RESERVING AND CAPITAL 23Oct07 by xiaoyounan




Product Classification (UK)

At a high level, the benefits available from this product at any time are related to the greater
of two quantities: the unit fund balance and the guaranteed minimum benefit. This suggests
classifying the business as unit-linked with guarantees, and fits in with being able to offer the
guarantee as a rider on an existing unit linked products if necessary.

Reserve Components

Under this unit linked classification, the gross reserves for the product will be calculated, in
accordance with generally accepted actuarial practices (INSPRU 1.2.10 (7) R) as:
            A unit reserve, plus;
            An option reserve for the investment guarantees (if the guarantee rider option
             was purchased), plus;
            An additional sterling reserve.

As a non-profit unit linked product, only the Peak 1 rules apply. Peak 2 rules would apply
only if the with-profits fund was used amongst the list of funds on which the guarantees are
written. Unit, additional sterling and aggregate expense reserves will be carried out in the
normal way for unit linked policies without investment guarantees.

Guarantee/ Option Reserve

The value of the guarantee costs will be determined using stochastic methods reflecting the
wide range of scenario outcomes that need to be valued. The choice of model would need to
take into account the professional and regulatory guidance in-force at the time. A risk
neutral, arbitrage free, market consistent model is recommended. This would be consistent
with the hedging approach that will be used to support the guarantees (and regulatory
guidance applicable to similar peak-2 embedded option liabilities). Margins for adverse
deviations would need to be added to the otherwise risk neutral valuation basis.

The option reserve will be calculated net of the value of future option premiums (guarantee
rider charges). Thus, within the stochastic projections, guarantee option claims are treated as
a positive liability and option premium charges as a negative cash flow, both of which are
discounted by the valuation interest rate. The concept of allowing for the value of future
premiums or charges is not new and ought not to be controversial. (Note that the proposed
method involves taking credit for future charges, not future profits). The important principles
are the avoidance of future valuation strain and that the collection of future premiums/
charges are consistent with PRE.
Although new regulations allowing negative mathematical reserves, the Consolidated Life
Directive still requires that no contract should be valued at less than its surrender value. It is
therefore likely that any any negative option reserve would be floored to zero on a per policy
basis. In particular, this will be necessary if the rider option can be lapsed in isolation
without surrender penalty (although strictly switch charges may apply), and as a result it
should be treated as a separate policy. By zeroising the reserve, expected profits inherent in
the rider charge premium basis will not be capitalised on the day the policy is sold, but will
fall into surplus over time as the charges are received and the actual cost of hedging due to
actual experience unfolds.

Valuation Basis

INSPRU 1.2.7R requires that mathematical reserves should be established using prudent
assumptions on all future cash flows expected to arise in respect of long term insurance
contracts. This suggests valuing the rider option using risk neutral market implied
parameters (reflective of the hedge assets backing the rider), but with volatility and other
assumptions adjusted to provide the margin. A possible benchmark measure for such
margins would be to compare with a CTE65 calculation of the liability option, which is the
emerging practice in the US and Ireland. The minimum requirement is for the margins for
adverse deviation to be greater than or equal to the relevant market price for the risks being

Selection of the mortality table would need to reflect the fact that there is a longevity
guarantee, as well as an early (non guaranteed) death benefit prior to age 75.

Traditionally a zero lapse assumption was used for similar statutory valuations, although a
case can be made to use an assumption involving dynamic policyholder behaviour (higher
lapses in rising markets when options are out-the-money, and lower lapse rates in falling
markets when options are in-the-money).

Additional Risk and Solvency Capital

Insurance Death Risk Capital Component
For any contracts with a GMDB, there is capital at risk on death. For unit linked business
UK regulation stipulates that 0.3% of this capital at risk (technically netted down for
reinsurance) be held as an Insurance Death Risk Capital Component of the solvency margin
(INSPRU 1.1.81-84R).

Insurance Expense and Market Risk Capital Component
UK regulation also requires an additional solvency margin component of 4% of reserves
(unit, sterling, aggregate expense and option) to be held for products with guarantees. This is
likely to apply regardless of whether the guarantee is written as a rider policy or not
(INSPRU 1.1.92G).

The requirement to hold solvency capital of 4% of reserves applies regardless of how onerous
(or non-onerous) the investment guarantee is. It is therefore recommended, that for prudent
and sound management of the business, the amount of capital actually required to support the
risk be assessed. We discuss this further in section XXX.

For a simple fixed quota share reinsurance, then given the discounted cashflow valuation
methodology, the option reserve would be reduced according to the reinsurance
proportion. However, the terms of the treaty may be such that the reinsurer rider charge
is different to the direct policy charge, in which case the option reserve will need to be
decomposed into premium and claim elements before proportioning can be applied.

Prudential margins would be included in respect of any uncertainty as to the amount or
timing of cashflows, and the risk of credit default by the reinsurer in the usual way.

Under current solvency-1 rules, there is limited relief available on the solvency margin –
currently 50% for the Insurance Death Risk Capital Component and 15% for the
Insurance Expense & Market Risk Capital Component, both on an aggregate portfolio

Note also that the impact of extreme events on the UK client and the reinsurance
arrangements should be considered under the credit and operational risk components of
Pillar 2.

Pillar 2 ICA and Economic Capital at Risk

Due to the self-assessment nature of this exercise, methodologies can vary from company
to company. In this paper we assume the following simplified approach:
XXX  to disucss at W//P

Legislative Framework

Insurance companies in Ireland are regulated by the Irish Financial Regulator (FR) under
the European Communities Regulations 2006 1 , which transposes EU’s third life (and
reinsurance) directives.

