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作成者 Diana Dodu |  2017年11月2日



保険契約者がそのリスクに応じて保険料を支払うようにすること、そして保険金コストを公平に分離することが、長い間保険料率設定の目的でした。自動車損害賠償責任保険では、年齢、性別、地域、車種、自動車の利用目的など先験的変数(a priori variables)と呼ばれる特定の変数が、同じリスクプロファイルを有することから、同じように料率設定が可能な同質の区分を形成する料率設定プロセスに利用することが可能でした。例えば、年齢の高い人が事故を起こす頻度が低ければ、その課される保険料は低くなり、また、保険会社が同じ保険料を課した場合には、逆選択に晒されることになり、保険金の支払いに対し、損失が増加し保険料が不足することになります。先験的変数の数を増やすことで、より多くの均質な区分を作成できますが、他の要因が事故の頻度に影響することがある一方で先験的変数で効果的に測定できないことがあるため、これがいつも可能なわけではありません。こうした要因として、運転スキル、走行距離、飲酒行動などがあります。リスクを正確にレーティングするには、保険料を事後的に、もしくは保険金支払事由発生後に調整すれば可能です。(例えば、無事故割引制度、あるいはボーナス・ペナルティ制度で、前年に保険金請求がなければ契約更新時の保険料削減に当たる「ボーナス」、前年に保険金請求があれば保険料の増額となる「ペナルティ」により、個人の保険金支払い履歴によって保険料を調整する機能を利用。)


In a typical bonus malus structure, insurance companies offer discounts for no claims in previous periods and penalise claims for benefits it has to pay. If this penalty, for example, is a two-class increase up the malus ladder and each claim-free year earns one class shift down the ladder, then in effect the result of an accident nullifies two years of being claim-free, so a policyholder who causes an accident every third year on average remains in the same area of the bonus malus system throughout that person's driving lifetime and has a claim frequency of a third.

A system that punishes an accident with two classes is “designed” for a claim frequency of a third in the sense that if claim frequency is indeed a third, the portfolio would not shift towards high discount classes over time. However, claim frequencies in most countries currently tend to be well under 10%. Based on data from countries that account for approximately 82% of total European motor premium income, 1 the motor third-party liability (MTPL) claim frequency (the number of claims—excluding nil claims—divided by the number of insured vehicle years) has been falling steadily, from 8.1% in 2002 to 6.0% in 2013.

Essentially, this translates into a movement of policyholders towards discount classes as the effective frequency is smaller than the frequency for which the systems are designed. The system thus becomes financially unbalanced. In effect, one would then need to have very strict systems (for example, punishing an accident with about nine to 10 malus classes for a frequency of 10%). A system that fails to do that, usually because of commercial reasons, and actually punishes an accident with, for example, two to three malus classes, would result in a decrease in the income or premium generated from insurance policies.

Creating balance for a bonus malus system has been amply investigated. Jean Lemaire analysed 30 bonus malus systems from around the world with respect to four measures, including the relative stationary average level (RSAL) of the premium (a measure of clustering in the lowest bonus classes), the coefficient of variation of the premium, the efficiency of the system and the average optimal retention. He shows that these measures are all positively correlated and that a system that penalises claims heavily will exhibit high RSAL, high premium variability, high elasticity and high average optimal retentions.

He states that an inevitable consequence of the implementation of a bonus malus system is a progressive decrease of the observed average premium level due to a concentration of policyholders in the high-discount classes. To illustrate, the average premium level of a policyholder with claim frequency of 10% was simulated for 30 years. At the end of 30 years, the average premium level ranges from around a high of 70% of the starting premium level in Belgium to a low of 40% in Japan.

There are several ways that one can build a financially stable optimal system. Penalising claims more heavily can be a solution for system balance, but because this is commercially unacceptable, other options have been vastly analysed.

