definitions and comments (4) A bonus-malus scale is usually downwards unbalanced with respect to seniority. As a consequence, the seniority of the policyholder plays an important role in the interpretation of the levels. If the bonus-malus scale does not enforce the rating structure but is used by all the competitors, it acts as an information sharing mechanism. 7

8 - II - Abstract of the paper (1) The paper considers the bonus-malus scales retained by Taylor (1997): nine levels, with new drivers starting at level 6. One step down (if possible) for a claimless year, two (mild scale) or four (severe scale) steps up after each claim at fault. For each level, coefficients are derived from simulations on observed and unobserved risk components, and on claim numbers with are Poisson distributed, with a parameter depending on these components. 8

9 Abstract (2) Observed risk components: simulations use a transition table between risk levels calibrated on a Spanish data base. Unobserved risk components: an AR(1) model is used on time-dependent random effects. See Pinquet, Guillén, Bolancé (2001) for experience rating schemes based on dynamic random effects. 9

10 Abstract (3) For each level of the bonus-malus scale, the coefficient is obtained from averaging ten year histories of policyholders starting with a ten year seniority. Averages are taken on 100,000 virtual policyholders, whose observable characteristics are generated at random from an empirical distribution fitted on a Spanish portfolio. The variable to average is the dynamic random effect written in a multiplicative way. 10

11 Abstract (4) Averages are weighted by risk exposures. The coefficient attached to each level is then obtained by setting equal to one the coefficient applied to beginners (level 6). Actual computations are a bit more intricate (results need to be smoothed). 11

12 Abstract (5): Example of bonusmalus scale (mild transition rules) Level Risk exposure Coefficient 1 80% % % % % % 1 7 1% % %

13 Abstract (6): Comments The minimum coefficient is 23% less than the average, which is a reasonable discount. The coefficient for beginners is almost four times greater than the minimum and three times the average, which is much. Explanation: Averaging coefficients on the risk level and mostly on seniority creates heterogenous classes. 13

14 Abstract (7): Comments For instance, the interpretation of level 6 strongly depends on the seniority of the policyholder. For a beginner, you have a high premium based on observable characteristics, but no experience. For an experienced policyholder, level 6 brings very bad news in terms of experience rating, especially here with a mild scale (only two steps up after a claim at fault). 14

15 - III Bonus-malus scales in the real world (1) Various market organizations in the real world can be seen in motor insurance. Examples which follow are given with decreasing regulation. 1) State monopoly: Quebec, bodily damage. The SAAQ uses a bonus-malus scale based on traffic violations, and a short memory (two year history). 2) Bonus-malus rules enforcing experience rating (no experience items in the base premium) in a competitive environment: Belgium until

16 Bonus-malus scales in the real world (2) 3) Bonus-malus scale forced on competitors but not as an experience rating rule: France. The base premium design is left free to the companies, which can use individual experience. 4) Complete deregulation in terms of rating (Spain, U.K.). Some insurance companies provide experience rating rules to their clients, some do not. 16

17 - IV The informational content of a bonus-malus scale (1) Let us comment the different regulation levels. 1) The state (province) monopoly is not the ideal solution for the private sector However welfare results are not bad (at least in Quebec). Using a recent event history (two years of moving traffic violations) means that incentive effects are prefered to actuarial fairness. 2) Enforcing experience rating rules in a competitive environment is certainly not a good idea. Indeed, this situation disappears in Europe. 17

18 The informational content of a bonus-malus scale (2) 3) Bonus-malus scale forced on competitors but not as an experience rating rule. The role of the bonusmalus scale is here to provide an information available to all the competitors. In this respect, it can be a substitute of a complement to an individual history of events (accidents, traffic violations) made available to all the companies. Let us give some comments on the informational content of a bonus-malus scale, with respect to the seniority of the policyholder. 18

19 The informational content of a bonus-malus scale (3) During the first years, the information brought by a bonus-malus scale increases quickly. After a few years, the efficiency is close to that obtained from an individual history of the same duration on the triggering events. Then policyholders begin to cluster on the floor. The overall efficiency does not improve much then, and even decreases for drivers at the lowest level of the scale. 19

20 The informational content of a bonus-malus scale (4) In order to improve the efficiency of the bonusmalus scale for these policyholders, a malus deductible (or bonus reserve) can be introduced. If the policyholder spends a given duration (3 years in France) at the lowest level, he is exempted from malus should a triggerring event occur. But then he loses the deductible. Such clauses significantly improve the efficiency of the bonus-malus scale. 20

21 - V - Information sharing between competitors in motor insurance markets (1) Bonus-malus scales provide a way to share information on claim histories between competitors. In a deregulated environment, the main competitors often share information without being forced to do it by public authorities. In Spain for instance was created the company TIREA (Tecnologias de la Informacion y Redes para las Entidades Aseguradoras) 21

22 Information sharing between competitors in motor insurance markets (2) Creation in 1997 to manage information transmission between the companies which accept to file claim histories to the TIREA. As of 2002: 165 members, 43% of companies operating in Spain, 80% of premiums). Web Site: Hence main competitors are members. In United Kingdom, there is also information sharing between main competitors in an informal way. 22

23 Information sharing between competitors in motor insurance markets (3) Rationale for information sharing: Competitors are reluctant to provide information about their policyholders, but are eager to obtain it for new business. Informal information sharing creates a risk of free riding behavior (i.e. manipulation during transmission). An external company (like TIREA) which collects event histories and makes them available to members is a solution to the free riding issue. 23

24 Information sharing between competitors in motor insurance markets (4) Another risk with informal information sharing is that it may create barriers to entry, if only major competitors are members of the club. Conclusion: what is the future of bonus-malus scales? If there is any, it can be within an information sharing system, but not as a way to enforce experience rating. 24

25 References (1) 1. Brouhns, N., Denuit, M., Guillén, M. & Pinquet, J. (2003). Bonus-Malus scales in segmented tariffs with stochastic migration between segments, The Journal of Risk and Insurance, Vol. 70, n 4, Lemaire, J. (1995). Bonus-malus systems in automobile insurance. Kluwer Academic Publishers. 25

26 References (2) 1. Pinquet, J., Guillén, M. & Bolancé, C. (2001). Allowance for the age of claims in bonus-malus systems, ASTIN Bulletin, Vol. 31, n 2, p Taylor, G. (1997). Setting a bonus-malus scale in the presence of other rating factors. ASTIN Bulletin, Vol. 27, n 2, p