1.3.1. Deterministic approach

We have assumed throughout this paper that the (re)insurer has chosen to use a deterministic approach for estimating its Solvency II technical provisions, rather than a stochastic approach. A stochastic approach would be equally valid, but at the time of writing, very few (re)insurers were using a stochastic approach. Most insurers are choosing to adapt existing reserve estimates for IFRS/GAAP accounts and/or actuarial opinions rather than calculate the Solvency II technical provisions from scratch. This may change over time, and it is not the purpose of this paper to advocate one approach over the other, but our experience is based on converting existing reserve estimates and so this is the approach that we have assumed here.

1.3.2. Expert judgement and proportionality

The Solvency II Directive and draft guidance makes frequent reference to proportionality and the application of expert judgement. How one determines what is proportional and where and how to ensure expert judgement is appropriate is important to the calculation of technical provisions, but not specific to technical provisions alone. In order to keep our scope manageable (given that each of these subjects could generate a paper on its own), we have decided not to try to cover either of these issues in-depth in this paper.

2.2.1. Appropriateness of data

For data to be considered appropriate, at least:

• ∙ the data are suitable for the purposes of calculating technical provisions;

• ∙ there is no undue estimation error arising from the amount or nature of the data;

• ∙ the data are consistent with the methods and assumptions used to calculate the provisions; and

• ∙ the data appropriately reflect the underlying risks.

2.2.2. Completeness of data

For data to be considered complete, at least:

• ∙ the data are of sufficient granularity and include sufficient information to identify trends and assess the characteristics of the underlying risk;

• ∙ there are data available for each homogeneous risk group in the calculation; and

• ∙ no relevant data are excluded from use in the calculation without justification.

2.2.3. Accuracy of data

For data to be considered accurate, at least:

• ∙ the data are free from material errors;

• ∙ data from different time periods used for the same estimation are consistent; and

• ∙ the recording of the data is consistent over time, and performed in a timely manner.

3.1.1. The guidance

This section of the paper is based principally on paragraphs 3.63 to 3.70 and 3.108 to 3.114 of CEIOPS final advice for Level 2 Implementing Measures, CEIOPS-DOC-33/09 and the European Commission Draft Implementing measures Solvency II, 31 October 2011 (“EC Draft L2”).

In relation to the claims provision, the EC Draft L2 states that:

In relation to the premium provision, the EC Draft L2 states that:

3.4.1. Claims provision: claims (incurred)

This is the expected present value of future cash flows relating to claim events which have occurred (i.e. past exposure).

Ignoring outwards reinsurance, the calculation of the undiscounted element of the claims provision is similar to the undiscounted claims reserve already estimated by (re)insurers on a regular basis to fulfil existing regulatory requirements. The key changes are the removal of any implicit or explicit margins for prudence and consideration of ENID.

The current norm is to use deterministic actuarial techniques to assess the undiscounted element of the earned claims reserves (such as chain-ladder/development factors, Bornhuetter–Ferguson, average cost per claim, etc.). This is likely to continue in the immediate future. Although stochastic techniques are possible, they have not as yet gained widespread use for this purpose. This may change over time as the techniques develop further, become better understood, more flexible, available in commercially available reserving products and as the link between reserving and internal models develops.

Assumptions and methods must be chosen on a best estimate basis (excluding any margin for prudence). For example, allowance should be made for negative incurred but not reported (IBNR) where it is expected that future profit will emerge from existing case reserves. The removal of any explicit margins for prudence in existing earned reserves may be relatively straightforward. Ensuring the removal of implicit margins is more complex insofar as these are based on actuarial judgements and embedded within calculations. This is discussed further in section 3.8.1.

It is good practice to clearly justify the quantification of the margin removed from a GAAP/IFRS-based estimate.

The present values of the cash flows can be calculated by applying a payment pattern to the undiscounted reserves to generate future cash flows, which are then discounted (at EIOPA-prescribed rates for specific currencies) and summed. Assessment of the appropriate payment pattern is likely to be based on historic payments where sufficient credible data is available. Further discussion on payment patterns and cohorts of claims (accident year (AY) versus underwriting year (UY)) is included in section 3.8.4.

Note that in some markets, elements from “expenses”, in particular, allocated loss adjustment expenses (ALAE) are included in the earned claims. One may think that this is not a problem in that Solvency II does not require the elements of the claims and premium provisions to be calculated separately. However, under the current proposal for reporting, (re)insurers will need to split out expenses, so this will need to be allowed for, explicitly or approximately, for reporting purposes. Also, the practitioner must take care not to either double count or omit allowance for all expenses.

3.4.2. Premium provision: claims (unexpired)

This is the expected present value of future cash flows relating to future claims events on existing policies.

Many (re)insurers are calculating this element of the premium provision using a loss ratio approach: applying a loss ratio to an unearned premium to come up with an estimation of the total undiscounted claims, then applying a payment pattern to generate future cash flows that can be discounted and summed to generate a present value.

How one chooses a loss ratio assumption will vary between (re)insurers. Strictly speaking, a loss ratio derived from a robust unexpired risk reserve (URR) calculation is the correct approach, but, in practice, many (re)insurers do not carry out detailed URR calculations unless they expect that the premiums for a class of business are insufficient. It may be sufficient to use alternative, more readily available approaches such as pricing loss ratios, plan loss ratios or a burning cost method, but care needs to be taken to ensure that the approach used is appropriate.

3.4.2.1. Suitability of pricing loss ratios

Pricing loss ratios are based on estimates of likely future experience and thus may be suitable as a base for premium provision loss ratios. However, pricing loss ratios may not be appropriate for several reasons. For example, the period of exposure for the pricing loss ratio may be very different from the period of exposure covered by the premium provision. For annual contracts, written uniformly over the calendar year (CY), the exposure for the premium provision will be weighted towards the first few months. Current pricing loss ratios are likely to assume a longer exposure period and thus if there are significant trends in claim costs, the pricing loss ratios may overstate trends for the premium provision.

3.4.2.2. Suitability of plan loss ratios

Plan loss ratios may be suitable for the premium provision, provided they have been estimated on a best estimate basis and either cover the same period of exposure covered by the premium provision, or trends in claims costs over time are insignificant. However, they are not suitable if:

• ∙ the plan loss ratios are out-of-date, perhaps because more recent experience has been significantly different than expected, or the type of business (e.g. rating factor groups) that has been written is different to what was expected when the plan was constructed;

• ∙ the plan is conservative or deliberately incorporates “stretch assumptions”; and/or

• ∙ plan loss ratios do not represent the reserving actuary’s best estimate. For example, for Lloyd’s syndicates, Lloyd’s may require the syndicate to adjust its plan loss ratio upwards as part of the SBF process, and the reserving actuary may not agree that the revised loss ratios are best estimate.

3.4.2.3. URR loss ratios

The projection underlying URR loss ratios and for a premium provision loss ratio, would typically start with an analysis of recent loss experience, most likely using the projected ultimate losses for recent AYs taken from the claims provision.

Adjustments are required to adjust the historic experience to the future exposure period covered by the unearned premium. Such adjustments may take account of, for example, changes in:

• ∙ exposure;

• ∙ the rating environment;

• ∙ the legal environment;

• ∙ policyholder behaviour;

• ∙ exposure;

• ∙ business mix;

• ∙ inflation and other trends;

• ∙ seasonality;

• ∙ reporting and settlement delays/term to payment;

• ∙ lapse rates;

• ∙ reinsurance coverage;

• ∙ investment return (future risk-free rates of return);

• ∙ unusual/exceptional events;

• ∙ coverage and policy wording; and

• ∙ socio-economic trends.

Attritional and large losses should be considered separately if such an analysis is warranted by the nature of the risks, availability of data and proportionality.

If the book is exposed to natural catastrophes these may need to be projected separately. Some natural catastrophes are seasonal. For example, US hurricanes are far more likely in August/September than in the rest of the year. This may be reflected by splitting the URR/premium provision exposure by quarter and varying the loss ratio according to the risk in each quarter.

It may not be necessary or indeed practical to adjust for all of the above factors, particularly as many may have already been considered as part of the original loss projection used as a starting point. However, any significant changes should be considered, particularly those of short-term impact and thus likely to apply to the exposure covered by the URR/premium provision.

URR loss ratios are often updated less frequently than the technical provisions, so, if they are to be used for the premium provision, will require careful consideration and possible adjustment when not recent. Care needs to be taken to ensure that URR loss ratios calculated, say, 6 months earlier, are still applicable. Changes in the balance of risks written over the period may mean that the URR loss ratios at the year-end are not suitable at, say, the half-year, because the nature of the portfolio is changing.

3.4.2.4. Burning cost method

An alternative to using loss ratios is to project burning costs based on a suitable exposure measure (e.g. policy count). These burning costs are then multiplied by a projection of the exposure. An advantage of this approach is that it considers the claim cost independently of the premium charged and rating actions, which do not always have a proportional impact on claims costs. This method does, however, require additional considerations:

• ∙ The mix of business should be allowed for in any projections. This involves altering the average cost per policy to reflect any changes in the profile of policies written. Assistance could be sought from pricing teams to quantify any changes in the policy/customer profile.

• ∙ An allowance for claim cost inflation should be included in the projections. The natural link to premium inflation is lost when using burning costs.

• ∙ Seasonality should be incorporated if claims costs are influenced by the time of year.

• ∙ Measures of exposure need to be consistent with the volumes of business underlying the unearned premium reserve (UPR) figure. Should the exposures be out of line with the UPR then an inconsistency would arise with other items taken from the IFRS/GAAP balance sheet.

3.4.2.5. Payment patterns (premium provision)

A loss payment profile assumption will be needed. Ideally, this should represent the timing of losses relating to the future exposure.

The materiality of this assumption to the premium provision depends on the term of the liabilities and prevailing yields. In recent years, yields have been very low, so payment pattern assumptions have been less of a concern than they otherwise would be.

If the reserving approach uses AY data cohorts one could first project incidence by underwriting period and then apply corresponding accident period payment patterns, or model inception patterns and losses based on time since inception.

If the reserving approach uses UY cohorts the situation is a little more complex. As the premium provision relates to future exposure, an exposure period payment pattern will be required. If this cannot be calculated directly a transform will be required to obtain a suitable accident period payment pattern from the underwriting period payment pattern. This pattern can then be applied to the projected incidence by underwriting period as above. In either case, a simple lag may suffice provided the simplification does not have a material impact.

We discuss cash flow projections further in section 3.8.4.

3.4.3. Expenses

Allocated and unallocated claim management as well as other expenses are discussed in detail in section 5.

3.4.4. Future premiums receivable (earned and unearned element)

This information should be known as part of the credit control process and as it is required to construct the asset side of the balance sheet. It is usually included in “premiums receivable”. The technical provisions should only include future premiums that are not “overdue”. Overdue premiums should remain part of “insurance and intermediaries receivables” on the Solvency II balance sheet.

The potential for confusion between Finance and Actuarial is significant in many organisations. Typical complications include

• ∙ lack of clarity as to what portion of “premiums receivable” relates to future exposure and what relates to overdue premiums; and

• ∙ data not existing at the same level of granularity as is required to produce the technical provisions.

It is important that Finance and Reserving functions reach a common understanding as to what falls into technical provisions and what will remain in other parts of the balance sheet. Without this there is a risk of double counting or omission.

Ideally, (re)insurers should be looking to collect the data at the level required for the technical provisions. If this is not being done yet, it may be necessary to use some approximate allocation, perhaps in proportion to the historical premiums written/earned taking care to allow for differences in the proportion of policies where premiums are spread over the term of the contract between reserving classes.

Further issues may arise if there is a need to split the future premiums receivable between the earned and unearned element. Though this approach is appealing, as it reinforces the concept of future and past exposure in the respective provisions, it increases the complexity of the calculation if rigorously applied. For many (re)insurers, the amount of future premium attributable to past exposure is likely to be low, and immaterial, so, on the grounds of proportionality, those (re)insurers may choose to allocate all future premium to the premium provision. We note that this should not have any effect on the overall best estimate and thus should take lower priority than issues that may affect the surplus assets when deciding on the approach and level of effort to expend.

The future premium receivable should be net of any expected premium defaults.

3.5.1. Binding or delegated authorities

Under a binding or delegated authority (binder) a (re)insurer agrees to underwrite future business that may be introduced by a third party under specified conditions. Binding or delegated authorities may also be known as partnership agreements. The key question, from a contract boundary perspective, is that if the insurer is legally bound to accept future business that could be introduced, should future insurance contracts that may be introduced under the binder be allowed for in the premium provision? There is still a lot of debate concerning legal obligations of insurance contracts and the treatment of binder business is an area the industry and regulators have yet to reach a stance on.

There are conflicting opinions. If future business is assumed to be profitable, then allowing for future business under a binder contract will reduce the premium provision, which would be imprudent, especially as the volume of the business to be introduced is not guaranteed. However, if the binder was loss making, then it would be prudent to allow for future new business under the binder contract.

Also, there is a question as to how much business the (re)insurer should allow for. One suggestion was that an (re)insurer should assume that it could terminate the binder and so need only allow for the volume of business expected in the notice period. This is still problematic in that binders may not have clearly defined notice periods. Indeed, the nature of the contract may be that the insurer will agree to continue to accept the business introduced until such time as the partner/binder cover holder can make alternative arrangements.

The Lloyd’s recommendation, and a view that is supported by several parties in the market, is that we should use a “look through” approach. A strict reading of the Solvency II guidance would imply that only the underlying policies that have been written but have not yet incepted as at the valuation date should be included within the valuation of technical provisions. This is because the contract between an insurer and a binding authority/managing general agent is not an insurance contract.

However, there are alternative approaches in use in the market, e.g., to include all future-obliged business that may be written through the binder or to include only legally obliged future business written in the period up to when the insurer can activate the cancellation clause. Lloyd’s, itself, will currently accept any of the above approaches by its managing agents, as long as the approach can be justified.

The treatment of binder business can make a significant difference to a (re)insurers technical provisions, so the current inconsistency in approach is unhelpful for those (regulators and other interested parties) who would like to compare (re)insurers’ balance sheets on a like-for-like basis. We hope that the regulators will be able to deliver clear guidance as to the approach that should be used by all (re)insurers. In the meantime, as a (re)insurer, it is important to maintain a flexible approach should you need to change it in the future.

3.5.2. Contracts where the insurer is obliged to requote

In some circumstances, a (re)insurer may not be able to cancel the policy and may have to offer renewal terms at the end of the policy term. This may be for a number of reasons including

• ∙ a legal obligation;

• ∙ because the terms of the contract do not permit the (re)insurer to cancel the policy, as may be the case for some medical insurance contracts where the insurer guarantees to offer renewal without re-underwriting individual contracts;

• ∙ due to informal industry agreements, for example, the former agreement between the Association of British Insures and the UK Government whereby the insurers agreed to continue to offer flood risk cover to domestic property in high-risk areas;

• ∙ because it is market practice to always offer renewal; or

• ∙ because the insurer feels a moral obligation to offer renewal, as may be the case, for example, in UK household insurance when a property has suffered from subsidence.

Under the terms of the contract boundaries rules (see section 3.5.), provided that the (re)insurer has a unilateral right to amend the premiums or the benefits payable under the contract in such a way that the premiums fully reflect the risks the (re)insurer need not allow for the cash flows related to premiums beyond the renewal date. The key question here is the degree to which the (re)insurer is able to amend the premiums or benefits, or cancel the policy.

