Calculation basis
As a calculation basis is called in the traditional actuarial science , particularly in the food and the (private) health insurance those used in actuarial calculations parameters , particularly in post - or covering capital formulas . In the last few decades, actuarial calculation methods have also been developed, especially for contributions in life insurance, in which there are no longer any calculation bases in the conventional sense. These are, in particular, methods for premium calculation that are oriented towards market prices and based on scenarios. The generic term used for all procedures is acceptance .
1st order bases of calculation are those bases of calculation that are particularly carefully determined, such as B. can be used to calculate the contributions or the actuarial reserve under commercial law , since careful calculations are required by law. In contrast to the "carefully" selected calculation bases of the 1st order, the "realistic" chosen calculation bases are called the calculation bases of the 2nd order . The calculation bases corresponding to the actual circumstances are also referred to as 3rd order calculation bases .
A distinction is made between biometric calculation bases, e.g. B. Mortality tables , the discount rate and cost rates.
Depending on the use, there are calculation bases for the premium calculation, the surrender value, the premium-free insurance and the actuarial reserve. These calculation bases do not have to be the same for the same contract, but can be agreed or selected independently for each purpose. Traditionally, however, the same calculation bases are used to calculate the actuarial reserve, the premium-free insurance and the surrender value as they were previously used to calculate the contributions. If the calculation of the actuarial reserve is less cautious than in the contribution within the framework of what is commercially acceptable, the contributions taken into account must be capped accordingly by a profit surcharge ( realization principle ). However, more cautious calculation bases may be necessary in individual cases. According to the Insurance Contract Act, premium- free insurance benefits may not be lower than those determined on the basis of the premium calculation, apart from an additional discount to be agreed. According to previous law, the calculation bases for the surrender value are to be selected in such a way that at least the current value of the insurance, possibly after an agreed deduction, results as the surrender value. According to the reform of the Insurance Contract Act, the surrender values of life insurances taken out from January 1, 2008 may not be lower than those determined with the calculation bases of the premium calculation; a deduction can also be agreed here. Deviations from this can always be made in favor of the policyholder , i.e. higher values can be agreed in the contract than legally stipulated.
Types of calculation bases
Discount rate
Since life and health insurance policies often run for decades, future benefits and contributions are discounted when calculating their current value. The interest rate used in actuarial formulas is known as the discount rate.
The highest permissible actuarial interest rate for calculating the actuarial reserve for new business in life insurance is specified in the actuarial reserve ordinance (DeckRV). With the exception of special tariffs or foreign currency insurance, it has been 1.75% since January 1, 2012. From 1994 to 2000 it had its highest level of four percent, since January 1, 2015 it has been 1.25% and was reduced to 0.9% on January 1, 2017.
The maximum interest rate in health insurance is 3.5%. Due to the low interest rates on the capital market, at the end of 2012 many insurers reduced the discount rate for new customer business to an average of 2.75 percent. According to a review by the Federal Financial Supervisory Authority , the interest earned in 18 out of 48 private health insurers is below the calculated rate.
Theoretically, the actuarial interest rate can be chosen freely for the calculation of the contributions, but according to statutory provisions, the contributions in sufficient amount must be agreed with the policyholders . Therefore, the actuarial interest rate for the contributions cannot be chosen too high compared to the actuarial interest rate used for the actuarial reserve.
Biometric calculation bases
Biometric calculation bases are the parameters with which the insured risks, such as mortality , occupational disability or medical costs are represented. As a rule, these parameters depend on gender and the age reached.
Important biometric calculation bases in life insurance are mortality, occupational disability and reactivation probabilities. On the basis of these one-year elimination probabilities , elimination orders (e.g. mortality tables) are calculated , which represent the reduction in size of an initial group with increasing age. A life table usually begins with a collective of 100,000 zero year olds (newborns). According to the probabilities used, this collective decreases every year. Health insurance uses both death and cancellation probabilities for its elimination regulations.
In health insurance, average medical costs per gender and age, so-called head injuries , are used as the basis for calculation.
Cost rates
Like all companies, insurers allocate their costs (operating expenses) to prices. The contribution parts provided for this in the contribution calculation are referred to as cost surcharges and these are part of the calculation basis for the contribution calculation. The unavoidable future operating expenses must also be taken into account when calculating the actuarial reserve and therefore the calculation bases for the actuarial reserve also contain cost surcharges in a carefully determined amount.