In his 1995 book Bonus-Malus Systems in Automobile Insurance, Lemaire designed an optimal bonus malus system based on game theory (the game framework being introduced by Fritz Bichsel and Hans Bühlmann in 1964). Each policyholder pays a premium proportional to the policyholder's own unknown claim frequency. Using an estimate of the claim frequency instead of the true unknown claim frequency is assumed to incur a loss to the insurer. The optimal estimate of the policyholder’s claim frequency is the one that minimises the loss incurred.

In their 1996 article, “A Financially Balanced Bonus Malus System,” Geert Coene and Louis G. Doray have designed a system which stays in financial equilibrium over the years. It is designed by minimising a quadratic function of the difference between the premium for an optimal bonus malus system (BMS) with an infinite number of classes and the premium for a BMS with a finite number of classes, weighted by the stationary probability of being in a certain class and by imposing various constraints on the system.

In their 1997 research paper, “Using Mixed Poisson Distributions in Connection With Bonus-Malus Systems,” J.F. Walhin and J. Paris obtained an optimal BMS using as the claim frequency distribution the Hofmann’s distribution, which encompasses the negative binomial and the Poisson-inverse Gaussian, and also using as the claim frequency distribution a finite Poisson mixture.

In his 1990 paper “A Bonus Malus System With Conditioned Bonus,” G. Sammartini constructed a bonus malus system which is financially balanced by permitting a driver to move to a lower class only if the claim frequency of that person's preceding class is lower than a fixed value. Nicholas E. Frangos and Spyridon D. Vrontos (2001), in their paper “Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component on an Individual Basis in Automobile Insurance,” propose a generalised system that takes into consideration simultaneously the individual’s characteristics, the number of accidents and the exact level of severity for each accident.

In this briefing note, we have analysed countries in Central and Eastern Europe (CEE) and Italy from the perspective of differences between designs while identifying unique systems. Bonus malus systems can vary in Europe as can be seen below:

  • Countries that do not have a specific system defined by law, such as Poland, where the system is fully liberalised and insurers have the liberty to provide own risk coefficients and load back the premium to obtain balance; Estonia, where insurers can design their own rules and where it may seem that the maximum bonus can be achieved within several years of claims free driving; and Lithuania, where according to the Law on Compulsory Motor Third Party Liability Insurance effective from 17 May 2007, premiums are fixed by the insurer and companies can take into account risk factors.
  • Countries where the bonus malus system is defined in the legislature, requiring insurers to take into consideration loss history, but which grant freedom to insurance companies to design their own rules, which is present in countries such as the Czech Republic and Slovakia.
  • Countries that are regulated by law, such as Italy and Romania, which are discussed below, and Hungary, where according to law NGM 21/2011, the number of classes are predefined as well as movement between classes depending on the number of accidents, and insurers are obligated to issue accident and claim certificates, but are also allowed to use historical data for the purposes of classification to calculate additional correction factors, and Serbia, where the bonus malus system is defined in the law on compulsory traffic insurance but insurers can use correction coefficients if they do not contradict the ones mandated by law.
  • Countries such as Croatia, where there seems to be a defined system, but companies offer extra benefits such as additional bonuses above the maximum and protection of the bonus (after several years of no claims, insureds can pay an additional premium to protect the bonus in case they have an accident in the subsequent year), and Slovenia, where you can also protect your bonus, while the future premium in cases of protection of the bonus would depend on the number of accidents in past periods.
  • Latvia, where companies can set premiums based on prior histories with a conversion system in which it seems that it is more difficult to move towards bonus classes and where the system is evaluated annually (on September 15).
  • Countries that have relatively more rigid systems, such as Macedonia, where MTPL is not liberalised and minimum and maximum technical premiums are proposed by the Commission to the Government with a bonus malus system implemented in 2006; Kosovo, where there is a requirement to prenotify tariffs as well as a regulation for implementation of the bonus malus system; and Montenegro, where MTPL price liberalisation had a five-year transitional period starting from publication of law No. 44/12 in 9 August 2012, with liberalisation foreseen by 2017 and bonus malus rules applying from 1 February 2016 based on data from the NBOCG Information Center (or based on the insurance policy and certificate containing data on the previous duration of insurance and the number of claims reported in that period, but only if there is no information about the insured in the information center).
  • Countries where this system is under a continuing process of implementation or non-consistent application like Bulgaria, the Federation of Bosnia and Herzegovina, and Albania, where for example, there is a draft law to determine insurers to include a bonus malus system (whose basis criteria should be set by the authority) in their premium calculation.