We, on the working party, cannot recommend a single all encompassing approach to these situations, as the “correct” approach is likely to vary according to the circumstances. We suggest that each (re)insurer needs to reach its own view as to the degree of flexibility it has to terminate policies and/or amend premiums and/or benefits. This view needs to be clearly documented to justify the approach taken to recognise cash flows arising from exposure beyond the renewal date.

Should the (re)insurer decide that it needs to allow for cash flows arising from exposure beyond the renewal date, prudence, while not a term majored on in the Solvency II guidance, dictates that the (re)insurer take care not to overestimate the future profitability of future renewals. It will be important to allow appropriately for lapse rates, not to overstate them if future renewals are expected to be loss making, nor understate them should future business be expected to be profitable.

3.6.1. UK GAAP/IFRS requirements for the UPR/URR

The UPR represents a portion of the written premium held as a liability to cover the expected claim and associated expenses arising from the remaining exposure on existing business. This is a retrospective calculation based on the written premium and an assumed earning profile. The UPR reserve is reduced by deferred acquisition costs (DAC).

The principle behind DAC is that the acquisition costs should be “earned” over the term of the policy in proportion to the risk over the exposure period. This DAC is an amount of acquisition costs that have been already paid but is deemed to relate to unexpired risk. Generally, the UPR is shown gross of DAC with DAC shown separately as an asset.

In the event that the UPR is expected to be inadequate to cover future losses and expenses, an URR should be held. This should be based on the expected amount of future claim payments and claims administration expenses from existing policies less any premiums receivable under the contracts. This is a prospective calculation.

The amount required in excess of the UPR shall be defined as the additional unexpired risk reserve (AURR).

If an AURR is required, credit can be taken for the expected investment returns on the assets backing the UPR net of DAC. Investment return is also allowed for in the calculation of the premium provision but only at the discount rates provided by EIOPA.

The URR may be reduced by any premium receivables, net of expenses, under the contacts which are not already contained in the UPR, e.g., unpaid instalment premiums not included in UPR.

The URR should be assessed for groups of business which are managed together, meaning that expected surpluses on policies can be used to offset expected deficits within the same group. However, the need to hold an AURR for a particular group of business cannot be offset by expected unearned profitability from other groups of business. This is a key area of difference as the Solvency II balance sheet, being based on an economic value basis capitalises margins relating to the unearned exposure.

3.6.2. Comparison with the premium provision

The premium provision is calculated on a best estimate cash flow basis and allows for all businesses obligated to at the valuation date. Therefore the key differences from the GAAP/IFRS requirements for UPR and URR are:

• ∙ The UPR/URR need only allowed for policies in force at the valuation date. The premium provision needs to include all policies that the (re)insurer is obligated to at the valuation date, including policies that have not yet incepted.

• ∙ There is no explicit allowance in the UPR/URR for ENID. Under current accounting rules, where an AURR is needed, it is sufficient for the URR calculation to allow for reasonably foreseeable events only.

• ∙ There is no concept of DAC in Solvency II: the premium provision only allows for future expense cash flows, so, for example, up-front commission is allowed for at the commencement of a policy only. For those policies already in-force initial expenses, such as up-front commission will have occurred in the past and so not be allowed for in the premium provision. For this reason, initial expenses need only be allowed for in respect of unincepted business where these expenses have not yet been paid at the valuation date.

• ∙ Under GAAP/IFRS, the (re)insurer cannot allow for future profits unless an AURR is required and then no offset is permitted between different groups of business. Capitalisation of future profits is discussed further in section 3.7.

3.8.1. Best estimate and removal of margin

If the reserving actuary/specialist is deriving the Solvency II best estimate from the IFRS/GAAP estimate, then he/she will need to consider the need to remove margins.

IFRS/GAAP reserves are unlikely to be a Solvency II best estimate. For UK (re)insurers, the ABI SORP on Accounting for Insurance Business states that The level of claims provisions should be set such that no adverse run-off deviation is envisaged. This is consistent with the requirement of paragraph 43 of Part I of Schedule 9A to the Companies Act 1985 that technical provisions should be sufficient at all times to cover any liabilities arising out of insurance contracts so far as can reasonably be foreseen. However, given the uncertainty in establishing a provision for outstanding claims, it is likely that the final outcome will prove to be different from the original liability established. In setting the provision, consideration should be given to the probability and magnitude of future experience being more adverse than assumed (ABI SORP 2005, paragraph 95).

For accounting purposes, the reserves will depend on each company’s reserving policy. Take, for example, a company with a single potential claim that will be either £100 or £0 with a probability of 50% for each outcome. Under Solvency II, the treatment is straightforward; the best estimate (before discounting and expenses) is £50. Under IFRS/GAAP, the treatment is far more likely to vary between companies. It is likely that the CFO of most (re)insurers with shareholders would rather see a release from reserves of £100 than a deficit of £50. Therefore, for IFRS/GAAP some (re)insurers would reserve £100, some may reserve slightly less because a small deficit is acceptable, and there may be some who hold reserves of £50 because that fits their reserving policy (and perhaps they do not have shareholders!).

In theory, the removal of any explicit margins for prudence in reserves would be relatively straightforward. In many cases, management margins are held as either a fixed amount or a fixed percentage of actuarial best estimate (ABE) reserves and for technical provision purposes these would simply be excluded. However, in practice, the explicit “margin” is often not pure margin. For example, it may include a management adjustment (MA) to allow for a change in the claims environment. If it is a best estimate of the impact of the change then that part of the “margin” should not be removed. This kind of adjustment is often subjective and prudent and the degree of prudence cannot be clearly articulated or quantified. This may be the case for several items that make up an “explicit” margin, so it can be time-consuming and politically stressful to agree the margin to be removed.

Where implicit margins in reserves are known to exist, due to conservative assumptions or methods adopted, an additional actuarial exercise may be required to assess reserves on a pure best estimate basis. Practically, margins in reserves may not be immediately apparent as they may have been unintentionally introduced via actuarial judgements or embedded within calculations. Validation and back-testing can be used to assess whether implicit margins remain, as discussed in section 10 on validation. Over a period of time margins may be identified via a systematic release of reserves.

This can be a sensitive area for management. For some (re)insurers, the concept of working to a best estimate is relatively new. Often management are far happier with the concept that the reserves are sufficient, rather than best estimate, and generate a positive run-off more often than not.

In addition, local accounting and/or regulatory standards may already specify that reserves should be best estimate, but this has not been strictly complied with historically. US GAAP only permits reference to a single best estimate, but this may not be equivalent to a Solvency II best estimate. To be compliant, and avoid confusion, it will be important to take care in the language that one uses in these situations: to make it clear that the financial reporting requirements differ from Solvency II requirements, and exactly what is meant by a “best estimate” in each context.

Other external considerations for management include:

• ∙ potential tax implications if the (re)insurer identifies a margin in the reserves used for their tax calculation;

• ∙ the impact on the audit opinion, especially if the (re)insurer is supposed to be booking “best estimate” reserves or the margin identified for the first time is larger than expected; and

• ∙ for (re)insurers required to have an actuarial opinion, whether the margins identified are consistent with that opinion.

3.8.2. Insurance and reinsurance receivables

Under Solvency I Insurance and Reinsurance Receivables are assets held on the balance sheet in anticipation of future payments relating to insurance and reinsurance operations. They include expected premium payments from policyholders and brokers and loss recovery and other payments from reinsurers.

The premium element includes premiums payments not yet due, because of credit terms and arrangements where premiums are payable by instalments, premiums overdue due to late payments or disputes and premiums Written But Not Incepted (WBNI).

It can also include reinsurance receivables covering amounts owed by reinsurers relating to reinsurance recoveries, return commission, profit shares or return of premiums relating to exposure adjustments. If reinsurance is paid for in advance, such as in the case when deposit or minimum premiums are paid to reinsurance, a reinsurance prepayment asset may be held.

Under Solvency II, the expected future cash flows from these assets should be included in the technical provisions. Splitting the Insurance and Reinsurance Receivables into what should be in the technical provisions and what should remain in the Solvency II balance sheet is not a straightforward exercise and there remains some uncertainty over the treatment of certain elements and practical issues.

IFRS/GAAP Insurance and Reinsurance Receivables may not be of sufficient granularity to be readily allocated to Solvency II classes of business. For premium receivables, the data may exist as part of the credit control process and the level of automation or information recorded may not lend itself to a seamless transfer to the actuarial projection systems.

Further complications arise if large amounts of recently received premiums are sitting temporarily in clearing accounts awaiting allocation to specific policies.

Our current understanding is that it is unclear how overdue premiums should be allowed for. The Lloyd’s approach has been to leave the provision for overdue premiums on the balance sheet and not make any allowance for future premium received on overdue premiums in the technical provision.

A similar issue arises when considering the reinsurance due on settled losses. Article 35 TP 22 seems to suggest, and Lloyd’s have interpreted it in this way, that such future cash flows should remain as an asset on the balance sheet. However, some uncertainty remains if this is the correct treatment.

It is important that when elements of the Insurance and Reinsurance Receivables move from the asset side of the balance sheet to form an offset to the technical provisions, that their value and finance’s interpretative insight is not lost in the translation.

3.8.3. Insurance and reinsurance creditors

Under Solvency I, Insurance and Reinsurance Creditors are liabilities held on the balance sheet to provide for future payments relating to insurance and reinsurance operations. Such items consist of premium payments due to reinsurers and amounts held for claims settled but not yet paid to policyholders.

The treatment of creditors remains unclear. Reinsurance premiums with credit terms attaching are not yet due. It might be consistent to treat such cash flows in a similar way to premiums not yet due and include them in the technical provision cash flows; however, issues may arise relating to granularity.

In practice, some companies may account for the reinsurance on a net basis and offset reinsurance premiums falling due against loss recoveries. This may further complicate data and granularity issues.

3.8.4. Estimating cash flows

Assumptions will be required to enable cash flows to be projected for each element of the claims and premium provision for all Solvency II LoB and significant currency at a minimum.

Claim cash flows can be generated in a number of ways but one of the most common is to apply the paid loss run-off pattern to the selected reserves. While this appears reasonably straightforward it is important to consider the existence and impact of model error, particularly if claims reserves and payment patterns have been based on different underlying methods and models.

For example, the claim reserves will not in many cases be estimated by simply projecting paid losses to ultimately using paid grossing-up factors. The projections will involve consideration of a number of different models overlaid by judgement frequently and, perhaps, external data. If the reserves selected differ to those arising from a simple paid projection; the difference is indicative measure of the extent of the model error.

If there is significant model error it is unlikely that the projected cash flows will be reliable. This may lead to problems when back-testing where the cash flows projected over the short term look very different to the recent activity. This may also lead to difficulties when trying to interpret actual versus expected outcomes.

There are a number of simple validations that may help refine the short-term cash flows. Look at the paid to outstanding trend over the recent past, allowing for any significant changes in exposure, and compare it to the short-term cash flow projections. If there is a significant discontinuity between the past and future ratios the cash flow may need modification before they can be used. It may also help to look at the areas where model error is largest by comparing the projected ultimate losses by origin year under the model selected and the simpler paid projection. Once the reasons for the differences have been understood it may be possible to determine an appropriate cash flow to be applied to the difference. Again, the resulting cash flows can be back-tested. Such model error and the importance of assumption consistency are discussed in more detail in section 10 on validation.

The payment pattern to be applied to the unearned component will also need to be considered. A pattern derived from the historical claims payment may not be suitable without adjustment owing to differences in exposure levels between the past and future origin periods. This problem is most significant if projecting payment patterns using annual or semi-annual origin periods. This issue can be addressed by lagging the payment pattern or by estimating payment patterns for shorter origin period intervals.

Data limitations can cause difficulties when trying to estimate the payment pattern of premiums received, commission and expenses. In many cases the data relating to the timing of such payment may not be recorded in the same data systems used for actuarial projections. In this case a pragmatic approach is required. As these cash flows are short term in nature, the impact of discounting should be relatively small. Provided the estimate of the absolute amount of the cash flows is reasonable the impact of estimation errors in the payment pattern should be small. Of course this assertion should be tested by assessing the sensitivity of the discounted cash flows to different assumptions.

3.8.5. Accident and underwriting cohorts

There are a number of practical issues depending on whether data triangles are based on an accident or underwriting period cohort.

For AY cohorts it is a relatively simple matter to categorise the elements into past and future exposure. The main challenge, however, is to estimate the profile of premium and unearned loss payment patterns.

It may be the case that premium payment information is not readily available as AY emphasis is generally on the earning profile of the business, with premium receipts generally recorded within the credit control systems, perhaps at a different level of granularity. It should, however, be possible to produce a reasonable premium payment pattern using judgement or data from the credit control system and validating by considering premium-weighted average credit terms.

The unearned claims payment profile can be estimated by looking at the future earning profile of the current unearned premiums and applying to each future tranche an expected payment profile. A simpler approach might be to use a lagged payment pattern although the materiality of such an approach would need to be investigated.

It is more challenging to produce cash flows relating to past and future exposure in the case of underwriting period cohorts. One method is to produce the cash flows for the full underwriting period and to calculate the unearned cash flows separately. The earned elements could then be derived by subtraction.

This approach has, however, its own complications. First, it requires an unearned payment pattern that may not necessarily be the same as the full underwriting period pattern.

If the underlying data triangle uses an annual origin period, the projections for recent origin periods may contain cash flows relating to unincepted and unbound business. These will have to be removed.

One option is to scale the ultimate projected amount by the ratio of written to ultimate premium for each UY.

In both instances complications may arise when using annual origin periods to produce cash flows based on incomplete exposure periods. This would arise on an AY basis if projecting at any point other than year-end. On an UY basis it will always be an issue.

3.8.6. Discounting when the liabilities are in multiple currencies

The best estimate should allow for the time value of money by discounting at the EIOPA-provided discount rates. EIOPA has committed to providing discount rates by currency, so, where the (re)insurer has liabilities (claims and/or expenses) in different currencies some thought needs to be given as to how to apply different discount rates to future cash flows in different currencies.

The “pure” approach would be to project cash flows by settlement currency before discounting. However, this may be difficult to do accurately if there is insufficient data. In that situation, there are various possible approaches including:

1. 1. Project the undiscounted liabilities based on combined currency, allocate them between currency using a suitable approach based on the data available (e.g. in proportion to incurred claims or premium), apply the overall claims payment pattern to derive cash flows for each currency and apply the appropriate EIOPA discount rate to each currency’s projected cash flows.

2. 2. Project the cash flows for all currencies combined. Apply a “blended” discount rate based on the EIOPA rates, e.g., weighted by the volumes of business in each currency.

3.8.7. Consistency

It is helpful to construct a simplified balance sheet so as to be able to understand the change in own funds (members’ balances in Lloyd’s) arising from the movement from the IFRS/GAAP basis to the Solvency II basis. This is important because there are a number of balance sheet items that change, the change often offset by an equal and opposite change in the technical provisions. Thus, one should not consider the absolute changes in technical provisions between the two regimes in isolation but in the context of the balance sheet as a whole.

We discuss the Solvency II balance sheet in more detail in section 9.

