PRU 7.3 Mathematical reserves

This section follows on from the overall requirement on firms to establish adequate technical provisions (see PRU 7.2.16 R). The mathematical reserves form the main component of technical provisions for long-term insurance business. PRU 7.3 sets out rules and guidance as to the methods and assumptions to be used in calculating the mathematical reserves. The rules and guidance set out the minimum basis for mathematical reserves. Methods and assumptions that produce reserves that are demonstrably equal to or greater than the minimum basis may also be used, though they must meet the basic requirements for methods and assumptions set out in PRU 7.3.7 R to PRU 7.3.27 G.

This section applies to all firms carrying on long-term insurance business and implements some of the requirements contained in article 20 of the Consolidated Life Directive. The implementation is designed to ensure that a firm's mathematical reserves in respect of long-term insurance contracts meet the minimum requirements set by the Consolidated Life Directive. A firm may use a prospective or a retrospective method to value its mathematical reserves(see PRU 7.3.7 R).

The required procedures are summarised in the flowchart inPRU 7 Annex 1G.

Firms to which PRU 2.1.15R applies are required to calculate a with-profits insurance capital component (see PRU 2.1.34 R). In order to calculate its with-profits insurance capital component, such a firm is required to carry out additional calculations of its liabilities on a realistic basis (see PRU 7.4), which it is required to report to the FSA (see Forms 18,19). A firm that reports its liabilities on a realistic basis is referred to in PRU as a realistic basis life firm. Such firms are subject to different rules relating to the calculation of mathematical reserves (see PRU 7.3.46 R and PRU 7.3.76 R) compared with those that apply to firms that report on a regulatory basis only (regulatory basis only life firms).

A number of the rules in this section require a firm to take into account its regulatory duty to treat customers fairly. In this section, references to such a duty are to a firm's duty to pay due regard to the interests of its customers and to treat them fairly (see Principle 6 in PRIN). This duty is owed to both policyholders and potential policyholders.

A prospective valuation sets the mathematical reserves at the present value of future net cash flows. A retrospective method typically sets the mathematical reserves at the level of premiums received (and accumulated with investment return), less claims and expenses paid. A prospective valuation is preferred because it takes account of circumstances that might have arisen since the premium rate was set and of changes in the perception of future experience. Circumstances in which a retrospective valuation might be appropriate include:

1. (1)

   where the assumptions initially made in determining the premium rate were sufficiently prudent at inception and have not been overtaken by subsequent events; and

2. (2)

   where the liability depends on the emerging experience.

PRU 7.3.10 R (2) prohibits only arbitrary changes in methods and assumptions, that is, changes made without adequate reasons. Any such changes would hinder comparisons over time as to the amount of the mathematical reserves and so obscure trends in solvency and the emergence of surplus.

The relevant factors referred to in PRU 7.3.10 R (4) may include, but are not limited to, factors such as future investment returns, expenses, mortality, morbidity, options, persistency and reinsurance (see also PRU 7.3.13 R to PRU 7.3.19 G).

The margins for adverse deviation are a prudential margin in respect of the risks that arise under a long-term insurance contract.

PRU 7.3.13 R sets the normal standard of prudence required for margins. PRU 7.3.16 G suggests benchmarks against which a firm should compare the margins it has set in accordance with PRU 7.3.10 R (4) and PRU 7.3.13 R. PRU 7.3.17 G gives guidance where a market risk premium is not readily obtainable.

When setting the margins for adverse deviation required by PRU 7.3.10 R (4) in relation to a particular contract, a firm should consider, where appropriate:

1. (1)

   the margin for adverse deviation included in the premium for similar long-term insurance contracts, if any, newly issued by the firm; and

2. (2)

   where a sufficiently developed and diversified market for transferring a risk exists, the risk premium that would be required by an unconnected party to assume the risk in respect of the contract.

The margin for adverse deviation of a risk should generally be greater than or equal to the relevant market price for that risk.