We present in this article several CEE countries (including Italy) with unique characteristics and marked differences in terms of the design of their bonus malus systems. We also offer some thoughts as to specific challenges they may be facing and propose some recommendations for improvement.


Under current Romanian legislation, specifically Norm 20/2017, any claim is penalised with a two-class increase while market claim frequencies tend to be under 5% for automobiles and physical persons and under 10% for automobiles and juridical persons as presented in a recent regulator-issued MTPL benchmarking report from May 2017.

In effect, the result of an accident nullifies two years of being claim-free, so policyholders who cause an accident every third year on average remain in the same area of the bonus malus system throughout their driving lifetimes. Thus, the Romanian system is designed for a claim frequency of one-third.

According to the same report, the premium reduction that was generated was approximately 21.3% for physical persons and 16.6% for juridical persons.

MTPL benchmark tariffs should be effectively loaded by about 21%, so that the premium remains balanced. This is a common practice among MTPL writers in order to balance the insurance equation.

The current bonus malus system has recently been changed in Romania. Whereas according to the previous no longer in force norm, specifically Norm 23/2014, there were 14 bonus classes and eight malus classes, according to Norm 39/2016 (which is also no longer in force), and the currently in-force Norm 20/2017, there are eight bonus classes and eight malus classes. The premium reduction was approximately 19% under Norm 23/2014, while for Norm 39/2016, it was approximately 21% for physical persons and approximately 16.6% for juridical persons. Under Norm 20/2017, the premium reduction is approximately 31% for physical persons and 23% for juridical persons.

Additionally, current legislation as defined above gives the insurer the freedom to analyse an insured’s claim history and to add additional correction coefficients to those already defined by law. However, these additions need to be justified.

The Romanian bonus malus system seems to be moving towards more regulation, increased bonuses and a need for insurers to use increased loadings if they use the system without correction coefficients in order to remain financially balanced.

Perhaps to achieve better balance, one could design the system to look at severity of accidents as well as attempt to increase the homogeneity of classes by including pricing variables such as driver skills. However, because current MTPL law 132/2017 and Norm 20/2017 mandate the usage of defined homogeneous classes whose structure needs to be followed by insurance companies or receive regulator’s approval to change it, it may not be easy to add additional variables.

Czech Republic

The MTPL law was introduced in the Czech Republic with Act No. 168/1999 Coll. on Motor Third Party Liability insurance with subsequent amendments. According to the law, the insurer is obliged to consider the loss history and discount the premium in case of a claim-free history or add a surcharge in case of payment of an indemnity. The rules, however, are not mandated by law. Insurers can obtain information about a prospective policyholder´s claim history from the database operated by the Czech Insurance Bureau or from the applicant in a formal statement.

The Czech bonus malus system is not strict as insurers can decide on the rules concerning premium rebates.

Insurers use their own rules for bonus malus system design, but there are common elements. Each policy, for example, is attached a duration (duration of uninterrupted contract—“crucial period” or “decisive period”). If there is an accident, the duration in months is shortened by crucial or decisive claims. A crucial or decisive claim is a claim resulting in the payment of insurance benefits on the basis of which the length of crucial time is reduced by, for example, 36 or 24 months. A person in a class with 84 to 95 uninterrupted months could move three classes to a class with 48 to 59 uninterrupted months after an accident or to a class with 60 to 71 uninterrupted months (a two-class increase, for example) and the discount would decrease appropriately based on company rules. If the amount of crucial time becomes negative, maluses start to apply.