3.8.8. Life insurance liabilities

Some general insurance policies, most commonly, but not exclusively, motor (re)insurance policies can give rise to liabilities known as periodical payment orders (PPOs). Under a PPO, an individual is awarded a lifetime income, or “annuity”, having suffered serious injury.

Where claim events give rise to the payment of annuities, the value of the technical provision for such annuity obligations should be calculated separately using appropriate life actuarial techniques. This is true for both the claims and premium provision.

However, in current practice, companies are still working on the best way to value annuity-type obligations and due to proportionality considerations, life techniques are not widely used. We expect this to change over time as annuity-type liabilities become more material to non-life (re)insurers and as valuation techniques become more sophisticated. This is an area where insurers may increasingly use stochastic methods.

4.1.1. Relevant references from the Solvency II Directive

Relevant sections of the Solvency II Directive include the following.

4.1.2. Implications

Article 77 of the Framework Directive requires that the value of reinsurance recoverables be calculated separately from the valuation of gross best estimates. For many (re)insurers, this is very similar to their current practice for reporting purposes.

However, other requirements of Articles 76–80 do give rise to significant implications for the calculation of reinsurance recoverables. These articles specify many high-level principles relating to the calculation of gross best estimates and technical provisions.

Some of the implications of the requirements within Articles 76–81 are listed below.

The significant changes to the calculation of gross liabilities will apply equally to the calculation of reinsurance recoveries. Many of these give the same challenges for an (re)insurer’s valuation of reinsurance. These include:

• ∙ consideration of reinsurance recoveries on a cash flow basis; and

• ∙ consideration of how the requirement to allow for “all possible future outcomes” may impact reinsurance valuation.

Changes to the calculation of gross liabilities could lead to further challenges when applied to reinsurance, owing to lack of data or additional complexity including, for example:

• ∙ requiring consideration of the timing of defaults or disputes; and

• ∙ the assessment of contract boundaries and what reinsurance contracts are treated as “existing” in determining which premiums and recoveries are to be included.

In addition to differences stemming from requirements to value in line with gross liabilities, there are also differences in requirements specific to the valuation of reinsurance. These include the requirement to allow for expected non-payment due to default or dispute.

As with many areas under Solvency II, there are a range of possible simplifications that may be used for reinsurance, though these may only be used where appropriate and where they do not materially mis-estimate underlying values. Some of these are discussed in this section, along with likely situations where they may be applicable.

4.3.1. Example 1

Assume a (re)insurer has LOD reinsurance cover incepting on 1 April following a 31 December valuation. The calculation of net technical provisions could:

• ∙ exclude the reinsurance cover;

• ∙ include the reinsurance cover in totality (which is unlikely to be realistic or acceptable); and

• ∙ include the reinsurance cover using correspondence.

The table 1 considers the options:

Table 1

LoD Example

All claims (whether occurred or not) from the policy incepting on 1 July 2012 must be included within the valuation as at 31 December 2012. Claims from the policy incepting 1 July 2013 will not be included as the contract was not classed as “existing” as at the valuation date.

Though the LOD reinsurance cover commencing 1 April 2013 does not strictly “exist” as at the valuation date, we recommend that the portion relating to cover for the 1 July 2012 policy is taken into account. Assuming an even allocation of reinsurance cost to the periods of cover, the example above shows an adjusted premium of 30−(3×30/4)=7.5, and recoveries of 6.0 for Q2 2013. This then gives a net cash flow out-flow of 20 [claims]+7.5 [adjusted reinsurance premium]−6.0 [reinsurance recoveries]=21.5.

The recommended approach is considered to be more realistic. This approach is also likely to increase technical provisions compared with an approach that excludes the reinsurance contracts that do not strictly “exist”.

4.3.2. Example 2

Assume a (re)insurer has a 12-month RAD reinsurance cover that will incept on 1 January following a 31 December valuation but which is “legally binding” by the valuation date. The calculation of net technical provisions could:

• ∙ exclude recoveries in respect of future inwards policies and adjust RI premiums for correspondence;

• ∙ include the RI recoveries and premiums in full (this is unlikely to be considered realistic); or

• ∙ include the RI recoveries and adjust RI premiums.

The table 2 considers the options:

Table 2

RAD Example

As the second RAD cover would only respond to any inwards contract incepting in 2013, of which none are contained in the valuation as at 31 December 2012, the recommended approach is to exclude all recoveries and adjust reinsurance premiums from this contract, which is considered to be more realistic. This approach is potentially open to more debate as it excludes recoveries for a contract that would strictly fall within the definition of an “existing” contract (though the recoveries excluded are driven by a contract that does not “exist”). This approach may appear less obvious than Example 1 but does ensure consistency between approaches. The rationale for the proposed approach in Method 1 is considered strong.

The contract may still be included outside of the technical provisions. In this case, the (re)insurer is committed to purchasing the reinsurance contract and the net cash flow (excluding discounting) is −6 (i.e. 30 of premium out with 24 of expected recoveries). This could be booked as a liability of six, relating to reinsurance creditors.

4.4.1. Considerations when applying gross to net simplifications

Gross to net techniques may be used as long as the particular methodology selected is proportionate to the underlying risks. Any methods used must ensure that:

• ∙ there is correspondence between gross and net best estimates of a homogeneous risk group;

• ∙ the net calculation is performed at a level that adequately matches the granularity of relevant reinsurance programmes and allows for the relevant features of this cover;

• ∙ the allowance for counterparty default is reflected appropriately;

• ∙ claims provisions and premium provisions are calculated separately;

• ∙ recoveries on WBNI business may need to be considered separately, similarly recoveries on binary events;

• ∙ calculation methodologies distinguish at least between LoB for premium provisions;

• ∙ calculation methodologies distinguish at least between LoB and between AYs not fully developed for claims provisions; and

• ∙ the simplifications are appropriate throughout the year. If the reinsurance programme or the gross business is not written uniformly over the year an appropriate approximation at year-end may be unsuitable at the mid-year, say.

(Re)insurers must ensure that relevant features of the reinsurance cover are adequately taken into account. There may be expert judgement required if the historical factors are to be adjusted to reflect changes in the reinsurance cover available over time. This needs to be done with great care and any assumptions clearly documented. For multi-year cover or reinsurance contracts spanning multiple homogeneous risk groups, gross to net techniques should be calculated at an appropriate level and apportioned.

4.4.1.1. Possible simplifications

Simplifications that could be considered include:

• ∙ estimating the future reinsurance cash flows by applying the business plan reinsurance to gross premium ratios to the estimated gross future premium cash flows;

• ∙ estimating reinsurance recoveries on WBNI claims by reference to business plan loss ratios; and

• ∙ estimating reinsurance recoveries on binary event loads by reference to past catastrophe events.

All the simplifications above require different implicit assumptions, the reserving actuary/specialist should consider the appropriateness of these assumptions to the business being reserved.

4.4.1.2. Situations where simplifications are likely to be acceptable

• ∙ Net-to-gross techniques are likely to be acceptable for most standard approaches (e.g. where triangles are used), though these will have to be justified.

• ∙ The choice of netting down factors is subjective, and are based on knowledge of the book and history and are only used where the Actuarial Function has sufficient knowledge and experience.

• ∙ Where segmenting by homogeneous risk group, line of business (LoB) and claims and premium provisions is possible.

4.4.1.3. Situations where simplifications may not be acceptable

• ∙ Exposure analyses: Where direct/explicit reinsurance calculations are often available.

• ∙ Complex outwards reinsurance programmes: Where simple or implicit methods would often be unsuitable.

• ∙ When consistency with gross calculation is required: For example, if an average cost per claims method is employed. For a frequency severity model, explicit modelling of reinsurance would be preferable.

• ∙ Where allowing for cover limits or exhaustion is required as simplification may not implicitly capture the risk appropriately.

4.4.2. Proportionality assessment

Draft Level 2 requires that (re)insurers should carry out a proportionality assessment to determine whether gross to net simplifications are appropriate as a valuation method. This assessment includes the following phases:

• ∙ assessment of nature, scale and complexity;

• ∙ assessment of proportionality of valuation method; and

• ∙ back-testing.

4.4.3. Summary

In practice, it is expected that gross to net techniques will continue to be commonly used, as is currently the case. This can, however, also introduce some additional complications, such as determining expected reinsurance payment patterns, which are discussed in section 4.6.

4.6.1. Using the timing of gross payments for reinsurance cash flows

A common approach will be to base the payment patterns for the expected reinsurance recoveries on the payment patterns estimated for the underlying gross claims.

Most commonly, the reinsurance payment pattern is assumed to be the same as the gross claims payment pattern. This may considerably simplify cash flow projections. In order to justify its application, (re)insurers should compare the expected timing of their inwards and reinsurance cash flows for the homogeneous risk groups used for calculating best estimates. This assessment should be based on historical experience, as well as expert judgement and external data, where appropriate. Furthermore, the decision to use this simplification should be adequately documented and explained.

The principle of proportionality should be taken into account when considering whether the timing of cash flows is “sufficiently similar”. As well as consideration of the differences in inwards and reinsurance cash flow patterns, this should also include an assessment of the expected impact on net best estimates. The expected impact is primarily through the effects of discounting, so will vary depending on the level of the EIOPA-provided interest rate term structure at the time of valuation. Recently, interest rates have been very low, thus increasing the likelihood that this simplification may be acceptable. However, the reserving actuary/specialist needs to take care to keep this under review as it may cease to be acceptable should interest rates increase in the future.

The focus of an assessment of similarity must be based on the gross and reinsurance payment timings, rather than the gross and net. However, when considering proportionality and the effect on overall net discounted best estimates, the net cash flow pattern can also be useful.

4.6.2. Illustration of effect

One way of describing differences between inwards and reinsurance cash flows is in terms of the lags and differences in overall term of the payment patterns. The following charts illustrate the effects on a simplified net payment pattern.

The gross payment pattern has been based on a simple lognormal distribution with projected cash flows discounted using a risk-free interest rate term structure. Reinsurance recoveries have been based on the same lognormal distribution, but incorporating a shift in the mean and a stretch to the overall term of payments. Reinsurance recoveries have been assumed to be a constant proportion of gross payments over the lifetime of the liabilities.

The two below charts illustrate the effects on the reinsurance and net payment patterns under different assumptions about:

• ∙ the shift in the mean for the distribution of reinsurance compared with direct payments (effectively giving a shift in the pattern); and

• ∙ the overall length of the pattern (effectively stretching or scaling the overall time before all reinsurance recoveries are made). In the examples below, the stretch is made evenly across the pattern.

4.6.2.1. Illustration of effect with limited reinsurance and small lags between gross and reinsurance

First, consider a situation where the mean shift from the gross to the reinsurance payment is small and there is little difference in the overall length of the development pattern. The timing of reinsurance cash flows will be very similar to those of gross cash flows. In this case, the conditions for using the direct pattern for the recoveries would presumably be met. The relative levels of discounting applied to both gross and reinsurance cash flows would be similar.

In addition, if reinsurance recoveries are a small proportion of gross payments (20% in this example), the overall effect on the net discounted best estimates of using the gross payment pattern would not be material. The derived net cash flow pattern would then be very similar to the gross, showing that the relative level of discounting applied within gross best estimates and the overall net best estimates are similar. This lack of a material impact would support the use of the simplification.

The Figure 3 illustrates this effect.

Figure 3

Illustration of Effect with Limited Reinsurance and Small Lags Between Gross and Reinsurance

4.6.2.2. Illustration of effect with more significant reinsurance and longer delays from gross payments

The chart below considers a situation where reinsurance recoveries occur significantly later and take longer to develop than gross payments. In this situation, the timing of reinsurance payments is significantly different and the simplification would not be appropriate. The chart below uses a reinsurance pattern following the same lognormal distribution as the gross, but with a larger shift in the mean and a larger scaling. In addition, if reinsurance recoveries are a large proportion of gross payments (60% in this example), the net best estimate would be significantly affected by applying the gross cash flow pattern to reinsurance payments. Note that because reinsurance is a large proportion of gross, and there is a significant lag between gross payments and recoveries, the net development pattern exceeds 100% of ultimate for many periods. The graph highlights this potential pitfall of using net data to define patterns.

Under the principle of proportionality, the differences between net best estimates with reinsurance payments using the gross cash flow pattern versus a separate reinsurance pattern would mean that the simplification would not be appropriate.

Figure 4

Illustration of Effect with More Significant Reinsurance and Longer Delays from Gross Payments

4.6.3. Worked examples

It is recommended that (re)insurers perform the sort of analysis detailed below to assess whether the assumption that the reinsurance and gross cash flow patterns are “sufficiently similar” and whether the simplification is appropriate. We would expect (re)insurers to consider three key factors:

• ∙ the extent to which the reinsurance cash flows are shifted from the direct payments;

• ∙ the extent to which the whole development pattern is stretched; and

• ∙ the overall effect on the discounted net best estimates.

The final point is most significant and should be considered to over-ride the first two, even if the pattern does not look significantly different (see Example 1b below for illustration of this).

The following examples are intended to illustrate the sensitivity of net best estimates to differences between the gross and reinsurance patterns, under the simplification that reinsurance recoveries follow a gross cash flow pattern.

The examples use simple cash flow patterns that follow lognormal distributions (with gross patterns fitted to real-world data), with the differences between gross and reinsurance patterns defined in terms of a shift from the gross mean duration and a stretched overall payment term (with total payment term actually defined in terms of the time difference between 1% and 99% developed to avoid distortion and make the periods reasonable).

The net best estimate where gross and reinsurance cash flow patterns are identical (i.e. a mean shift of 0 and a pattern length that is not stretched) have been normalised to a value of 100.

4.6.3.1. Example 1a: short-tail LoB with limited reinsurance

The following example considers the overall impact on net best estimates for a short-tail LoB with limited (in this case 20% proportional) reinsurance cover. Table 3 sets out the calculated net best estimates under a number of assumptions about the difference from the gross cash flow pattern and the reinsurance recovery cash flow pattern.

Table 3

Impact of Differences Between the R/I and Gross Payment Patterns: Short-Tail with Limited R/I

The green cell above represents the net best estimate with reinsurance recoveries following the same development pattern as the direct payments. This has been normalised so that the net discounted best estimate if the reinsurance cash flow pattern is identical to the gross is 100. This base pattern shows a time difference between time when payments are 1% and 99%, developed of 11.5 years.

The blue cell, selected as an example only, represents the value of the net discounted best estimate if the underlying reinsurance recovery pattern has a mean duration that is 2 years longer (mean shift of 2.0), followed by a similar stretch to the pattern (with a difference between the time when the pattern is 1% and 99%, developed now at 14.5 years). The net discounted best estimate is 102.7 or 2.7% more than the best estimate obtained using the gross pattern for recoveries.

The cells highlighted with red text represent those combinations of differences in the reinsurance and gross cash flow patterns that result in a 5% or greater difference from the net best estimate with no difference in patterns. The threshold of 5% has been chosen arbitrarily for purposes of illustration.

As can be seen, even if the reinsurance pattern is significantly different from the gross pattern, the overall impact on the net best estimates is not marked. Therefore it is envisaged that simplified approaches or assumptions could be applied in practice under these conditions.

The concept of applying a variation on the proposed simplification (i.e. rather than use the gross inwards pattern directly the idea would be to use the gross pattern but with a simple lag or stretch) may be a suitable alternative to the pure simplification.