Where a risk premium is not readily available, or cannot be determined, an external proxy for the risk should be used, such as adjusted industry mortality tables. Where there is a considerable range of possible outcomes, the FSA expects firms to use stochastic techniques to evaluate these risks. In time, for example, longevity risk, where this constitutes a significant risk for the firm, may fall into this category.

The margins for adverse deviation should be recognised as profit only as the firm itself is released from risk over the duration of the contract.

Further detailed rules and guidance on margins for adverse deviation are included in PRU 7.3.32 G to PRU 7.3.91 G. In particular, the cross-references for the different assumptions used in calculating the mathematical reserves are as follows:

1. (1)

   expenses (PRU 7.3.50 R to PRU 7.3.58 G);

2. (2)

   mortality and morbidity (PRU 7.3.59 R to PRU 7.3.61 G);

3. (3)

   options (PRU 7.3.62 R to PRU 7.3.72 G);

4. (4)

   persistency (PRU 7.3.73 G to PRU 7.3.77 G); and

5. (5)

   reinsurance (PRU 7.3.78 G to PRU 7.3.91 G).

The rules and guidance on margins for adverse deviation in respect of future investment returns, which are also required in the calculation of mathematical reserves, are set out in PRU 4.2.28 R to PRU 4.2.48 G.

PRU 1.4.53 R requires firms to maintain accounting and other records for a minimum of three years, or longer as appropriate. For the purposes of PRU 7.3.20 R, a period of longer than three years will be appropriate for a firm's long-term insurance business. In determining an appropriate period, a firm should have regard to:

1. (1)

   the detailed rules and guidance on record keeping in PRU 1.4.51 G - PRU 1.4.64 G;

2. (2)

   the nature and term of the firm's long-term insurance business; and

3. (3)

   any additional provisions or statutory requirements applicable to the firm or its records.

PRU 7.3.22 R to PRU 7.3.91 G set out rules and guidance for the separate prospective valuation of each contract. These may be applied instead to groups of contracts where the conditions set out in PRU 7.3.22 R (2) are satisfied.

A separate prospective valuation for each contract may identify contracts for which the value of future cash inflows exceeds that of outflows, that is, the contracts have an asset value, rather than liability value. However, the surrender value of a contract is always greater than or equal to zero and the Consolidated Life Directive requires that no contract should be valued at less than its guaranteed surrender value. As a result, no contract should be treated as an asset.

The valuation of each contract, or group of similar contracts, should allow for the possibility, where it exists, that contracts may be surrendered (wholly or in part), lapsed or made paid-up at any time. The valuation assumptions include margins for adverse deviation (see PRU 7.3.13 R). PRU 7.3.26 R requires mathematical reserves to be established such that, if future experience is in line with the valuation assumptions, there would be no future valuation strain.

All cash flows are to be valued using prudent assumptions in accordance with generally accepted actuarial practice. Cash flows may be omitted from the valuation calculations provided the reserves obtained as a result of leaving those cash flows out of the calculation are not less than would have resulted had all cash flows been included (see PRU 7.3.22 R (2)). Provision for future expenses in respect of with-profits insurance contracts (excluding accumulating with-profits policies) may be made implicitly, using the net premium method of valuation (see PRU 7.3.43 R below). For the purposes of PRU 7.3.28 R (2), any charges included in expenses should be determined in accordance with the firm's regulatory duty to treat its customers fairly.

PRU 7.3.29 R (4) requires regulatory basis only life firms to make allowance for any future annual bonus that a firm would expect to grant, assuming future experience is in line with the assumptions used in the calculation of the mathematical reserves. Final bonuses do not have to be taken into consideration in these calculations (see PRU 7.3.9 R). For realistic basis life firms, except for accumulating with-profits policies, the mathematical reserves may be calculated as the amount required to cover guaranteed benefits as for such firms full allowance for discretionary benefits is made in the calculation of the realistic value of liabilities (see PRU 7.4.105 R (5)). The calculations required for accumulating with-profits policies are set out in PRU 7.3.71 R (1).