In the Czech Republic, the bonus malus system is personalised, allowing insurers to attract better customers and be more competitive. However, an accident seems to be punished with two or three classes, and although this is not a rule, the system is thus designed for a claim frequency of approximately a third or a fourth, which is lower than observed frequencies in European markets. This would put pressure on the financial balance of insurers and result in lower premiums collected. If companies use generalised linear models (GLMs) that calculate the “pure” bonus malus coefficients and these calculations cannot be used for commercial reasons because they penalise insureds significantly, then companies may adjust these loads and/or reload the premium by a bonus malus loading to achieve balance, which partially defeats the system’s purpose.

It would be interesting to see in countries where the bonus malus system is “liberalised,” like the Czech Republic, studies performed by motor insurer bureaus or guarantee funds to optimise such systems.


Regulation 4/2006 with subsequent amendments has defined the universal conversion system in Italy. Under the Italian system, bonus malus classes are called merit classes and they are used by insurance companies to determine the annual tariff. Each company manages the system differently based on the universal conversion system. For example, an insurer is given the freedom to apply a greater reduction coefficient than the one mandated by law.

In the state system, there are 18 universal classes. The first one offers the most advantageous rates, while the higher ones are more expensive (malus). When buying insurance for the first time, one automatically enters into the 14th class of merit, the Universal Class, unless the person takes advantage of the Bersani Decree. According to the Bersani law from 2007, specifically Law 40/2007, when buying insurance for a second vehicle purchased by the owner of the first vehicle or by a member of the first owner’s household, the insurer is obligated to apply the same merit class of the first owner. This is considered the household bonus. In addition, the Bersani law requires that the insurer apply the malus only when the policyholder bears the primary liability, while cases of minor liability and equal joint liability are excluded.

According to the universal system, if there are no accidents throughout the year, the customer will be rewarded with a merit class, and otherwise that person will be downgraded, resulting in increased insurance costs and maluses. If there are no accidents in the past one to five years, the insured can also benefit from certain merit classes (e.g., for five years without claims). If there is one claim incurred during the past year, there would be a two malus class increase, with more accidents causing a greater increase up the malus ladder.

An analysis performed in 2011 by the National Association of Insurance Companies (ANIA) pointed out the worsening premium imbalance due to the Bersani law. They show that, in 2010, 65% of policyholders were in the best bonus class, while approximately 12% of those were placed in that class due to the Bersani law (if the Bersani law had not been passed, the proportion of first-class members would have been around 55%). They claim that “portfolio creep” is inevitable because more than 95% of insureds do not cause any accidents for which they are primarily responsible.

According to IVASS, the insurance regulatory body in Italy, in the third trimester of 2016, the average classes seemed to be 1.92 with 79.3% of insureds clustered in the first class (a marked increase from 2010).

In addition to bonus discounts, Italy is advanced in using telematics products (pay-as-you-drive). Policyholders who install a telematics black box in their vehicles receive a significant discount on their MTPL policies.

According to IVASS, black boxes were present in 15.8% of policies in the fourth quarter of 2015. In 2015, the percentage of policies with a black box grew by 2.2 percentage points.

The diffusion of black box policies varied by region with the top provinces using them in southern Italy (Calabria, Campania, Puglia and Sicily), where more than 20% of the policies had black boxes. The lowest rate (less than 10%) was found in the northeast, while in central Italy, the northwest and Sardinia, their use was relatively moderate (10% to 20%).

In Italy, there is pressure on the financial balance of insurers as seen by the clustering of a high proportion of policyholders in the lowest merit class. In addition, the Bersani law puts additional downward pressure on insurance company premiums, which is due to additional merit classes offered to drivers who may be inexperienced and who would have higher loss ratios (e.g., young drivers), but who can benefit from bonuses nonetheless.

Systems using telematics, which is also an a priori system, are able to make classes more homogeneous by potentially introducing pricing variables such as driving skills and mileage. The need for “a posteriori systems” such as bonus malus could decrease, thus potentially leading to a solution for the premium reduction.