4.6.3.2. Example 1b: short-tail LoB with significant reinsurance

The following example considers the overall impact on net best estimates for a short-tail LoB with significant (in this case 60% proportional) reinsurance cover. Table 4 sets out the calculated net best estimates under a number of assumptions about the difference from the gross cash flow pattern and the reinsurance recovery cash flow pattern.

Table 4

Impact of Differences Between the R/I and Gross Payment Patterns: Short-Tail with Significant R/I

As can be seen from the pattern of cells that are highlighted above, the differences between gross and reinsurance cash flow patterns are significant, even if the reinsurance pattern is not particularly different from the gross. The simplification would not be appropriate and more risk-sensitive methods should be used.

4.6.3.3. Example 2a: long-tail LoB with limited reinsurance

The following example considers the overall impact on net best estimates for a long-tail LoB with limited (in this case, 20% proportional) reinsurance cover. As in the previous examples, Table 5 sets out the calculated net best estimates under a number of assumptions about the difference from the gross cash flow pattern and the reinsurance recovery cash flow pattern.

Table 5

Impact of Differences Between the R/I and Gross Payment Patterns: Long-Tail with Limited R/I

As can be seen from the pattern of cells that are highlighted above, the differences between gross and reinsurance cash flow patterns are not significant in most of the table, even if the reinsurance pattern is very different from the gross. This should mean, under the principle of proportionality, that the simplification or similar simplifications would be appropriate in many cases (though perhaps not with combinations of mean shift and difference in length of pattern that are too extreme).

4.6.3.4. Example 2b: long-tail LoB with significant reinsurance

As can be seen from the pattern of cells that are highlighted above, the differences between gross and reinsurance cash flow patterns are significant, even if the reinsurance pattern is not particularly different from the gross. Whether this simplification is appropriate should be considered under the principle of proportionality and in light of overall uncertainty in the reserves. Assuming the overall uncertainty is not particularly high, the simplification would not generally be appropriate.

Table 6

Impact of Differences Between the R/I and Gross Payment Patterns: Long-Tail with Significant R/I

4.6.4. Conclusion

The examples given above illustrate that the most important consideration is the amount of reinsurance, as would be expected. If reinsurance recoveries are expected to be large, then assuming that reinsurance recoveries follow the gross payment timings is unlikely to be appropriate. This would be the case even if the actual differences between the patterns are relatively small. The reserving actuary/specialist under Solvency II would need to consider these factors carefully in deciding on the approach to take for technical provision valuation regarding reinsurance recoveries. The approach taken should be carefully documented and justified. In summary:

• ∙ when reinsurance is low, the discounted net reserves are fairly insensitive to the differences between gross and reinsurance cash flow patterns and so the simplified approach would be acceptable; and

• ∙ when reinsurance is high, the results are far more sensitive and this assumption becomes inappropriate.

There are many circumstances where reinsurance recoveries may not follow a simple pattern and more explicit and potentially subjective estimation will be required, for example, relating to catastrophes or very large claims. In this instance, more of an exposure-type approach will be adopted and payments can be assumed to be more stepped and not follow a pattern. This will tend to be based on expert judgement more than the general pattern approach.

4.7.1. Simplifications

A full calculation by individual counterparty will be time-consuming and potentially complex.

A suggested simplification, based on proportionality, is to

• ∙ assess the counterparty risk as a simple deterministic value based on the estimated mean term of cash flows (as opposed to a pure cash flow analysis);

• ∙ group counterparties together by credit ratings and value the risk of the group (as opposed to individually);

• ∙ use a deterministic probability of default to apply to the whole exposure (as opposed to varying by time); and

• ∙ use a static single estimated recovery rate in the case of a failure (as opposed to a random variation).

This approach is similar to current techniques and it is expected that many (re)insurers will elect to use the simplification suggested. This is likely to result in similar groupings to current practice.

In many cases this simplification would be appropriate and is given as:

$${Adjustment}\,{\rm for}\,{counterparty}\,{default}={\minus}\max \left( {\left( {1{\minus}{RR}} \right){\times}{BE}_{{{\rm Rec}}} {\times}{Dur}_{{{\rm mod}}} {\times}\left( {{{{ PD}} \over {{1\minus{\hyphen}PD}}}} \right)\,,\,0} \right)$$

where RR is the recovery rate of the counterparty; BE _Rec the best estimate of recoverables before the expected loss because of default of the counterparty; Dur _mod the modified duration of the recoverables; PD the probability of default of the counterparty for the time horizon of one year.

4.7.1.2. Example 1: short-tail LoB

Table 7 shows that, as expected, when the underlying probabilities of default are low (e.g. <1%) then the differences between the simplifications and the true value for counterparty default is small. Hence the simplification would be appropriate.

Table 7

Effect of Simplification on the Allowance for Counterparty Default – Short-Tail

Table 8

Effect of Simplification on the Allowance for Counterparty Default – Long-Tail

4.7.1.3. Example 2: long-tail LoB

Although the differences are larger for the longer tail classes the conclusion is broadly the same, i.e., that the simplification holds in most instances where the underlying reinsurance security is good.

4.7.1.4. Conclusion

The simplification formula itself defines how the simplified calculation would differ from a full calculation with changing parameters. This is illustrated by the tables above, which highlight that the differences between the simplified and calculated allowance are small for lower probabilities of default. However, it is clear that use of the simplification becomes less appropriate for liabilities of a longer duration where probabilities of default are high.

In addition, another assumption required for this simplification is that there is one probability of default that remains constant over time. With a small duration and low initial probability of default, this assumption may be reasonable. However, over a longer period of time, (re)insurers may expect the probability of default to increase for cash flows further into the future.

The simplification is effectively an extension of the current common approach to counterparty default risk where it takes the form of “factor” multiplied by “expected recoveries” where the factor is based on the credit rating of the reinsurer.

4.9.1. Accounting for cash flows related to reinsurance recoveries

The calculation of reinsurance provisions should include at least:

Cash in-flows:

• ∙ recoverables from reinsurance and SPV contracts in respect of claims payments;

• ∙ recoverables from reinsurance and SPV contracts in respect of allocated claims expenses; and

• ∙ revenues from reinsurance commission and profit sharing arrangements (from technical sources relevant to individual reinsurance contracts).

Cash out-flows:

• ∙ future premiums payable for or in respect of reinsurance and SPV contracts; and

• ∙ if relevant, out-flows from profit sharing arrangements.

Expenses related to the internal processes for reinsurance and SPVs (such as administration or management) should be allowed for in the expenses forming part of the gross best estimate.

One important consideration is for consistency between expected reinsurance recoveries and future premiums, especially items such as reinstatement premiums.

4.9.2. Accrued reinsurance assets

All estimated future recoverables from reinsurance contracts should be allowed for.

However, any recoveries due on paid gross claims (i.e. those where collection notes have been sent out but not received often referred to as “reinsurance accruals”) are part of the Solvency II balance sheet but do not sit within the assets relating to technical provisions and are outside the scope of this paper. In other words, the principle of correspondence should be followed.

Any deposits made in respect of the reinsurance cash in-flows or out-flows must be shown separately in the balance sheet. In this case, suitable adjustments must be made to the recoverables to avoid any double counting.

4.9.3. Collateral against counterparty default allowance

Instruments used to mitigate the effects of counterparty default risk (e.g. collateral or letters of credit) should be taken into account in the adjustment for counterparty default, but any associated credit risk must also be taken into account. The default risk of the underlying instrument should be included as equivalent to the default risk of the reinsurance.

One solution is to assign the credit rating of the underlying collateral to the reinsurance rather than the credit rating of the reinsurer but only to the extent any collateral exists (i.e. it may not cover all the expected recoveries).

4.9.4. Set off

The cash flow projection used in the calculation of the best estimate shall take account of all potential cash in- and out-flows required to settle the insurance and reinsurance obligations over their lifetime. Therefore, all cash flows incurred in meeting liabilities should be identified and valued but there is no explicit requirement to calculate all cash flows separately. However, the best estimate must be calculated gross, with separate calculation of the amounts recoverable from reinsurance contracts and special purpose vehicles.

A common concept is set off where potential inwards claims are “set off” against outwards recoveries (and vice versa) with only the net effect booked. When moving to a cash flow basis, it may be appropriate to include the full inwards and full outwards expected cash flows. This would depend on materiality but the reserving actuary/specialist will have to consider (if relevant).

4.9.5. Non-traditional triggers

Where recoverables from special purpose vehicles depend upon external indicators (such as a parametric trigger), rather than directly indemnifying for losses, allowance for recoveries related to either claims or premiums provisions should only be taken into account to the extent that they can be verified in a “deliberate, reliable and objective manner”. The basis risk of the contract not being triggered must also be considered. In addition, only payments related to underwriting risk should be accounted for in recoverables. All payments that do not relate to underwriting risk (e.g. those that relate to market risk) should be accounted for elsewhere.

5.2.1. Solvency II Directive, Article 78: Other elements to be taken into account in the calculation of technical provisions (extract)

In addition to Article 77, when calculating technical provisions, insurance and reinsurance undertakings shall take account of the following:

1. (1) all expenses that will be incurred in servicing insurance and reinsurance obligations;

2. (2) inflation, including expenses and claims inflation;

3. (3) ....

5.2.2 Solvency II Directive, Paragraph 55 (extract)

… the value of technical provisions should correspond to the amount which another insurance or reinsurance undertaking (the reference undertaking) would be expected to require to take over and fulfil the underlying insurance and reinsurance obligations. The amount of technical provisions should reflect the characteristics of the underlying insurance portfolio. Undertaking-specific information, such as that regarding claims management and expenses, should therefore be used in their calculation only insofar as that information enables insurance and reinsurance undertakings better to reflect the characteristics of the underlying insurance portfolio.

5.2.3. EC Draft L2, Article 17, TP 5

… Unless otherwise stated, assumptions underlying the calculation of technical provisions shall be based on the characteristics of the portfolio of insurance and reinsurance obligations, where possible regardless of the undertaking holding the portfolio. Undertaking-specific information, including information on claims management and expenses, shall be used in the calculation only insofar as that information enables insurance and reinsurance undertakings to better reflect the characteristics of the portfolio or where the calculation of technical provisions in a prudent, reliable and objective manner without using that information is not possible.

5.3.1. Expense cash flows

Under Solvency II, the best estimate provisions should reflect all future cash flows arising from expenses that will be incurred servicing existing policies during their lifetime.

This includes (but is not limited to):

• ∙ administration expenses, including:

  • ○ salaries;

  • ○ property costs (including rent, depreciation, heating, lighting, cleaning);

  • ○ IT costs; and

  • ○ expenses in relation to the management (actuarial, finance, risk, commercial, data) or administration of reinsurance contracts or SPVs.

• ∙ other administration expenses;

• ∙ investment management expenses;

• ∙ claims management expenses (including claims handling expenses);

• ∙ acquisition expenses (including commissions);

• ∙ costs associated with arranging and managing outwards reinsurance; and

• ∙ insurance premium tax.

5.3.2. Calculation of expense cash flows

The guidance (see sections 5.2.2 and 5.2.3) states that the principle is to allow for the expenses that another (re)insurer would be likely to incur if they were taking over the management of the business at the valuation date. We assume that this ignores the costs of any transfer of the business between (re)insurers. Thus, the expense assumptions should be appropriate for the reference undertaking (new (re)insurer) and not necessarily the same as those of the (re)insurer for whom we are calculating the technical provisions. It is still acceptable for the (re)insurer to base the expense assumptions on its own experience provided that this reflects what another insurer might be expected to incur.

In practice, we believe most (re)insurers do and will base their expense assumptions on their own experience. One of the reasons for this is the lack of sufficiently detailed and relevant market data.

The assumptions should only relate to future expenses attributable to business that the (re)insurer is obligated to, in other words, rising from commitments made on or before the valuation date only.

Expense assumptions should include allowance for future cost increases. In particular, assumptions about future inflation should be made, which need to be consistent with the assumptions made elsewhere in the calculation of technical provisions and in the internal model, if there is one. The inflation rate used should be appropriate to the driver of the expense.

Assumptions about cash flows should consider future changes in the environment (such as legal, demographic, medical, technological, social or economic).

5.3.3. Going concern or run-off basis

The expenses which are included in the technical provisions should be assessed on the assumption that the reference undertaking (new (re)insurer) will continue to write new business (i.e. on a “going concern” basis) unless a decision has been made by the existing (re)insurer to cease writing further business, or this is very likely to happen in the near future. If that is the case, a run-off assumption should apply.

5.3.4. Allocation to currency

Future expense cash flows should be expressed in the currency in which they are likely to occur and discounted at the appropriate EIOPA-provided discount rate for that currency.

5.4.1. Claims expenses

ALAE are typically included in the claims data and therefore implicitly projected as part of the claims projection, i.e., assuming the same payment pattern. Adjustments may be required, however, if the allocated costs are changing as a percentage of reported or paid losses, or if the timing of expenses is expected to be significantly different than that of claims. For the premium provision, they are likely to be allowed for in the loss ratio assumption.

It is unlikely that any data will be available to discern a future payment pattern for ULAE though it seems reasonable to assume these will run-off in line with losses.

It is difficult to come up with a “one size fits all” approach to adapting a (re)insurers ULAE expenses to Solvency II because the definition of what is included in ULAE differs between (re)insurers. The reserving actuary/specialist must take care to allow for this by understanding what is currently included to avoid double counting or omitting expenses.

A common approach to estimate unallocated claims management costs is to look at historic paid unallocated claims management costs and relate them to paid losses over the same period. Typically, adjustments are made to allow for the uneven incidence of expense over the life cycle of the claim, for example, by allowing for different costs on opening and closing. Such an analysis tends to result in a percentage uplift that is applied to total outstanding losses.

A simple approach is to apply a similar uplift factor to the future expected losses, be they true IBNR or premium provision losses. It is reasonable to assume that, usually, the uplift would usually be expected to be higher than for reported claims because all claims due to be notified in the future are unopened by definition and therefore likely to incur higher future expenses on average than known unsettled losses. In addition, any change to the company’s cost structure and the impact of future inflation on both loss and costs would need to be considered if materially different.

5.4.2. Acquisition expenses

Given that technical provisions are calculated on a cash flow bases, it may seem strange that we need to allow for acquisition expenses at all. However, many (re)insurers will have to because we need to allow for business that has been accepted before the valuation date for which cover has not yet commenced and the acquisition costs may not yet have been paid.

Thus, acquisition expenses assumptions may be required for the premium provision calculation.

Usually acquisition cost assumptions are relatively straightforward to derive and the necessary analysis may already have been done to derive a pricing assumption. Commission is likely to be a large part of acquisition expenses and current commission rates should be reflected in the assumption.

5.4.3. Profit commission

Profit commission, whether or not you choose to define it as an acquisition cost, may be far more complicated to calculate than acquisition costs more generally, because it is based on claims experience.

The (re)insurer may need to allow for profit commission in both the premium and claims provision. The appropriate approach will depend upon the terms and the timing of profit commission payments. Some profit commission payments may be known, or estimated with reasonable certainty and the date upon which they are due may be fixed at some point in the future, e.g., a contract anniversary. Others may be quite complicated to estimate accurately owing to a complex relationship with future claims experience. In this case, it may be worth considering possible simplifying methods and/or assumptions on the grounds of proportionality.

5.4.4. Administration expenses and overheads

The best estimate needs to allow for all expenses that will be incurred including future administration costs and overheads.