More detailed rules and guidance about the valuation of cash flows are set out in PRU 7.3.33 R to PRU 7.3.91 G.

The rules in PRU 4.2.28 R to PRU 4.2.47 R set out the approach firms must take in setting margins for adverse deviation in the interest rates assumed in calculating the mathematical reserves. This includes a margin to allow for adverse deviation in market risk and, where relevant, credit risk. The requirements set out in PRU 4.2.28 R to PRU 4.2.47 R protect against the market risk that the return actually achieved on assets may fall below the market yields on assets at the actuarial valuation date.

PRU 7.3.46 R and PRU 7.3.47 G apply to the valuation of with-profits insurance liabilities for a realistic basis life firm. PRU 7.3.38 R to PRU 7.3.45 G apply to a regulatory basis only life firm.

For non-profit insurance contracts no specific method of valuation for future premiums is required by PRU. However, the method of valuation used should be sufficiently prudent taking into account, in particular, the risk of voluntary discontinuance by the policyholder.

The valuation method for future premiums in PRU 7.3.38 R retains the difference, if any, between the gross premium and the net premium as an implicit margin available to finance future bonuses, expenses and other costs. It thus helps to protect against the risk that adequate resources may not be available in the future to meet those costs.

PRU 7.3.41 R permits three alternative methods. However, the third method is only possible where a meaningful comparison can be made between the terms of the contract (as changed) and the terms upon which the firm was effecting its new contracts of insurance at the time the contract was changed.

PRU 7.3.43 R allows a firm to spread acquisition costs over the lifetime of a contract of insurance, but only if it is reasonable to expect those costs to be recoverable from future premium income from that contract. Further prudence is provided by the limitation of recoverable acquisition expenses to 3.5% of the relevant capital sum. This adjustment for acquisition costs is sometimes termed a Zillmer adjustment.

In determining the extent, if any, to which it is reasonable to expect acquisition costs to be recoverable from future premium income, the firm should make prudent assumptions as to levels of voluntary discontinuance by policyholders.

The gross premium is the full amount of premium payable by the policyholder to the firm. The gross premium method contrasts with the net premium method which is required from regulatory basis only life firms (see PRU 7.3.37 R to PRU 7.3.45 G).

PRU 7.3.48 R prohibits a firm from taking credit for recurring single premiums under accumulating with-profits policies. As there is no contractual commitment to pay any future premiums the amount and timing of which are uncertain, the recognition of any potential margins would not be prudent. Where the payment of a future premium would give rise to a liability in excess of the premium a provision should be established.

For with-profits insurance contracts where the net premium valuation method applies, an implicit provision arises because the future premiums valued are limited to the net premium adjusted as permitted by PRU 7.3.43 R. This excludes the allowance within the gross premium for expenses (other than recoverable acquisition expenses). It also excludes other margins within the actual premium that are a prudential margin in respect of the risks that arise under the contract or that are needed to provide for future discretionary benefits. To the extent that these other margins are not needed for the purpose for which they were originally established, they may also constitute an implicit provision for expenses.

An implicit provision may also arise for other types of long-term insurance contract where, for example, no value is attributed to future premiums, but the firm is entitled to make deductions from future regular premiums before allocating them to secure policyholder benefits.

A firm should only reduce the provision for future expenses to take account of expected taxation recoveries related to those expenses where recovery is reasonably certain, and after taking into account the assumption that the firm ceases to transact new business 12 months after the actuarial valuation date. An appropriate adjustment for discounting should be made where receipt of the taxation recoveries is not expected until significantly after the expenses are incurred.