Recently, a new law affecting bonus malus in Italy is now in effect. This law is Competition Act 124/2017, which for car insurance means that there will be mandatory premium reductions given (to be calculated by IVASS) a) for those who installed black boxes or similar devices, b) for customers who agree to have the car inspected or c) for those who install vehicle electronic mechanisms that prevent the engine from starting if the driver is found to have a higher alcohol content than the limits of the law. There will also be additional premium reductions for good drivers who have not caused accidents in the last four years and who reside in high premium (high risk) areas.

IVASS will issue the applicable regulations to the new law in the near future, but there seems to also be a decrease in the freedom of insurers to use internal BM classes. Possibly, this new regulation may mean higher potential clustering in the high bonus classes in the future (because these measures are designed to reduce the frequency of accidents), and it can put additional pressure on insurers’ premiums; however, these effects are still under study.


The Latvian system seems to have five malus classes (1-5) and 12 bonus classes (6-17). The default class for first-time insureds is class 6. The bonus malus (BM) calculation takes into account the number of insurance days from effective to expiry date and the number of accidents. For insureds, BM classes are recalculated once a calendar year—specifically on 15 September.

The bonus malus class may be increased by one class towards better bonus classes if the total number of insurance days calculated in the interval of 12 months from 1 September to 31 August is at least 275 days (for half-year policies, the previous year is considered as well), and if in the previous 11 periods (in years) no insurance cases have occurred (and during these 11 periods there has been no period with fewer than 275 insurance days).

In the event of an insured event, the previous bonus malus class is lowered towards malus, as a percentage, depending on the number of insurance incidents in the year and the number of insurance days. The amount of insurance premiums or bonus depends on the BM class and it is determined by each insurance company also considering insurer’s loss history.

This conclusion is also supported by the Motor Insurers’ Bureau of Latvia (LTAB). From a press release of 19 September 2017, according to the current year annual assessment of insurance risks in the bonus malus system (taking place as mentioned above on 15 September), the number of drivers who had an improvement in the BM class has increased slightly faster than in other years, i.e., 11%, but the redistributions of the bonus malus classes are not significantly different from those in other years. Moreover, the average BM class for physical persons was 9.28, while for legal entities it was 8.61 (much higher than Italy, for example).

It seems that in Latvia it is more difficult to move up bonus classes and have significant discounts (i.e., one condition being that you need 11 claim-free periods, in years, to move up one bonus class). Thus, there may be less downward pressure on insurance companies’ premiums.

Compared to Italy, where the average class is around 1.9 (almost best bonus), in Latvia there seems to be less significant pressure on premiums with average classes of around 8 to 9 (considering that 17 is the best bonus class). However, according to the same press release, this year saw the largest increase in the class 17, which implies that there is some upward portfolio pressure.


Before 2015, insurance companies active in the MTPL market offered bonus malus on a voluntary basis. The bonus malus system was introduced in 2015 as a result of the changes to the law on MTPL insurance (Act on Compulsory Motor Third Party Liability Insurance No 381/2001 Coll., updated as at 1 April 2015). As per Article 8, paragraph 3, the insurer is obliged to take into account the policyholder’s overall previous claim record, either by providing a discount on the premium where there are no claims or by adding an extra charge if an insurance benefit has been paid in respect of MTPL insurance when determining the contractual amount of the insurance premium to be paid.

In practice, insurers decide on their own rebates and premium surcharges. For example, the duration of an uninterrupted contract is called a decisive period, which can be interrupted by a decisive event. For every decisive event, the length can be reduced by a number of months- for example, 36- so persons can move down a malus class by two or three classes (or move down a bonus class depending on the number of decisive events).

In Slovakia, because insurers can decide on their own rules, it is possible to have the premium bonus reduced depending on the number of decisive events. For example, more than one event occurring can reduce the bonus (but not just one event occurring), in which case policyholders may remain in the same class despite the fact that they had one accident. Thus, policyholders have more propensity to cluster around the highest bonus classes, so the premium reductions for these insurers may be more significant. This would put pressure on the financial balance of insurers as claim frequencies are much lower than that in European markets as specified above. Increasing the homogeneity of classes by relying more on telematics systems would be beneficial.