If budgeted expenses are available, and are best estimate, these may be suitable to be used to derive loadings to cover administration and overheads. One needs to check whether they are appropriate. Questions the reserving actuary/specialist might ask include:

• ∙ Are they best estimate?

• ∙ Do they include allow for anticipated efficiency improvements?

• ∙ Do they include any one-off costs, such as implementation of new systems or processes?

• ∙ Is the allowance for inflation in costs appropriate?

• ∙ To what period do the budgeted expenses apply? Do we need to adjust them so that they are suitable for the exposure period we are considering?

Care needs to be taken to ensure that expenses are not double counted or omitted.

If it is not appropriate to use the budgeted administration expenses, the expenses can be projected based on historical figures, for example, as a proportion of earned premium.

Depending on the source of administration expenses, these could be allocated using in-force policy counts, relative staff hours spent on different lines, unearned premiums or volumes of best estimate provisions.

As administration expenses are defined as expenses incurred servicing existing business a proportion of these expenses may be attributed to the run-off of existing policies. In addition, we may wish to remove any non-recurring or “one-off” costs from the expenses.

The (re)insurer may decide that a loading for administrative expenses should apply to the premium provision only. This can be appropriate if one is confident that all of the expenses relating to the ongoing management of incurred claims are included in loadings applied to the claims provision. Whether this happens depends very much on how overheads (general management, finance department, actuarial department, internal audit, etc.) costs are allocated. It is not reasonable to assume that all of these overheads need to be carried by future exposure. To check that the balance is appropriate, one might consider the hypothetical scenario where the liabilities relating to past exposure (covered by the claims provision) and the liabilities relating to future exposure (covered by the premium provision) were to be passed on to two different reference (re)insurers who continue to write new business. Would the loadings for expenses in each of the claims and premium provisions be sufficient to cover the expenses for each reference (re)insurer?

5.4.5. Investment expenses

Investment expenses cannot be allowed for by reducing the discount rate.

Investment expenses could be allocated based on the level of funds under management; they could be split into Solvency II classes using (net) best estimate provisions.

5.4.6. Reinsurance costs

The costs associated with purchasing and managing reinsurance should be allowed for in the gross claims and premium provisions. As the technical provisions are calculated on a cash flow basis, one would generally allow for expenses as and when the cash flows occur. However, as discussed in section on Reinsurance, in applying the principle of correspondence, one may have to adjust expense cash flows associated with reinsurance so that only those relating to reinsurance cover corresponding to the inwards risks that the (re)insurer is obligated to at the valuation date are taken into account.

5.4.7. Allocation to currency

Strictly speaking, the expenses should be estimated in the currency in which they will be incurred and discounted at the appropriate EIOPA-provided discount rate for that currency. In practice, this may be difficult to do accurately: for example, some expenses may be head office and based in the currency there, others such as loss adjustors costs may occur in the currency where the risk is based. On grounds of proportionality, the (re)insurer is likely to adopt a pragmatic approach using simplifying assumptions that do not have a material impact on the overall technical provisions. Some sensitivity testing may be required to demonstrate that the impact of the simplification is not material.

6.3.1. Solvency II Directive: Article 77 (2)

The best estimate shall correspond to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.…. The cash-flow projection used in the calculation of the best estimate shall take account of all the cash in- and out-flows required to settle the insurance and reinsurance obligations over the lifetime thereof.

6.3.2. Groupe Consultatif: Valuation Of Best Estimate Under Solvency II For Non-life Insurance Interim Report

With the best estimate being the probability weighted average of future cash-flows, some weight has to be given to losses with low probability but high cost within the best estimate valuation. We call these ‘binary events’. This will be a change as the majority of companies currently consider these types of risk as part of their capital assessment rather than best estimate reserves. Examples of binary events include the occurrence of a new type of latent claims or a change in legislation impacting claims payment retrospectively; or a high inflation environment.

6.3.3. CEIOPS Advice: CEIOPS DOC 21/09 CEIOPS Advice for Level 2 Implementing Measures on Solvency II: Technical Provisions: Elements of Actuarial and Statistical Methodologies to Calculate the Best Estimate

This advice was released in October 2009. It includes further discussion of what is meant by “best estimate” and then addresses ENID specifically. The explanatory text on definition of best estimate includes the following:

The advice in the document, after a discussion of methodologies, concludes with specific reference to ENID:

The wording appears to distinguish between latent claims and ENID.

6.3.4. LTGA and QIS5

The Technical Specifications for QIS5 (July 2010) and the more recent Technical Specification for the Long Term Guarantee Assessment (October 2012) appear to make less of the ENID issue. The following is an extract from both of the specifications.

TP 2.1 The best estimate should correspond to the probability weighted average of future cash-flows taking account if the time value of money.

TP 2.2 Therefore, the best estimate calculation should allow for the uncertainty in the future cash flows. The calculation should consider the variability of the cash flows in order to ensure that the best estimate represents the mean of the distribution of cash flow values. Allowance for uncertainty does not suggest that additional margins should be included within the best estimate.

TP 2.3 The best estimate is the average of the outcomes of all possible scenarios, weighted according to their respective probabilities. Although, in principle, all possible scenarios should be considered, it may not be necessary, or even possible, to explicitly incorporate all possible scenarios in the valuation of the liability, nor to develop explicit probability distributions in all cases, depending on the type of risks involved and the materiality of the expected financial effect of the scenarios under consideration. Moreover, it is sometimes possible to implicitly allow for all possible scenarios, for example in closed form solutions in life insurance or the chain-ladder technique in non-life insurance.

6.4.5. Lloyd’s guidance (March 2011)

Lloyd’s issued detailed technical Provisions Guidance in 2010, updated March 2011. The guidance was built on the earlier material from CEIOPS and Group Consultatif. The guidance included the following illustration of ENID (binary events):

There is a very large range of possible events that could fall into this category. For illustrative purposes, the following list gives some ideas of events that could (but not necessarily would) fall into the category of binary events. Also, depending on an insurer’s risk profile, some of the events may not even give rise to significant losses at all. It is also worth noting some historic events that might fall into this category, the health hazard type of losses such as asbestos and US pollution of the 1980s are prime examples. Other such as the LMX or PA spirals may also be considered to be in this category. There is also the risk of extreme events not included in pricing assumptions impacting the premium provisions for unexpired exposures. Examples of these could be meteor strike, tsunami hitting Florida and unexpected volcanic eruptions.

Products impacting health

• ∙ Nanotechnology

• ∙ Aspartame

• ∙ Electro magnetic fields

• ∙ GM crops

• ∙ Nuclear waste

Social/environmental issues

• ∙ Global warming linked to current polluters

• ∙ Director liabilities widened

Legislative/political changes

• ∙ Step change in court rulings (e.g. Ogden tables)

• ∙ Political intervention

• ∙ Rulings that ignore underwriting conditions “for the greater good”

Contact/wording issues

• ∙ Removal of claims made wordings

• ∙ Retrospective change in conditions (e.g. surplus lines in Florida)

• ∙ Specific exclusions removed

• ∙ Not fully understanding exposures

Events

• ∙ Meteor strikes

• ∙ Mega volcanoes

• ∙ Florida tsunami

This list is illustrative but certainly not exhaustive.

Lloyd’s also provided the following suggested methods for allowing for ENID.

The basic concept when allowing for binary events is to remove the truncation inherent in a parameterisation based only on observed historic data. In practice, such an allowance could typically be done in one of three ways:

1. 1. Adjusting the underlying assumptions within the best estimate to ensure the likely impact of the event is included in the projection.

2. 2. Calculating the best estimate reserve separately under the assumptions that a binary event either does or does not occur. The two projections could be combined with a probability weighting.

3. 3. Adding an explicit amount or load to the best estimate excluding binary events.

Currently, methods similar to the first are the most common way of allowing for events outside of the scope of historic data. That is, some allowance for latent claims is often made by selecting more prudent assumptions to take account of the possibility of losses of a scale not contained in the history. In the first and third methods, events would not necessarily be identified explicitly.

One of the underlying principles of Solvency II is transparency, meaning any load or assumption to adjust for binary events should be explicit. The methods chosen should also be relatively simple to avoid spurious results. In most circumstance this would rule out the first method of “just being more prudent” to allow for uncertainty.

Practical suggestions

In reality there are many possible approaches to allowing for binary events. Three are highlighted below:

1. Use history as a guide

Investigate the historical proportional impact on reserves of latent or extreme events. This could be conducted at a line of business level over the last 30 or 40 years. This would be mainly health hazard type claims such as: asbestos, pollution, tainted blood products, silicone implants, Agent Orange, DES, etc.

The result is an estimate of frequency (e.g. X latent claims in 30 years) and severity, average impact is y% of average reserves over the period.

Advantages of this type of approach are that it would give an explicit load for latent/binary claims and is relatively straight-forward to calculate. Disadvantages are that historic events may not be a good guide to future events and that it may not cover “all possibilities”. It would also not necessarily provide an allowance for large events in unearned provisions.

2. Estimate vulnerability to a range of current threats – “scenario” approach

Build a probability and severity database of current possible binary events. These could be explicitly valued and included within the technical provisions calculations.

Advantages of this type of approach are that it would give an explicit load for latent/binary claims and is relatively straight-forward to calculate once assumptions have been made. However, it would be almost impossible to assign realistic probability/severity assumptions for such losses. It would also, by definition, be impossible to allow for “all possible” outcomes.

3. Uplift reserve to allow for limited range of understanding

Actuarial functions use their expert judgement in setting technical provisions and will aim for mean reserves. The resulting mean is expected to underestimate a true mean as it will only include information which is realistically foreseeable. If an assumption is made about the level at which events are realistically foreseeable (e.g. up to a 1:200 year level) then derived uplifts could be applied to estimate a mean allowing for incomplete information.

Using a combination of data available and judgement for fitting a tail, an assumption can be made about the distribution of reserves. This could also be derived using a bootstrap-type methodology.

An assumption can then be made about the likelihood of events included within the data (the 1 in X year events).

For consistency with capital setting, this level for “realistically foreseeable” events could be assumed to be 1 in 200.

An uplift factor can be derived as the ratio of the “true mean” to the “mean only” including realistically foreseeable events. Reserves are calculated using standard techniques and the uplift factor applied.

To illustrate the example, if it is assumed that the reserves estimated using current techniques (i.e. only allowing for reasonably foreseeable events) will exclude the tail of the distribution beyond the 1:200 point and the loss distribution is of a certain type (e.g. lognormal) then the difference between the estimated mean (using current techniques) and the “true” mean can be explicitly calculated and added as a binary event load.

This approach would be subjective and rely on the assumptions made to fit a distribution, approximate the tail of the “true” distribution and about the level of likelihood of events seen in the data. It would be very sensitive to any of these assumptions. The method may also be very sensitive to assumptions about how quickly any such uplift ratios are expected to run-off for older years of account.

It is proposed that, unless further developments are made, method 3 is encouraged and reserves are explicitly uplifted at a Solvency II line of business level to allow for binary events.

Separate uplifts will apply to claims and premium provisions. In all cases the method and allowances for binary events should be well documented.

6.5.1. The starting point

At the time of writing, most (re)insurers are calculating their Solvency II technical provisions by adjusting the reserves calculated for reporting and management information purposes.

In determining an ENID loading (and, indeed, whether one is required at all), in the first instance, the (re)insurer should determine what exposures and risks are included in the “best estimate”, usually estimated based on current reserving practices. If, for example, the (re)insurer’s process is to book an ABE plus an MA, some of the ENID are likely to be considered in the MA. So, provided the rationale for the MA identifies specific (usually adverse) events, these can be brought into the ENID “bucket” or, if not, one must take care not to double count them.

MAs are unlikely to allow for potential positive outcomes (e.g. changes to the terms and conditions or processes to exclude/reduce certain types of claim) and generally represent a margin above the best estimate based on a cautious view. In addition, there may well be potential future events that have not been allowed for explicitly.

Where MAs do not relate to specific events, they are likely to be removed from the Solvency II calculation as margin.

6.5.2. Identifying ENID

One can attempt to identify ENID, as best one can, by bringing together those parties who understand the (re)insurer’s exposure (what has been written, policy terms and conditions, the sort of things that may give rise to claims, etc.) to brainstorm possible future events that could affect the future cash flows. Such parties would potentially include underwriters, claims managers, reserving and pricing actuaries, and reinsurance managers.

Discussion should cover:

• ∙ factors that could affect future settlements relating to past claim events, reported and unreported; and

• ∙ factors and potential future claim events relating to the exposure remaining on business the (re)insurer is obligated to at the valuation date.

Note that the exposure period is limited. (Re)insurers need only consider potential future events covered by business that they are obligated to at the valuation date, so, for example, if an insurer writes only annual policies and only accepts new business/renewals within a month of cover commencing, the insurer need only consider potential future claim events over the next 13 months.

The following could be considered:

• ∙ catastrophe exposure;

• ∙ potential large one-off claims;

• ∙ legislative change;

• ∙ court awards;

• ∙ other environment changes;

• ∙ accumulations, etc.;

• ∙ changes in policy terms and conditions; and

• ∙ changes in claims processing

Ideally, (re)insurers will need to form a view as to the probability and potential severity of the events considered. Consistency should also be considered with reverse stress testing, the risk register, pricing models, catastrophe modelling and the internal capital model.

Estimation is likely to be subjective and require significant judgement. Evidence to support decisions and assumptions made for ENID could be produced by way of minutes of discussions held and process documentation.

6.5.3. Is it necessary to identify potential ENID?

It is not necessary to identify potential ENID to calculate an ENID loading and, indeed, one could reasonably argue that, for most insurance it is impossible to identify all potential future outcomes. However, there are several persuasive arguments for carrying out the exercise described above, including:

• ∙ It could be used as the basis for probability/severity approach to calculate an ENID loading.

• ∙ A loading calculated using a probability/severity approach could be used as a check on an alternate method of calculation, such as a truncated distribution method.

• ∙ The exercise of “blue sky thinking” about potential risks to which the (re)insurer is exposed has value in its own right in terms of increasing awareness of the risks underlying the business. Those who participate get the opportunity to discuss risk with those of other disciplines and gain a different perspective. They have the opportunity to challenge ingrained perceptions about the likelihood of certain risks and to challenge “closed thinking”. It is likely to produce useful insight into risk and senior management’s attitude to risk and complement other exercises such as reverse stress testing.

• ∙ Given the insight that can come out of such an exercise, it is likely to be viewed favourably by regulators.

6.7.1. Can we benchmark our ENID loading?

It would be comforting to actuaries and management alike if we could benchmark our ENID loadings. Unfortunately, there are persuasive arguments why, in practice, one is unlikely to be able to, and if one can, care will need to be taken to ensure the comparison is not misleading.

Reasons for exercising care in benchmarking ENID loadings:

• ∙ Every (re)insurer’s reserving policy will differ. In the same way that (re)insurers may choose different reserves for the same claim, (re)insurers will allow for different things in their IFRS/GAAP “best estimate”.