In life insurance, surcharges for administrative costs are usually unit costs or depend on the premium or the sum insured. The imputed acquisition costs are based partly on the premium amount and partly on the sum insured (previously: only the sum insured). Due to regulatory restrictions, the calculation of the actuarial reserve may only be used to a limited extent (usually a maximum of 40 per mille of the premium amount), acquisition costs before the contributions that cover these are due. In this respect, the calculation bases for the premium calculation differ from those for the actuarial reserve, as the calculation bases for the premium calculation usually provide for higher cost surcharges that are not required for ongoing administration. In the calculation bases for the actuarial reserve, the imputed closing costs are therefore divided into one-off Zillmer surcharges , which are initially taken into account , and amortization surcharges that are continuously taken into account with the premium payment . After the reform of the Insurance Contract Act, special rules for the consideration of imputed acquisition costs that deviate from the premium calculation must also be observed for the calculation bases for the surrender value.
The closing costs in health insurance are measured in monthly contributions. Further costs are set in proportion to the contribution or as unit costs.
Profit surcharge
An explicit profit surcharge is unusual in traditional actuarial mathematics. The other calculation bases are chosen carefully so that they leave enough profits. The amortization surcharge applied as part of the imputed closing costs when calculating the actuarial reserve is, however, economically pure profit surcharge. Otherwise, a profit surcharge is to be applied when calculating the actuarial reserve, which, according to the realization principle, may only be received proportionally to the contribution payment actually made, if the calculation bases of the actuarial reserve are less careful than those of the contributions. When calculating the actuarial reserve, only the contribution reduced by this profit surcharge, known as the standard contribution, is then taken into account.
Choice of 1st order calculation bases
Life insurance contracts usually run for decades without the possibility of a premium adjustment (with a few exceptions). The calculation bases must therefore be chosen so “carefully” for the premium calculation that they are likely to be sufficient over the term of the contract. In order to calculate the actuarial reserve, however, it is not sufficient that the calculation bases are only selected as “sufficient”; they must also contain an element of caution in order to be sufficient even in the event of unfavorable deviations. Since, according to the statutory provisions, the contributions must be agreed with the policyholders so high that they also enable the formation of the actuarial reserve, the premium calculation is usually based on this even more cautious standard.
In (private) health insurance, premium adjustments are possible and common. The calculation bases can therefore always be adapted to current developments. However, a certain amount of caution is also required for health insurance companies.
Principles
The principles for the choice of "cautious" calculation bases for the actuarial reserve in life insurance are, in addition to the general requirements in commercial law, laid down in the DeckRV, which - although it is a regulation of supervisory law, unfolds under commercial law according to § 341e HGB . With the exception of the surcharges for acquisition costs, the amount of which is already known when the contract is first accounted for, the calculation bases must be provided with sufficient securities.
When determining first-order mortality, one starts with observed deaths. Security surcharges or discounts are then included for the risk of error and the risk of change. As a result, in the case of insurances with a death character, the first-order mortality used for the tariff calculation is higher than the actual mortality. In the case of survival insurance ( pension insurance ), a mortality rate is expected that is lower than the observed mortality. This also includes a trend to account for the future improvement in mortality.
Furthermore, the determined probabilities of death are smoothed.
Basis of calculation for contributions and actuarial reserves
In the old life insurance portfolio, the bases of calculation for the calculation of the actuarial reserve are usually determined in the business plans of the insurers according to those of the premium calculation. In the case of certain, especially older, contracts, however, there may be differences compared to, in some cases from the beginning, in others due to a later adjustment of the calculation bases, as these turned out to be no longer cautious enough. There are also special requirements for taking into account acquisition costs in the case of the actuarial reserve. In the new portfolio, there are no specifications for the premium calculation due to the freedom of calculation required by European law; they just have to be sufficiently agreed. On the other hand, the DeckRV sets requirements for the calculation bases for the actuarial reserve.
In health insurance, the calculation bases for calculating the contributions and the actuarial reserve are the same in accordance with the Calculation Ordinance (KalV).