The firm's actual expenses in the 12 months prior to the actuarial valuation date may serve as a guide to the assumptions for future expenses, taking into consideration the mix of acquisition and renewal expenses. The expense assumptions should not be reduced to account for expected future improvements in efficiency until such efficiency improvements result in a reduced level of actual expenditure. However, the assumptions should take account of all factors which might increase costs including earnings and price inflation.

The provision for future expenses, whether implicit or explicit, should include a prudent margin for adverse deviation in the level and timing of expenses (see PRU 7.3.13 R to PRU 7.3.19 G). The margin should cover the risk of underestimating expenses whether due to, for example, initial under-calculation or subsequent increases in the amount of expenses. In setting the amount of the margin, the firm should take into account the extent to which:

1. (1)

   an appropriately validated method based on reliable data is used to allocate expenses by product type, by distribution channel and as between acquisition and non-acquisition expenses;

2. (2)

   the volume of existing and new business and its distribution by product type or distribution channel is stable or predictable;

3. (3)

   costs vary in the short, medium or long term dependent upon the volume of existing or new business and its distribution by product type or distribution channel; and

4. (4)

   cost control is well-managed.

In setting the margin, the firm should also take into account:

1. (1)

   the length of the period over which it is necessary to project costs;

2. (2)

   the extent to which it is reasonable to expect inflation to be stable or predictable over that period; and

3. (3)

   whether, if inflation is higher than expected, it is reasonable to expect that the excess would be offset by increases in investment returns.

Where a firm has entered into an agreement with any other person for the sharing or reimbursement of costs, in setting the margin it should take into account the potential impact of that agreement and of its discontinuance.

The rates of mortality or morbidity should contain prudent margins for adverse deviation (see PRU 7.3.13 R to PRU 7.3.19 G). In setting those rates, a firm should take account of:

1. (1)

   the systems and controls applied in underwriting long-term insurance contracts and whether they provide adequate protection against anti-selection (that is, selection against the firm) including:

   1. (a)

      adequately defining and identifying non-standard risks; and

   2. (b)

      where such risks are underwritten, allocating to them an appropriate weighting;

2. (2)

   the nature of the contractual exposure to mortality or morbidity risk including:

   1. (a)

      whether lower mortality increases or decreases the firm's liability;

   2. (b)

      the period of cover and whether risk charges can be varied during that period and, if so, how quickly; and

   3. (c)

      whether the options in the contract give rise to a significant risk of anti-selection (for example, opportunities for voluntary discontinuance, guaranteed renewal at the option of the policyholder and rights for conversion of benefits);

3. (3)

   the credibility of the firm's actual experience as a basis for projecting future experience including:

   1. (a)

      whether there is sufficient data (especially for medical or financial risks and for new types of benefit or new methods of distribution); and

   2. (b)

      whether the data is reliable and has been appropriately validated;

4. (4)

   the availability and reliability of:

   1. (a)

      any published tables of mortality or morbidity for the country or territory of residence of the person whose life or health is insured; and

   2. (b)

      any other information as to the industry-wide insurance experience for that country or territory;

5. (5)

   anticipated or possible future trends in experience including, but only where they increase the liability:

   1. (a)

      anticipated improvements in mortality;

   2. (b)

      changes arising from improved detection of morbidity (including critical illnesses);

   3. (c)

      diseases the impact of which may not yet be reflected fully in current experience; and

   4. (d)

      changes in market segmentation (such as impaired life annuities) which, in the light of developing experience, may require different assumptions for different parts of the policy class.

An additional provision for diseases covered by PRU 7.3.60 G (5)(c) may be needed, in particular for unit-linked policies. In determining whether such a provision is needed a firm may take into consideration any ability to increase product charges commensurately (provided that such increase does not infringe on its regulatory duty to treat its customers fairly), but a provision would still be required for the period until such an increase could be brought into effect.