  For example, two (re)insurers may choose to use what they call their ABE as the basis for calculating their Solvency II technical provisions. Blinkered Actuary Re’s ABE may be based purely on historical data. It may ignore the new approach to tackling claims that is expected to reduce future claim settlements by 5% and a legal case that may materially affect the settlement of outstanding claims. This is not a problem because management make an adjustment to the ABE, called the “Management Adjustment” that covers the things that the actuary has not allowed for, plus a “bit of margin for uncertainty”. If Blinkered Actuary Re chooses to use the ABE as their best estimate for Solvency II, their ENID loading will need to allow for the new approach to tackling claims and the legal case (but not for the uncertainty loading).

  In contrast, Super Actuary Re, in exactly the same situation, may have an ABE that factors in the legal case, but probably not the new approach to claims. (We are actuaries, after all, and we do like our prudence.) Super Actuary Re’s ENID loading should therefore be different to that of Blinkered Actuary Re.

• ∙ Every (re)insurer’s business is different, with different exposures, terms and conditions, etc. and hence different exposures to low-probability high severity events.

  For example, if a travel insurer covers volcanic ash, they will need to allow for it in their ENID (or best estimate). A travel insurer who does not cover volcanic ash-related claims would not need to.

6.7.2. Available benchmarks

We are not aware of any reliable benchmarks for ENID loadings currently available. Lloyd’s have said that the figures they suggested in the Lloyd’s Technical Provision Guidelines should not be used as benchmarks.

7.4.1. Non-life

The minimum LoB into which non-life technical provisions must be split are set out below. Annex I of the EC Draft L2 gives fuller description of what is to be included in each LoB.

1. 1. medical expenses insurance;

2. 2. income protection insurance;

3. 3. workers’ compensation insurance;

4. 4. motor vehicle liability insurance;

5. 5. other motor insurance;

6. 6. marine, aviation and transport insurance;

7. 7. fire and other damage to property insurance;

8. 8. general liability insurance;

9. 9. credit and suretyship insurance;

10. 10. legal expenses insurance;

11. 11. assistance; and

12. 12. miscellaneous financial loss.

13–24. proportional non-life reinsurance (relating to insurance obligations included in LoB 1–12);

1. 25. non-proportional health reinsurance (relating to insurance obligations included in LoB 1–3);

2. 26. non-proportional casualty reinsurance (relating to insurance obligations included in LoB 4 and 8);

3. 27. non-proportional marine, aviation and transport reinsurance (relating to insurance obligations included in LoB 6); and

4. 28. non-proportional property reinsurance (relating to insurance obligations included in LoB 5, 7 and 9–12).

7.4.2. Life

The only life LoB likely to be of interest to general insurers are:

1. 33. annuities stemming from non-life insurance contracts and relating to health insurance obligations;

2. 34. annuities stemming from non-life insurance contracts and relating to insurance obligations other than health insurance obligations.

7.10.1. Allocation: high-level principles

Homogeneous risk groups should be considered the most important segmentation level for modelling technical provisions and it is this level that should be considered first. In the event that a homogeneous risk group contains risks falling to more than one of the minimum Solvency II LoB, (re)insurers should use reasonable methods to allocate the results of the calculation to these LoB.

There is no mandated allocation methodology and it is the responsibility of each (re)insurer to ensure that the methodology used is appropriate. There are, however, some high-level principles that the reserving actuary/specialist could consider when determining the methodologies to use:

• ∙ Ensure that there is consistency between projection and allocation methods. For example, where IBNR is projected based on premium then allocations should be based on premiums.

• ∙ Ensure consistency between gross and net allocations, where appropriate. Outwards reinsurance covers should be allocated in proportion to the gross losses they cover, if practical.

• ∙ Allocate very large claims, such as catastrophes, individually, especially where any exposure analyses underlie the projections.

In addition, (re)insurers should note that:

• ∙ proportional allocations (e.g. allocating IBNR between classes based on incurred claims) are reasonable in many situations, although these will need to be validated;

• ∙ expenses can be split in proportion to claims reserves but not necessarily by currency (if expected to be incurred in a different currency);

• ∙ allocations are estimates and, as such, there should be reasonable materiality thresholds set;

• ∙ they must be able to support, justify and document the methodologies used for allocation; and

• ∙ considerations of proportionality and spurious accuracy are key – where there is a risk of spurious accuracy, a simple (but reasonable) approach is recommended.

Note that the approaches set out in this paper are suggestions only and each (re)insurer should use the allocation methods considered most reasonable for them.

7.10.2. Allocation methodologies

Premium, paid and outstanding claims data should be available by reserving class for use in allocation methodologies. The following section sets out some possible allocation methodologies based on different items. Note that the methodologies will not be appropriate for use in all situations and specific circumstances should be considered before selecting a method.

7.10.2.1. Outstanding claims (case estimates)

IBNR and IBNER will be calculated by (re)insurers using their homogeneous risk groups (often a firm’s own classes of business). Data on outstanding claims may then be used to proportionally allocate the IBNR and IBNER to each of the underlying classes and currencies making up the homogeneous risk group.

Methodologies based on this data may also be appropriate for allocation of some of the expense items, such as future ULAE (and other non-ULAE expenses, depending on their drivers).

Care must be taken when applying this method, especially on immature cohorts where many claims may not have been notified, and also on older cohorts where the number of open claims is small and the impact of individual claims can be significant.

7.10.2.2. Incurred (or paid) claims

Similarly to the above, data on incurred claims may also be used to proportionally allocate IBNR and IBNER between underlying classes and currencies. Calculations based on this information may also be used to allocate elements of the premium provision.

Incurred claims projections are a common base to calculate IBNR/IBNER (i.e. incurred chain-ladder) and may help consistency if used. If paid claims underlie projections rather than incurred then paid claims can be used to allocate reserves from which notified outstanding claims can be deducted to obtain IBNR/IBNER.

7.10.2.3. Premium

Use of premium data may be the most appropriate measure for allocation of some homogeneous risk group best estimates where there is little other data (such as reported outstanding or incurred claims in recent years of account) to base a split on. This will ensure consistency where common projection methods such as Bornhuetter–Ferguson are employed. This is likely to be particularly relevant for elements of the premiums provision where claim events are yet to occur.

Allocation of future premiums may also require use of premium data for the most appropriate split. Note, however, that (re)insurers should consider what is driving the expected future premiums, as a claims measure may be more appropriate for some types of future premiums.

7.10.2.4. Policy-by-policy analysis

(Re)insurers may calculate some of the required best estimate figures directly on a policy-by-policy or exposure basis, for example, for large claims or events. If so, these amounts can be removed from the homogeneous risk group, the remainder allocated using another of the methods, and then the directly calculated best estimates added to the class required.

This is expected for very large claims such as catastrophes that could otherwise distort results materially.

7.10.2.5. Combination of approaches

In line with the high-level principles set out above, the most appropriate methodologies should be used. These would be expected to differ by year of account and class of business and will include a combination of approaches.

The Actuarial Function is expected to either own or have significant input into the decision over what methods to use, and for which years of account; the person responsible for the approaches chosen should be clearly identified and be able to provide justification and evidence.

7.10.3. Allocation to geographical location

Various data sources may be available to perform this split, including specific location data, data on insured’s head office or an allocation based on historic location information. The allocation of outwards reinsurance cover would, in general, be consistent with that of the underlying inwards gross business allocation.

We expect that, once the standard formula is finalised, (re)insurers will need to be able to confirm that the estimated geographical splits are reasonable, especially for worldwide covers where allocations will be needed.

7.10.4. Allocation to currency

(Re)insurers may need to allocate best estimate technical provision elements between currencies where these are not calculated at currency level.

(Re)insurers will probably report in their major settlement currencies but only if there is supporting evidence that this split of settlement currencies does capture all the material underlying currencies. For example, if Australian dollars represents an immaterial currency and is settled in sterling, then this may be reported within the sterling bucket. The key consideration is materiality.

The reserving actuary/specialist needs to be careful where in aggregate, the total of the (individually) non-material currencies become material. In this case, the largest one or two (or three) of the (individually) non-material currencies in those buckets should be identified and reported separately or (re)insurers may choose to analyse all the non-material currencies separately from business that is reported in original currency (e.g. sterling business and non-sterling business converted to sterling could be reported separately).

Splitting the provisions by currency can occur at different stages of the process. Clearly, of there is enough credible data, then it makes sense to split the raw data down to currency before reserving takes place. Where there is no credible data, then allocation may take place before discounting; then the payment pattern derived from the combined data may be used for each currency group together with the correct EIOPA yield curve for discounting. Finally, there is the option of using a blended discount rate to estimate the discounted reserves and then doing the allocation. In using this approach, the reserving actuary/specialist will need to demonstrate that the simplification is appropriate: in particular, that the risk of materially misstating the provision by using the blended discount rate is low. This is most likely in an environment where

• ∙ the yield curves in the different currencies are very similar;

• ∙ yields are very low; and/or

• ∙ the liabilities are very short.

If the impact of discounting does not vary materially between classes to which a homogeneous risk group is being allocated, then, on the grounds on proportionality, a simplified allocation by currency is likely to be acceptable. If there are differences, then adjustments to the allocation methodology may need to be taken to allow for this. This may occur if there emerges a material difference over time between the risk-free yields in different currencies.

7.10.5. Allocation of other elements

There are other elements of the technical provisions that may be more challenging, or require additional assumptions in order to allocate to the required levels. Some of these are discussed below.

7.10.5.1. Expenses

There may be several possible approaches for allocating expenses in a reasonable way. These should consider the drivers of the expense item and also proportionality. For example, premium measures may be the most appropriate way to split the provision for future acquisition expenses between class. The claims elements of claims and premium provisions (i.e. not including the negative impact of future premiums) may be a more appropriate measure to split the claims administration expenses.

It is important to consider the currency features of the expenses that are being split. For example, it may not be appropriate to split out expenses into all currencies if they are actually to be incurred in sterling.

In practice, we do not expect to see very detailed expense allocation. For many classes of business the expenses will be far less material than the claims liabilities and the use of approximate approaches to allocating claims liabilities would make a detailed expense allocation incongruous.

7.10.5.2. Future premiums

If there are expected to be future premiums the reserving actuary/specialist should consider the extent to which these are expected in a particular segment. It may be acceptable to assume that future premiums are likely to be split in proportion with the premiums received to date, but if the balance of the business written recently has changed from the recent past, this assumption may not be acceptable.

7.10.5.3. Reinsurance

The reinsurance share of the technical provisions must also be split by class and currency. In many cases, the approach taken should follow the approach taken for the allocation of the gross best estimates. However, there may be cases where this is not straightforward and more detailed analysis can be carried out to work out more explicitly which class reinsurance recoveries should be allocated to.

A key consideration is consistency between the allocations of gross amounts and reinsurers’ shares to ensure outwards recoveries correspond to the inwards claims. For example, if all the IBNR for a particular class of business is allocated to one class or currency then, in most cases, all the outwards reinsurance IBNR would also be expected to be allocated to the same class/currency.

(Re)insurers will need to consider how to allocate reinstatement premiums across the classes within a homogeneous risk group. A reasonable approach would be to assume that these reinstatement premiums are allocated in the same way as the claims that they are linked to. However, where such reinstatement premiums are considered immaterial, it may be reasonable under a principle of proportionality (and more simple) to allocate these based on the underlying premiums.

Where reinsurance recoveries are defined in a currency that does not match that of the underlying gross claims these should be reported as such. If these are immaterial, the allocation methodology could be allocated in line with the underlying gross claims.

Where reinsurance covers multiple LoB, the reserving actuary/specialist must consider the most appropriate way in which the best estimates of reinsurer share should be allocated to class and currency. This should be based on the expected contribution of the underlying gross business to the expected recoveries. It is recognised that this element can be problematic (as it may depend on timings of losses, etc.), but the key principle remains reasonableness with justification. For example, in most cases, whole account stop loss reinsurance IBNR may be allocated in proportion to the gross inwards IBNRs. That is, it may be reasonable to allocate expected recoveries from whole account covers in proportion to the (already) allocated inwards reserves. However, firms should not expect whole account (or multiline) covers to be allocated to single class/currency splits where the underlying business covered is clearly not.

7.10.5.4. Risk margin

Solvency II requires the risk margin to be calculated at a whole account level. This must then be allocated to the Solvency II LoB, adequately reflecting the contribution of each of LoB to the overall SCR as used in calculation of the risk margin. This allocation may use output from an internal model, if available, or a broad simplification may be appropriate. This is discussed further in section 8.3.

7.10.6. Materiality and complexity of approach

In allocating liabilities to the necessary level of granularity, materiality ought to be a key consideration throughout. Apart from exposure analyses where explicit calculations will exist, in many cases the use of complex allocation techniques may add spurious accuracy.

7.10.7. Simple worked example for allocation

For an example of how to apply allocation, we refer the reader to the simple worked example in the Lloyd’s publication, Solvency II, Technical Provisions Data, Suggestions for Allocation Methodologies.

8.10.1. How to estimate the future SCRs

For a (re)insurer that will be operating an internal model there may still be a question over whether the model can reliably produce estimated SCRs at all future time periods for the current obligations.

This is because of the issues surrounding circularity (estimated future SCRs depends on movements in technical provisions that in turn reply on future estimates of SCRs), general complexity/scale where circularity can be overcome, run time problems associated with the complexity and materiality.

Taking these into account it is expected that many (re)insurers will use a simplification and that it is likely to be a proportional run-off approach as described above.

A (re)insurer using the standard formula could attempt to estimate future SCRs using the formula but this is unlikely and the same (proportional) simplifications are likely to be used.

8.10.2. Who will calculate the risk margin?

Given the risk margin is heavily based on the estimation of future SCRs, it may follow that the “capital team” of a firm is better placed to calculate the risk margin.

Conversely, the reserving/Actuarial Function of a firm will be responsible for the calculations of technical provisions (which includes the risk margin).

Where simplifications are employed, the reserving actuary/specialist may calculate the risk margin, with an initial SCR provided by the capital team. Where an internal model produces a “full” set of future SCRs, it is likely the capital team would be responsible for the risk margin.

In both circumstances the capital and reserving teams must communicate to ensure consistency of approaches. The Actuarial Function retains responsibility for the technical provisions and so will need to fully understand the work carried out by the capital team in its contribution to the technical provisions.

8.10.3. Are there any data issues?

It is unlikely that the risk margin calculation will provide any significant new data issues. This follows as either the internal model will produce the necessary expected future SCRs directly or a simplification is employed that mainly utilises a current calculation of an SCR and output from the reserving process (such as the expected future cash flows).

Other data items such as the expected cost of capital and yield curves will be provided by EIOPA.

8.10.4. Communicating the risk margin

It is easy for the risk margin to be misinterpreted by management, especially given its name. There are some simple points that could be made when introducing the risk margin:

• ∙ It is not a margin on the reserves. It is intended to represent an amount to transfer to a third party for the third party to cover the expected cost of future regulatory capital on the business transferred, i.e., a market value margin to be added to the best estimate.

• ∙ It is not a method for smoothing results. The method remains the same under all conditions and in fact if the best estimate liabilities change then the risk margin may also change owing to changes in reserving risk, not necessarily by the same magnitude as the change in best estimate or in the same direction. For example, an increase in the volume of business (and best estimate) could mean a proportionately smaller increase or even reduction in the risk margin, if previously the volume was small and the experience volatile, whereas now the volume is higher, the experience is likely to be more stable and predictable.

• ∙ It is not discretionary. Management cannot manipulate the risk margin as a normal “margin”.

In many cases using the alternate phrase “market value margin” may be more appropriate and aid communication.