Adjustment of calculation bases
If it becomes apparent in life insurance that the bases of calculation used to calculate the actuarial reserve are not sufficiently reliable, an adjustment of these bases of calculation is necessary for the calculation of the actuarial reserve. The actuarial reserve is then calculated on a more cautious basis, which leads to an increase in the actuarial reserve ("subsequent reservation"). Due to the size of the actuarial reserve, this can lead to significant losses.
A current example is the industry-wide increase in the actuarial reserve for pension insurance, since the old DAV 1994R pension table has proven to be insufficient. But increases due to insufficient cost rates are also conceivable. A lower discount rate than originally calculated is also to be used if the current or future investment income is not sufficient to generate the previously used discount rate.
It is not permitted to adjust the actuarial reserves' calculation bases, resulting in a reduction in the actuarial reserve (continuity requirement).
A subsequent adjustment of the calculation basis of the premium calculation and thus a subsequent change of the contributions is generally not permitted, as the contributions are part of the contract and are relevant in the amount in which they were agreed between the parties when the contract was concluded.
In life insurance there is a statutory right of the insurer to increase under certain circumstances, which is to be further expanded as part of the reform of the Insurance Contract Act. The calculation bases (calculation bases and calculation methodology, i.e. the formula) may be adjusted here, even if the reform of the Insurance Contract Act only speaks of the calculation bases. In this respect, the term “calculation bases” will in future be legally extended to include the calculation method.
In health insurance, premium adjustments are required under certain conditions and occur frequently in practice. All calculation bases are checked and the contribution is recalculated. Usually the contribution is increased. One then speaks of a “restructuring” of the tariffs concerned.
Responsible for the calculation bases
The board of directors of the insurer is primarily responsible for the choice of the calculation bases, both for the calculation bases to be agreed in the contracts and for contributions or surrender values . The responsible actuary of the respective insurer has an additional legal responsibility for monitoring the calculation bases used for the contributions and the actuarial reserve. The supervisory authority monitors compliance with the statutory provisions as a whole, and the auditor monitors the basis for calculating the actuarial reserve.
The calculation of the contributions and the actuarial reserves for death benefit funds and regulated pension funds as well as for old life insurance policies is set out in the business plan. A change therefore requires the approval of the supervisory authority.
In health insurance, premium adjustments require the approval of an independent trustee .
Common biometric calculation bases
In life insurance, for the most part, the same calculation bases are used for the biometric calculation bases across the industry, namely the tables drawn up by the German Actuarial Association . Important current mortality tables are the DAV 2008T tables for insurance with a death character, DAV 2004R for new business in pension insurance and DAV 2004R inventory for reserving the inventory of pensions. Larger insurance companies in particular sometimes use their own company boards.
In health insurance, the biometric calculation bases are largely company-specific. The exception is the life table, which, however, is less important than in life insurance given the fact that cancellation is also included.
2nd order calculation bases
General
Life insurers are obliged to continuously review the basis of calculation that they use for the actuarial reserve. In the surplus breakdown, they are individually compared with the situation that actually occurred, which must then be submitted to the supervisory authority. So you put z. This compares, for example, with how much risk contributions for the risk of death according to the actuarial provisions of the actuarial reserve were received via the company's stock of risk contributions and how much of this was used for the actual deaths.
Based on this experience, realistic calculation bases, i.e. calculation bases of the 2nd order for the future, are derived from the actual events (3rd order calculation bases) .
The observed mortality rates are set in relation to the currently used or current mortality table. B. 60% of the DAV table 2008T.
use
The second-order calculation bases are used to prove that the exemplary information provided to the policyholders at the time of conclusion of the policy on possible future profit shares is not improperly excessive (proof of financial feasibility).
Before new tariffs are introduced, extrapolations are made as to which profits can be expected (profit test). This is based on 2nd order calculation bases and assumptions about future profit sharing .
Web links
- Ordinance on calculation bases for the actuarial reserves (DeckRV)
- Ordinance on the actuarial methods for calculating premiums and calculating the provision for aging in private health insurance (KalV)
Individual evidence
- ↑ 5 facts about the maximum technical interest rate. In: gdv.de. GDV, accessed on May 23, 2016 .
- ↑ Private health insurers cannot achieve calculated interest. In: sueddeutsche.de , accessed on June 10, 2013.