An option exists where a policyholder is given a choice between alternative forms of benefit, for example, a choice between receiving a cash benefit upon maturity or an annuity at a guaranteed rate. In some cases, the contract may designate one or other of these alternatives as the principal benefit and any other as an option. This designation, in itself, is not one of substance in the context of reserving since it does not affect the policyholder's choices. Other forms of option include:

1. (1)

   the right to convert to a different contract on guaranteed terms;

2. (2)

   the right to increase cover on guaranteed terms;

3. (3)

   the right to a specified amount on surrender; and

4. (4)

   the right to a paid up value.

The firm should provide for the benefit which the firm anticipates the policyholder is most likely to choose. Except for the "option" of voluntary discontinuance in the case of regulatory basis only life firms (see PRU 7.3.74 R), past experience may be used as a guide, but only if this is likely to give a reasonable estimate of future experience. For example, past experience of the take-up of a cash payment option instead of an annuity would not be a reliable guide, if, in the past, market rates exceeded those guaranteed in the annuity but no longer do so. Similarly, past experience on the take-up of options may not be relevant in the light of the assumptions made in respect of future interest rates and mortality rates in the valuation of the benefits.

Many options are long-term and need careful consideration. Improving longevity, for example, can increase the value of guaranteed annuity options vesting further in the future. Firms also need to have regard to the fact that policyholder behaviour can change in the future as policyholders become more aware of the value of their options. The impact on policyholder behaviour of possible changes in taxation should also be considered.

In accordance with PRU 7.3.7 R and PRU 7.3.13 R, take-up rates for guaranteed annuity options should be assessed on a prudent basis with assumptions that include margins for adverse deviation (see PRU 7.3.13 R to PRU 7.3.19 G) that take account of current experience and the potential for future change. The firm should reserve for option take-up at least at a prudent margin over current experience for options shortly to vest. For longer term options where the option becomes increasingly valuable in the future due to projected mortality improvements, increased take-up rates should be assumed. In view of the growing uncertainty over take-up rates for projections further in the future, for guaranteed annuity option dates 20 years or more ahead at least a 95% take-up rate assumption should be made.

Where there is considerable variation in the cost of the option depending on conditions at the time the option is exercised, and where that variation constitutes a material risk for the firm, it will generally be appropriate to use stochastic modelling. In this case prices from the asset model used in the stochastic approach should be benchmarked to relevant market asset prices before determining the value of the option. Where stochastic modelling is not undertaken, market option prices should be used to determine suitable assumptions for the valuation of the option. If no market exists for a particular option, a firm should take the value of the nearest equivalent benefit or right for which a market exists and document the way in which it has adjusted that valuation to reflect the original option.

Where the option offers a choice between two non-discretionary financial benefits (such as between a guaranteed cash sum or a guaranteed annuity value, or between a unit value and a maturity guarantee) and where there is a wide range of possible outcomes, the firm should normally model such liabilities stochastically. In carrying out such modelling firms should take into account the likely choices to be made by policyholders in each scenario. Firms should make and retain a record of the development and application of the model.

The value of a contract with an option is greater than the value of a similar contract without the option, that is, the option has value whether it is expected to be exercised or not. Although in theory a firm can rebalance its investments to match the expected cost of the option to the firm (including the time value of the option), this takes time to achieve and the market may move more quickly than the firm is able to respond. Also, there are likely to be transaction costs. Firms should take these aspects into consideration in setting up mathematical reserves.

In PRU 7.3.71 R (1)(a) firms must take into consideration, for example, a market value adjustment where such an adjustment has been described in representations made to policyholders by the firm. However, any discretionary adjustment, such as a market value adjustment, cannot be included in the amount calculated in PRU 7.3.71 R (1)(b).

PRU 7.3.76 R and PRU 7.3.77 G apply to the valuation of the with-profits insurance liabilities of realistic basis life firms. PRU 7.3.74 R and PRU 7.3.75 G apply to the valuation of all other liabilities.