10.8.1. Enhancement of documentation

An argument can be made that the Solvency II validation standard simply enhances the existing documentation found in the actuarial standards.Footnote ^2, Footnote ³ One such enhancement is the inclusion in the Actuarial Function annual report of conclusions from the back-testing procedure and explanations of deviations.

10.8.2. Non-uniformity

The validation of method and model assumptions, together with the corresponding extended documentation produced, takes many forms. Many actuaries have developed company-specific approaches, which, in addition to complying with existing actuarial standards of practice, are intended to satisfy the new Solvency II regulatory demands. This reality translates into a lack of uniformity in the industry.

10.8.3. Inconclusiveness

The results from validation process can offer statistical support for the use of various methods, and/or provide diagnostics through which the practitioner can enhance their understanding of statistical nature of the underlying data. It is rare, however, that the validation process conclusively justifies the appropriateness of any assumption or method. Further, it is often the case that statistical tests may support the use of an alternative assumption or approach, which is not ultimately selected by the practitioner.

The goal of the validation exercise is not necessarily an improvement of the accuracy of estimation, but rather an improved understanding of the comprehensive data set; an improved understanding of the interactions observed; and an enhanced level of documentation so that an independent third party can understand the logic and rationale behind each material assumption.

10.8.4. Governance issues

The Actuarial Function is charged with the coordination of the calculation of the technical provisions. Each (re)insurer may decide who should perform the calculation of the technical provisions, as long as conflicts of interest are properly managed. For (re)insurers where full segregation of tasks is considered unreasonable and disproportionate, the persons performing the calculation should be separate from the persons giving an opinion on the calculations. Achieving “sufficient explicit and adequate internal control around the establishment of the technical provisions”Footnote ⁴ requires a process of independent review. Persons performing conflicting tasks are expected not to report to the same person, or (at a minimum) appropriate segregation of duties should be demonstrated.

10.8.5. Frequency of validation

The more sensitive the result of the calculation is to a single assumption, the more frequent validation tests should be undertaken for that assumption. For assumptions related to inflation (e.g. trends in severity and frequency, etc.), more frequent validation is warranted and straightforward. For assumptions based on limited information (e.g. tail factors) validation on a more frequent basis might not add much value in the context of supporting the underlying assumption.

More often than not, the data upon which assumptions are based, such as premium rate indices are themselves calculations which include subjective assessments. In this case, an assessment of the reliability and uncertainty of the underlying raw data as well as various forms of the compiled data, where subjectivity is introduced, is important.

10.8.6. Thoroughness of validation

Whichever methodology is employed in the calculation of the best estimate; the person reviewing the documentation from the validation exercise needs to be convinced that the selected approach is reasonable. Where a non-standard approach has been employed, a higher than normal validation standard should be employed, leading to more detailed documentation. The reviewing expert will need to be satisfied that the non-standard approach is indeed more appropriate than the standard approach, based on documented rationale. Non-standard approaches are generally necessary when the observable past is not a reliable basis (or no longer a reliable basis) for the measurement of future expectations.

10.8.7. Deliverables from the validation process

The deliverables from the validation process should be part of management information and integrated into other processes. At the highest level, there should be documentation that confirms that validation has been carried out, the extent of the validation and any actions/feedback from the validation exercise. At the most granular level, the validation output should summarise the validation exercises carried out, the results of the exercises and the actions/recommendations. Validation exercises may include:

• ∙ back-testing: testing predicted against experience;

• ∙ assessment of the reasonableness of key assumptions;

• ∙ percentiles and analysis of residuals (influential observations outliers/clustering of claims);

• ∙ ratios (drivers and causes of patterns, settled/reported, paid/incurred, etc.);

• ∙ graphical validation of patterns;

• ∙ appropriateness of the treatment of large losses;

• ∙ expense assumptions relative to historical expenses and to budgets;

• ∙ stress and scenario testing (non-linearity, uncertainty and tail of distribution considered); and

• ∙ sensitivity analysis (sensitivity to underlying assumptions – changes in parameters, benchmarking, impact of changes in cover, deductibles or external factors).

10.9.1. Back-testing and assumption consistency

The application of multiple deterministic methods and subsequent weighting of results in order to select a best estimate is considered current actuarial best practice in most situations. Regardless of how many deterministic methods have been utilised in the formation of a best estimate, future incremental expectations can be calculated, for example, by combining cumulative expectations from each method using analogous weights and taking consecutive differences to get expected incremental amounts.

Table 19

Back-Testing Example: How Paid Expected from Different Methods Could be Combined

One sticky point with respect to calculating future incremental expectations is that the practitioner needs to combine the future payments (from paid methods) with future incurred amounts (from incurred methods) at each development period in cases where weight has been given to methods using both paid and incurred methods. One approach, resulting in expected future paid amounts, is to convert future incurred amounts from an incurred methodology (e.g. chain-ladder, Bornhuetter–Ferguson, etc.) to be future payments, based on the ratio of ultimate loss from the paid method and incurred method (e.g. chain-ladder, Bornhuetter–Ferguson, etc.), respectively. An analogous approach can be used to convert future paid expectations to be future incurred amounts. Such an approach is necessary as the both paid and incurred methods are influencing the ultimate loss selected, and therefore the best estimate.

Table 20

Back-testing Example: Combining Paid and Incurred Based Estimates to Come Up with Expected Paids

The same issue arises when modelling uncertainty for the predictive distribution. The use of a bootstrap of a single model (e.g. paid chain-ladder Over Dispersed Poisson (ODP) model) can introduce an inconsistency between the deterministic assumptions and the uncertainty assumptions. If the expected distribution of possible future outcomes are the result of bootstrapping the paid chain-ladder ODP in isolation (perhaps with the mean shifted to be the best estimate, as often seen in practice), it may be inappropriate to use this distribution in order to back-test expectations that are based on significantly more analysis (a weighting of multiple methods) and information (paid and incurred data). And if an actuary does use this distribution based on a single model, there is some question as to whether they have really back-tested the best estimate calculation or back-tested the result of the paid chain-ladder. It is important to reinforce the fact that the paid chain-ladder was at least partially rejected during the selection of the deterministic best estimate as soon as weight was given to methods other than the paid chain-ladder.

There are generally well founded and documented reasons why actuaries rely on deterministic incurred loss and/or Bornhuetter–Ferguson methods for immature AY. Often the reasons are tied to the additional volatility observed in the paid (or incurred) chain-ladder loss development factors (LDFs) for immature AYs and the resulting high dependency on a single (or a few) observation(s) of the AY aggregate paid (or incurred) amount in isolation. Uncertainty conclusions resulting from the weighting of distributions from multiple bootstraps, then, is the only approach that can claim to use an assumption set consistent with an underlying deterministic analysis that uses multiple methods.

10.9.2. Back-testing and granularity

The comparison and assessment of actual accruals relative to expectations by AYFootnote ⁶ and LoB, as well as CYFootnote ⁷ (sum of AY) and LoB, could be considered a minimum standard and flows easily from the output of standard actuarial reserving methodology. The assessment of actual accruals at higher levels of granularity (e.g. across LoBs) necessitates that the underlying analyses have taken correlation into account.

10.9.3. Back-testing and defining a threshold

By definition, an amount falling outside of a wider confidence interval (e.g. between the 5^th and 95^th percentile) should happen infrequently, unless easily explainable by “something rarely seen”, by the invalidation of a prior assumption, or by acknowledgement that the inherent uncertainty in the estimate was under-appreciated. In this context, a threshold can be defined based on reserve uncertainty expectations (e.g. two standard deviations, n ^th and (1-n)^th percentile, actuarial judgement, etc.). Such a threshold enables the assessment of deviations from the expected amount.

The smaller the threshold, the more frequently the threshold will be breached. Note that the conclusion from an investigation after a threshold was breached does not automatically mean that the reserves are inadequate or the underlying methodology was flawed. Indeed, it could simply mean that the corresponding uncertainty was underestimated due to, for example, the use of a limited data set. It is important to keep in mind that even with perfect estimation, random outcomes are expected to occur at extreme levels occasionally (i.e. 1 out of 100 observations should reach the 99^th percentile).

Company-specific thresholds should be chosen which are aligned with the strategy of the risk-management function, and the following considerations should be taken into account:

• ∙ Symmetry: There is no reason why the thresholds should be symmetrically applied.

• ∙ Size of range for each LoB: The tighter the range, the more observations will fail the test.

• ∙ Size of range for aggregate results: The (percentile) threshold may be larger for a specific AY and LoB, relative to the threshold used in aggregate as variations across AY may offset each other.

• ∙ Multiple level threshold: Multiple levels allows a company to differentiate the decision to escalate a response based on the significance of the fail.

10.11.1. Applicability and relevance of method(s) used

In most reserving exercises, no single method is clearly “optimal”, so it has become standard practice to implement multiple methods, reconcile differences between results of multiple methods, employ judgement to select an estimate and document the reasons for the final selection of results.

Many assumptions are set based on an analysis of historical data. There is therefore a presumption that past performance is a good indicator of future performance. Every validation exercise should consider the validity of this presumption. In particular, changes in the underlying exposures, terms of business, and claims handling should be investigated and documented. Where such a change has occurred, it may be appropriate to consider whether the data (adjusted or unadjusted) or method (adjusted or unadjusted) continues to be valid and to conclude (or not) that it is appropriate to rely on the data or method.

For triangular methods, a common assumption is that the expected value along the next diagonal is equal to the product of the current valuation (value on the latest diagonal) and a LDF based on the relationship of consecutive columns. Mathematically, this is a set of assumptions, for each AY w, described as:

$$E\left[ {c\left( {w{\rm ,d}\,{\rm {\plus}}\,{\rm 1}} \right)\,{\rm \,\mid\,}\,c\left( {w{\rm ,1}} \right){\rm ,\,\ldots\,,}c\left( {w{\rm ,d}} \right)} \right]\,{\rm =}\,c\left( {w{\rm ,d}} \right)\,{\rm \times}\,F\left( {\rm d} \right)$$

This set of assumptions can be tested by plotting cumulative values of columns d and d+1 on the x and y axes, plotting the line y=a×x (where a is the selected LDF), and observe whether the points roughly align on the line. As shown by Brosius (1993), the all year loss-weighted average (AYLWA) LDF, as shown below, is an unbiased estimator. Variation from the AYLWA, which is a common occurrence, can be considered an additional assumption and as such the logical justification should be documented.

Figure 9

Observations Verses Expected Using the AYLWA

Another common triangular method assumption is that AYs are independent. Mathematically, this assumption is described as:

$$\left\{ {c\left( {i,{\rm 1}} \right),\,\,\ldots\,,\,c\left( {i,n} \right)} \right\}\,\,{\rm and}\,\,\left\{ {c\left( {j,1} \right),\,\,\ldots\,,\,c\left( {j,n} \right)} \right\}\,{\rm are}\,\,{\rm independent}\,\,{\rm for}\,\,i\,\,\ne\,\,j$$

In fact, this is often not the case, and it is necessary to consider the possible impact of the invalidity of this assumption on appropriateness of the method. Mack (1993) suggests that this assumption can be tested by searching for “calendar year effects”, meaning evaluating the probability of observing large or small development factors (relative to the median) along a diagonal.

Table 21

Looking for Calendar Year Effects in the Triangles

10.11.2. Identification of relevant and material assumptions of the best estimate

For practical reasons, one needs to identify the key assumptions, i.e., those to which the results are most sensitive, in order to focus validation effort. This may be done by sensitivity testing.

Examples of key assumptions for validation:

• ∙ LDFs;

• ∙ tail factors;

• ∙ if Bornhuetter–Ferguson, assumptions about the strength of premium rates (pricing indices);

• ∙ if Cape-Cod, assumptions about the measurement of exposures over time;

• ∙ decomposition and review of results into frequency/severity components;

• ∙ underlying processes (payment of claims, case reserving) have not changed over time;

• ∙ underlying environment is unchanged (legal/social);

• ∙ the ability of average past inflation to replicate future inflation; and

• ∙ other explicit inflation assumptions (if used).

Again, at an overall level, it is important to consider any changes, or potential changes in the business that may invalidate the assumption that the past experience is representative of future experience. Where there have been changes, one needs to check that these have been appropriately allowed for in the selection of assumptions, e.g., by restricting the data set upon which the assumptions have been based, or by judgementally adjusting assumptions for known changes. Where judgement has been applied, evidence and supportive arguments should be documented.

More often than not, the data upon which assumptions are based, such as premium rate indices are themselves approximate, or subjective assessments. In this case, an assessment of the reliability and uncertainty of the underlying raw data as well as various forms of the compiled data is important.

After future expectations have been calculated, assessing the relative importance of deviations from expectations is a challenge. Sometimes differences from expectations are simply due to process error or random error, and still within a confidence interval of acceptable outcomes, given prior assumptions. Other times, the differences from expectations are due to errors in estimation or model error. It is important to keep in mind that method parameters change over time and as such, it is important that selected method parameters balance accuracy with stability. This means accounting for the latest trends without adding unnecessary volatility.

10.11.3. Modelling uncertainty in expectations

Actuarial reserve analyses have historically focused on the point estimates. Within each analysis, various assumptions are made with respect to future paid and incurred amounts, underlying frequency and severity trends, and premium level. The Solvency II validation requirements imply that these assumptions need to be explicitly documented, so that they can be tested against the future reality as observed in the subsequent period. For some of these assumptions, the actuary will need to use actuarial judgement.

Keeping proportionality in mind, a more sophisticated approach to producing ranges for expectations would be to use the results of internal models (which by definition produce expected future scenarios given current expectations of amount and variability of a data element). As the parameters for such models are generally based on the actuarial analysis, however, this approach tends to put the cart before the horse.

The underlying actuarial analyses, which support internal model parameters, are the best source for expectations and commensurate acceptable ranges. Stochastic models, such as a bootstrap, or closed form solutions, such as either Mack or the Wuthrich & Merz (W&M) algorithm, are often implemented to support internal model parameters. With little manipulation, these approaches can provide a distribution of expected incremental output (or an estimate of the standard error for the incremental output) at various levels of granularity.

It is important to note that the use of a closed form solution introduces the need for an important additional assumption regarding a specific distributional form. Further, it is hard to imagine how one would validate this distributional form assumption without using a bootstrap technique and comparing the output to various distributions.

10.11.4. Some key assumptions of the bootstrap model

Before proceeding down the path of bootstrapping multiple models, a few key assumptions need to be identified and documented. The following is a non-exhaustive list of issues that arise when modelling using bootstrap techniques.Footnote ⁹ In each case, a solution that fits the statistical framework is available. Use of bootstrap models which do not allow for the explicit adjustment for such issues can be considered black boxes by the regulator and leave the actuary in a position where a number of new assumptions remain undocumented and not validated.

• ∙ Non-zero average of residuals: The residuals that are calculated in a bootstrap are error terms that are assumed to be identically distributed with a mean of zero. Since residuals are random observations of the errors given the assumed model of expected results, observing non-zero average is not necessarily a problem. The question is whether or not the residuals should be adjusted so that their average is zero, via the addition of a single constant to all residuals. It can be argued that the non-zero average of residuals is a characteristic of the data set and should not be removed.