MTPL pricing was liberalised in 2013 when Croatia joined the European Union, but companies still need to notify tariffs as per Act on Amendments to the Act on Compulsory Insurance within the Transport Sector 76/2013.

The bonus malus system is defined, with an accident causing movement of three classes, and a maximum discount of 50%. Additionally, it is possible to transfer the bonus obtained on the basis of checking damage records from the Information Center of the Croatian Insurance Bureau. The right to a bonus and or malus is related to the owner, but it can be transferred to a new owner in several situations for personal vehicles, for example:

  • In case of death of the insured, the bonus can be transferred to other members of the immediate family (spouses, children, parents, grandchildren, grandparents, brothers and sisters)
  • Sale of the vehicle to members of immediate family

Companies in Croatia seem to offer additional bonuses, called a super bonus (for example, for personal cars), above the maximum defined of 50% and, in addition, they can also offer bonus protection after several years of no accidents, so that the 50% maximum bonus is maintained.

In Croatia, similarly to Italy, bonuses can be transferred, and in addition, higher bonus can be provided. This puts significant pressure on premiums of insurers with high clustering in the bonus classes.


MTPL pricing is not liberalised and minimum and maximum technical premiums are proposed by the Commission to the Government with a bonus malus system implemented in 2006. Additionally, recently, in October 2017, the Government of Macedonia has reviewed and adopted the Information on the Proposal Amendments to the Tariff for MTPL insurance premiums for legal entities (trucks and taxi transport). This decision also specifies the method of calculation of bonus and malus.

Using relatively more rigid systems can decrease product choice and create less ability for companies to select better customers and be more competitive as they are not able to personalise the premium to the full extent possible. Less competitiveness on the market can result in higher tariffs for policyholders. Because of stricter designs, a bonus malus system may also necessitate the use of loadings in MTPL pricing to achieve balance, which partially defeats the system’s purpose. This may not be possible due to defined tariff structure. Allowing more personalisation of the tariff could be beneficial in terms of achieving balance.


Bonus malus systems are designed to improve safety of driving and evaluate risk correctly. They can also add a personal note to the insurer’s premium rates, thus increasing the company’s competitiveness in the market. This personalisation can allow increased product choice and creates more ability for companies to select better customers and be more competitive, possibly resulting in lower tariffs. They tend, however, to be unbalanced because of low frequencies of accidents and can result in significant premium reductions.

These systems have been analysed in the literature using several measures in terms of their toughness, with tougher systems tending towards better financial equilibrium. Insurers have several measures to insure stability, including changing relativities, changing base premiums or loading the tariffs for bonus malus. However, these measures may partially defeat the system’s purpose and cause a lack of transparency or a discrepancy between the discount meant to be defined by the system and the effective discount given as a result of changing pricing elements, which is not beneficial to policyholders.

Companies that can differentiate risks using a valid risk characteristic that others are not using may achieve favourable selection and gain a competitive advantage. This could be done, for example, if companies started offering telematics in a country where this is not the norm. Better pricing by using telematics to create more homogeneous classes can put insurers at an advantage and may decrease the need for a posteriori systems.

Designing optimal systems by analysing at a country level the frequency of accidents (allowing an insured to move towards a better bonus class if that person's frequency is low enough), or having policyholders pay a premium proportionate to their individual frequencies, as well as analyses that look at the severity of accidents, may be important steps that can be pursued to achieve balance and a bonus malus system that works.

How Milliman can help

Our consultants have been involved in advising our clients on MTPL pricing in Italy and the CEE for many years. We have specialist insurance consulting teams and an excellent understanding of the markets. Our team has knowledge of the issues that is second to none from our involvement in a number of key assignments with leading market players on a variety of themes, including MTPL pricing and Solvency II. This work has included deep knowledge and extensive experience of best international practice in pricing MTPL business and an understanding of the practical difficulties involved in order to address challenging markets where various local factors introduce constraints which prevent a “technically perfect pricing.” We also have extensive experience with independent MTPL tariff certification in Italy and Romania.

1European Motor Insurance Markets (November 2015).