The rate of voluntary discontinuance (that is, lapse, surrender or paying up) is often difficult to predict and may be volatile especially in the short term during stressful economic conditions. Depending upon the circumstances and contract terms, voluntary discontinuance may increase or decrease the firm's liability. In effect, PRU 7.3.74 R requires a firm to assume that there will be no voluntary discontinuance if assuming voluntary discontinuance would reduce the liability. This protects against the risk that arises from volatility in the rate of voluntary discontinuance. In addition, there is the risk of assets not being realisable when needed due to the rates of discontinuance exceeding expected levels.

The prudential margin in respect of assumptions of voluntary discontinuance should be validated both in relation to recent experience and to variations in future experience that might arise as a result of reasonably foreseeable changes in conditions. In particular, where estimates of experience are being made well into the future, the assumptions should contain margins that take into account the increased risk of adverse experience arising from changed circumstances. Firms should also consider the possibility of anti-selection by policyholders and of variations in persistency experience for different classes and cohorts of business.

The prospective valuation of future cash flows to determine the amount of the mathematical reserves includes amounts to be received or paid under contracts of reinsurance in respect of long-term insurance business (see PRU 7.3.28 R (4)). This applies even where those cash flows cannot be identified as related to particular long-term insurance contracts (see PRU 7.3.22 R (3)).

In valuing reinsurance cash flows, a firm should establish prudent margins for adverse deviation (see PRU 7.3.13 R to PRU 7.3.19 G) including margins in respect of:

1. (1)

   any uncertainty as to the amount or timing of amounts to be paid or received; and

2. (2)

   the risk of credit default by the reinsurer.

In assessing the risk of credit default, the firm should take into account the rules and guidance in PRU 3.2 (Credit risk in insurance).

It will not necessarily be appropriate to use the same assumptions in PRU 7.3.79 R as for the underlying contracts. For example, if only a subgroup of the original contracts is reinsured, it may be appropriate to use different mortality rates.

Only reinsurance cash inflows that are triggered unambiguously by the insurance risks of the firm that are reinsured may be valued. Reinsurance cash inflows that depend on other contingencies where the outcome does not form part of the valuation basis should not be given credit.

Firms should assess the extent of margins in the valuation of the existing contracts of insurance where these provide implicit provision for the reinsurance cash outflows in PRU 7.3.79 R. Where the reinsurance asset exceeds the estimated value of the future surplus under reinsured contracts firms should assess their credit risk exposure to the reinsurer.

For the purposes of PRU 7.3.85 R, a contingent liability means a liability that would only arise upon the happening of a particular contingency, even where that contingency is not expected to occur. For example, if the firm has a reinsurance arrangement in force that in the event the firm were wound up would give rise to repayments other than out of surplus emerging, the reinsurance cash outflows should be valued as a liability.

PRU 7.3.85 R allows a firm not to value reinsurance cash outflows provided the contingencies in which the reinsurance would require repayment other than out of future surpluses are limited to termination clauses concerning fraud, misrepresentation, non-payment of reinsurance premiums by the firm or a failure by the firm to obtain the agreement of the reinsurer to a transfer of business by the firm.

Where the reinsurance cash outflow is payable by a fund or sub-fund that generates such profits, charges or transfers, the firm need make no provision for such payments provided that repayment to the reinsurer is linked unambiguously (as defined in PRU 7.3.85 R) to the emergence of future surplus. Where the profits, charges or transfers arising under a block of business are payable by a fund or sub-fund to another part of the firm then only where the firm has committed to remit such profits, charges or transfers directly to the reinsurer would it be acceptable for no provision for payments to the reinsurer to be made.

In PRU 7.3.78 G to PRU 7.3.89 G references to reinsurance cash outflow include any provision for the reduction in policy liabilities recognised as covered under a contract of reinsurance or for the reduction of any debt to the firm previously created under a contract of reinsurance. In PRU 7.3.90 R analogous non-reinsurance financing agreements include contingent loans, securitisations and any other arrangements giving rise to charges on future surplus arising.