• ∙ Long-term average LDFs: Deterministic analyses often “select” LDFs from various reasonable metrics (all year average, 5-year average, average excluding high and low, etc.). While this is a common approach for calculating a best estimate, the removal of observations in a reserve uncertainty analysis (via individual outliers, complete AYs, or observations older than n CYs), should be done carefully as this tends to remove the uncertainty that is being modelled. The removal should be based on an assessment of the resulting fit of the model to the observable data and, if possible, deterministic and stochastic assumptions should be consistent.

• ∙ Heteroscedasticity: The residuals that are calculated in a bootstrap are error terms that are assumed to be identically distributed with a mean of zero. For this reason, the bootstrap model is able to take a residual from one location and apply it to fitted loss in another location in order to produce sample values. Heteroscedasticity refers to the challenge that some development periods have residuals that appear to be more variable than others (i.e. they appear to have different variances).

• ∙ Heteroecthesious data: The bootstrap model requires both symmetrically shaped triangles (e.g. AY×AY, AQ×AQ, etc.) and homoecthesious data. Heteroecthesious data simply means that exposures are incomplete or uneven at interim evaluation dates. The two most common examples are triangles with a partial first development year (e.g. as of 9, 21 and 33 months) and triangles with a partial last calendar period (e.g. but for the last diagonal which includes values as of 30/9/AY, the triangle is 31/12/AY×31/12/AY).

• ∙ Exposure adjustments: The bootstrap model can perform poorly in situations where exposures have changed dramatically over time (e.g. rapid growth, run-off). Exposures in this context can include variables used in the pricing of a policy (e.g. car years, sums-insured and payroll) or variables observed or estimated based on actual experience (e.g. ultimate claim counts or on-level premium). If such earned exposures information is available for each AY, a useful option is to bootstrap the pure premium (i.e. losses divided by exposure) instead of total loss. The results of such an analysis would require subsequent multiplication by exposure in order to restate the results in terms of total loss values.

10.11.5. Validation of key assumptions of the bootstrap model

A CAS working partyFootnote ¹⁰ identified 20 criteria (diagnostic tools) for gauging the quality of a stochastic model in their report on quantifying variability in reserve estimates. The working party also noted that no single diagnostic tool (or group of tools) could be considered definitive in determining an “optimal” model.

According to Shapland and Leong,Footnote ¹¹ diagnostic tests are designed for three purposes:

• ∙ to test various assumptions in the model;

• ∙ to gauge the quality of the model fit; and

• ∙ to help guide the adjustment.

By analysing the results of diagnostic tests, the fit of a model may be improved. The objective is not to find the best model, but rather a set of reasonable models. This is consistent with the goals of a deterministic analysis. Shapland and Leong describe number of diagnostics for the bootstrap, which serve as a good foundation for validation tests, including:

• ∙ review of residual graphs before/after heteroscedasticity adjustments;

• ∙ normality tests before/after heteroscedasticity adjustments; and

• ∙ review of simulated incremental values (mean and standard deviation) by development period.

Such diagnostic tests are in fact validation exercises, which require documentation if the resulting model is used to estimate uncertainty in the back-testing exercise

Figure 10

Residual Graphs Before Heteroscedasticity Adjustments

Figure 11

Residual Graphs After Heteroscedasticity Adjustments

Figure 12

Normality Plots Before and After Heteroscedasticity Adjustments

Before heteroscedasticity adjustments:

After heteroscedasticity adjustments:

Normality tests before/after heteroscedasticity adjustments:

Review of simulated incremental values (mean and standard error) by development period

Before looking at the results of the back-test, based on our deterministic analysis and complementary multiple model bootstrap analysis, it is important to be reminded of the following:Footnote ¹²

• ∙ Models do not provide answers, they provide information.

• ∙ All models make assumptions that may or may not be correct, or that are only correct in certain circumstances.

• ∙ One must be highly sceptical of model results that claim high degrees of precision.

• ∙ Choose a model that is appropriate for the decision being made, and understand its assumptions and limitations before using it and while interpreting results.

• ∙ The “ERM regulatory paradigm”: There may be an increase in reliance on computer models by that subset of decision makers who do not understand them and have perverse incentives to treat them as black boxes.

• ∙ Actuaries are in a unique position of understanding the models and the questions they are designed to address. We have the tools, education, and experience to design and build them, to understand those built by others, and to understand their role in decision making. We can, if we so desire, play a very important role in limiting their misuse.

Table 22

Simulated Incremental Values (Mean and Standard Error) by AY and Development Period

10.11.6. Application of back-testing for plain vanilla gross claims

Once the uncertainty analysis has been completed, based on the bootstrap of analogous methods and weights from the deterministic analysis, the incremental cash flow output can be analysed to determine the threshold and the pass/fail metric. In the discussion below we use a symmetrical two-level threshold system that identifies values below the 5^th and 25^th percentiles and above the 75^th and 95^th percentiles. We also show values that are provided for example purposes.

Figure 13

A Symmetrical Threshold System

Each valuation exercise begins with a back-testing exercise. The initial back-testing exercise compares the new diagonal of information to the assumptions in the prior analysis. After completing the valuation, the expectations for the next future diagonal are set and these amounts can be compared with the future accruals. The loop begins again when the next valuation exercise begins.

Before beginning the new valuation, expectations for time (t=0) can be inferred from the prior valuation (t=−1). In this example, the books are closed in preparation of the 31 December 2008 valuation.

Assuming the company wrote three LoBs, each with nine independent AYs and one CY testable paid loss and incurred loss result; there would be 80 observationsFootnote ¹³ (aggregate observations require correlation assumptions). The 80 observations would be expected to fall uniformly across the percentiles and calibration tests can be set up to observe this. In other words, 5 in 100 observations would be expected to exceed the 95^th percentile.

Table 23

For our Example, Observations in the Percentile Ranges

Over time, such observations of back-testing results add informational value to the underlying uncertainty (for each segment) and correlation (for aggregation of segments) analyses.

For simplicity, we have ignored the highest level of granularity (aggregate (re)insurer) in this example.

At a middle level of granularity (LoB), possible deficiencies in the prior models can be identified. In this example, early warnings can be generated regarding the AY<CY paid (99.6^th percentile) and AY<CY incurred (99.9^th percentile), which both fell above the selected threshold. In this context AY<CY refers to all AYs before the most recent AY which is the same as the current CY. The most recent AY is not included as it did not exist in the prior reserving exercise and as such does not have a comparable value. A comparable value can be gleaned from planned figures or (if applicable) the mean prospective expectation inherent in the output of an internal model.

Table 24

Results of the Back-Test: Commercial Auto: expectations based on 31 December 2007, actuals accrued during CY 2008

At the most granular level (LoB and AY), early warning would be generated for AY 2000, 2003 and 2005 through to 2007 paid and incurred, as well as AY 2002 and 2004 incurred.

Both tabular (above) and graphical (below) depiction of the results of the back-test can be valuable as the actuary attempts to distinguish between the possible explanations for the failure of the back-test. Recall that the possible explanations include:

• ∙ a mis-estimation of the mean (we never get this exactly right);

• ∙ a mis-estimation of the uncertainty; or

• ∙ random chance.

Figure 14

Graphical Display of the Results of the Back-test

Summary of paid and incurred back-test for Commercial Auto (AYCY):

In this example, the actuary could begin by checking with departments outside of the Actuarial Function to verify that there are no known systematic changes in the internal reserving process. Next, the actuary may want to check whether the weights given to the paid and incurred methods in the deterministic analysis were unreasonably biasing the selected ultimate loss downward (mis-estimation of the mean). After that, the actuary may want to check whether the weights given to the paid and incurred models in the bootstrap are unreasonably under-appreciating the uncertainty (mis-estimation of the uncertainty).

The automated back-test also enables the Actuarial Function to provide management with a warning of a potential increase or decrease in reserve, consistent with the 1 year time horizon calculations. In the table below, the expected reserves for three LoBs as of 31 December 2008 using data as of 31 December 2007 are lower than the new conditional reserves using data as of 31 December 2008. The increase in the conditional reserve (i.e. the “actuary in a box” result) can be considered a preliminary estimate of the conclusion of the updated analysis before any change in actuarial assumptions. The actual reserve change would, of course, depend on a deeper review of the data and the assumptions used to estimate reserves.

Table 25

Illustrating How an Automated Back-Test Can Provide Early Warning of Changes to Reserves

In this particular example with respect to Commercial Auto, a CY trend was under-appreciated as of 31 December 2007. The analysis of residuals, as documented in the validation section of an actuarial report, shows the increasing trend which was ignored.

Figure 15

Plot of Residuals Shows Trend Not Allowed for

There are two substantial benefits of identifying this oversight in the prior analysis at the beginning of the current analysis (which is now even easier to identify after the trend has continued for another year), other than the obvious ability to allocate actuarial resources to segments that require additional attention. First, identification enables actuaries to ask questions of non-actuaries in order to better understand the portfolio, from which the soft information received can improve the current analysis. In this case, the claims department could be solicited to help identify the cause of the observed trend. The back-test and subsequent research enables a question that includes the observed old trend (1.9%), the observed new trend (3.6%) and the rough point in time when the new trend appears to have manifested (2004). Such details are welcomed by actuaries and non-actuaries alike, as it more precisely defines the issue at hand and allows for a more targeted search for explanation.

Second, identification enables actuaries to test “what could have been done” in the context of methodology, which may serve as a basis for what “will be done” going forward.

In this case, a GLM model, which more appropriately incorporates CY trends, was implemented. The alternative methodology directly allows for the CY trend that appears to have increased from 1.9% to 3.6% per annum at 2004.

Figure 16

Plot of Residuals After Changing to a New Model

Comparing the result of the new model (GLM Paid Model) with the old (ODP Paid Model), the enhanced approach seems to produce expectations more in line with what was observed. Such evidence could support a change in methodology for the segment and motivate the search for similar effects in other related segments. Note that, as expected, the validation exercise does not provide conclusive evidence that the GLM approach is superior in all cases. In fact, some values still breach the threshold even if the new approach was given 100% weight. The important take away, therefore, is not that the new approach is superior, but rather that the actuaries analysing the data have potentially improved the understanding of the drivers of uncertainty in the portfolio.

Table 26

Comparison of Bootstrap Results on the Old and New Models

11.1.1. Discussion of issues

The working party has considered six main issues with regard to reporting:

1. 1. form of disclosure;

2. 2. what will need to be disclosed;

3. 3. translation of actuarial output into layman’s terms;

4. 4. report templates;

5. 5. timing of reporting; and

6. 6. confidentiality.

11.3.1. Best estimate methodology

As is currently the case with a Technical Actuarial Standards (“TAS”)-compliant report, the RSR and SFCR will need to detail the high-level methodology used in the reserving process, for both gross and net provisions. Based on CP58, CEIOPS advised that the SFCR will need to set out both relevant information on the determination of the technical provisions with key assumptions and methodologies and the impact of reinsurance on the assessment of technical provisions.

11.3.2. Risk margin

Both the RSR and SFCR will need to explain the calculations and rationale behind the derivation of the risk margin. Again, the difference between the two reports will lie in the level of detail, and the extent to which the company feels any disclosure around the calculation methodology, assumptions or results is commercially sensitive. The methodology for calculating risk margins is considered in section 8.

11.3.3. Other factors

Both the RSR and SFCR will need to set out details of material changes since last report and these changes will need to be explained. Examples of changes which may occur include significant deviations from expected development of premiums and claims. The back-testing and validation carried out as part of the technical provisions process will help to gauge these deviations. Again, materiality will play a key role in deciding which changes need to be covered in the report.

As discussed in section 11.1., reconciliation to financial statements will also need to be considered.

11.5.1. E1

There are two versions of this template: one which will be completed annually and is not for public disclosure, and one which will be completed quarterly, and is for public disclosure, although this disclosure will only take place annually. Both templates will contain an overview of the non-life technical provisions, broken down into their key components, including best estimate, risk margin, reinsurance recoveries, premium and claims provisions, and cash flows, and further split out by reporting class (or “segment”).

11.5.2. E2

This template will set out projected cash flows, again at a segment level. These will help the regulator to gauge the development of cash flows over time, and will form a key part of the balance sheet supervisory process. This template will be completed annually, and will not be for public disclosure.

11.5.3. E3

This template will set out triangulations of paid claims, notified outstanding claims (referred to as Reported But Not Settled or RBNS), and undiscounted best estimate claims provisions (equal to RBNS plus IBNR) for each LoB and all material currencies; on a gross, ceded and net of reinsurance basis. The template will be produced annually, and although the full E3 template will not be for public disclosure, a simplified version will be.

11.5.4. E4

This template will set out the movement in claims provisions in the context of movement in the number of claims, split by claims which were open at the start of the period, reported during the period and closed but reopened during the period, by segment. The template will be completed annually and will not be publicly disclosed.

11.5.5. E6

E6 will set out the development of the severity distribution for claims incurred during each of the past 15 UYs or AYs as at the end of the financial year. The template will be completed annually and will not be publicly disclosed.

11.5.6. E7A and E7B

These templates will set out a summary for each LoB of the individual and market-wide risk profile of the peak risks (based on net retention) that are exceptional in nature (E7A) and mass risks (E7B). This will help to provide an illustration of the risk profile of the portfolio. These templates will be completed annually and will not be publicly disclosed.

In addition to the non-life templates set out above, there will be a requirement for information relating to annuities that stem from non-life insurance obligations to be included in life templates: F1, F2 and F4.

While it is not yet required by the PRA that (re)insurers complete the templates, syndicates at Lloyd’s have already been required to submit quantitative templates. The interested reader can find further information at: http://www.lloyds.com/~/media/files/the%20market/operating%20at%20lloyds/solvency%20ii/2013%20quantitative/pillar%203%20returns%20instructions%20march%202013final.pdf#search=‘pillar 3 returns’

12.6.1. Purpose

One of the first things that requires explanation, and should be referred back to, is the purpose of the Solvency II technical provisions and what they will be used for. Until such time as the board, management and other users of the technical provisions become comfortable, it is worth reiterating that:

• ∙ The Solvency II technical provisions are a key part of the Solvency II balance sheet. The Solvency II balance sheet, and in particular, the excess of the assets over the liabilities plus SCR, should be a key consideration in strategic decision making.

• ∙ The Solvency II technical provisions are a key input into the SCR calculation, whether this is based on standard formula or an internal model.

12.6.2. Consistency

As Solvency II aims for capital to reflect underlying risk, it is important that all elements of the technical provisions calculation are clearly linked to underlying risk factors and how these impact the business in practical terms.

It is important to ensure consistency across the business so the approach and assumptions used in the assessment of technical provisions should be consistent with those informing capital, pricing and wider strategic decisions. Ensuring understanding of the key drivers affecting the technical provisions should naturally form part of the more holistic approach to risk management under the Solvency II framework. The ORSA process should result in management being highly engaged and taking strategic decisions based on the impact on the risk and solvency profile of the company. This may impact the underwriting strategy and the results that are needed by LoB to generate economic value. The technical provisions, how they respond to business decisions and how the uncertainty underlying the technical provisions responds to business decisions are a key consideration.

All stakeholders must also understand how their input feeds in to the technical provisions process so that they can provide the correct information in a timely manner. Thus “horizontal” communication (to parallel functions such as Finance and Claims) may be as important as “vertical” communication (to governance committees, etc.). Any material changes that affect the risk profile or experience could necessitate the recalculation of elements of the technical provisions and capital requirements.