Two general over-arching requirements are:
 that technical reserves must be determined “in accordance with the Insurance
  Accounts Directive” and that the FR may make rules with respect to technical
 “Life insurance undertakings will be required to have technical provisions
  determined by a Fellow Member of the Society of Actuaries in Ireland with due
  regard to the principles of Article 20 of the Consolidated Life Directive.”

Product Classification

As for the UK, the product could be classified as “linked to investment funds”, with
guarantees. For reference, “linked to investment funds” is defined as:

A [reinsurance] contract shall be deemed to be “linked to investment funds” if the
investment return, as it affects the claim payments under the [reinsurance] contract, is
directly related to the actual investment performance of a segregated pool of assets. This
pool of assets should be clearly identified within the [reinsurance] contract.

This definition appears to fit the characteristics of the VA business. Where only the
guarantee rider is carried on an Irish balance sheet, the linkage is not 1:1, and a case can
be made to classify as non-linked, however the same reserving methodology would apply
to the option liability.

Reserve Components

As with the UK, the direct writer’s reserves for the product will be calculated, in
accordance with generally accepted actuarial practices as, a unit reserve, plus an option
reserve for the investment guarantees, plus an additional sterling reserve.

In some situations, the Irish company (or reinsurance company) underwrites only the
guaranteed benefits and, therefore, will only hold (for this line of business) the option

Reserving Method

    For reinsurance business, this would be: “European Communities (Reinsurance) Regulations 2006”
The Consolidated Life Directive sets a number of over-riding requirements for the
calculation of reserves:-
a)      Use of a prudent prospective actuarial valuation taking into account all future
        liabilities and taking credit for future premiums due;
b)      Prudent infers inclusion of margins for adverse deviations in relevant factors;
c)      The prudence within the reserve calculations must have regard to the assets
        covering the reserves.
d)     Reserves must be calculated separately for each contract (which in this case, the
       minimum requirement is on a treaty level);
e)      Reserves must be equal to the minimum guaranteed surrender value under the
        reinsurance contract;

These principles are the over-riding reference point within the interpretation of Irish
regulations and consideration of guidance provided by the regulator. In addition, the
Irish regulator will check with the Board of the reassurer and the Signing Actuary
whether they are happy that these principles are being adhered to, e.g. that there are
appropriate levels of prudence

As with the UK, the value of the guarantee costs will be determined using stochastic
methods projecting both guarantee cost claims and guarantee charge premiums. It is now
well established practice to demonstrate that the model parameters are selected such that
the model can re-produce the market price of a suitable set of calibration assets.

In addition to the stochastic model, the reserves will also be tested against deterministic
stress tests. These tests will be set by the reassurer (and Signing Actuary) but will
normally have regard to the minimum resilience tests that the FR requires direct writers
to apply. The FR published minimum stress tests that he expects to be used from time to

The Irish also follow the principle of avoidance of future valuation strains and flooring
the option reserves at a contract level.

Valuation Basis

For VA business, there is a growing practice to justify the margins for adverse deviations
in the valuation basis either by comparison with or through direct calculation of a CTE-
65 of the net option liability, consistent with the growing use of this methodology in the
US. Prudent2 dynamic policyholder behaviour (higher lapses/ withdrawal utilisation in
rising markets when options are out-the-money, and lower lapse rates in falling markets
when options are in-the-money) should be considered although a simplified zero lapse
assumption will often be satisfactory, especially for compulsory purchase business.

    Prudent does not imply perfectly rational, nor does it imply a worst case scenario.
Note that in Ireland the regulator is less prescriptive towards one particular approach vs
another, but rather is more concerned that the company (and Signing Actuary) are able to
confirm that they are happy that the approach adopted is prudent. This provides the
company with the option of exploring these alternative approaches if it wishes.

Additional Risk and Solvency Capital

Companies are required to hold a solvency margin equal to the greater of:-
a)   The minimum amount required by regulations, and;
b)   A modelled amount which provides for a given confidence level of solvency

The regulatory minimum solvency margin is 4% of reserves. The FR has requested that
insurance companies generally aim to hold 200% 3of this minimum margin for the first 3
years, and 150% thereafter. This is a soft, rather than a hard, requirement. Companies
will be permitted to hold less than the 150%/200% margin but could, for example, be
asked to submit more frequent reporting to the FR (probably quarterly).

An important distinction between the UK and Ireland is that in Ireland, where the
guarantee benefits have been bifurcated into a separate rider insurance from the base unit-
linked product, the reserve for the carrier of the guarantee benefit will only be the option
reserve, not the full unit linked unit reserve. In this situation, the modelled amount
would likely be larger.

Modelled Minimum Solvency Amounts

The modelled amount, or so-called Augmented Solvency Model (ASM) may allow for
the movement of both assets and liabilities under stressed scenarios, so that a portfolio
with an effective hedge is likely to require less capital under the ASM then would
otherwise be the case.

The principle is to compute the amount of capital that needs to be set aside to cover
future losses. Generally this involves projecting the future cash flows (options premiums
and claims) as well as reserve and hedge asset movements under a range of scenarios, and
determining the capital value of the profit/ (loss) outcomes under each scenario. The
minimum solvency capital would then be taken as either the CTE90 of the worst capital
value of loss outcomes on a run-off basis, or the VAR-99.5% with a one year time
horizon. Until recently, the CTE-90 approach has been the industry norm, however there
is a trend towards the VAR99.5% in view of the emerging specifications for solvency-2.

Nested stochastic scenarios are in theory needed to project future reserve and hedge asset
movements within each outer scenario. In practice this can only be done on a model
point basis, and therefore alternative methods (typically gross premium calculations) are
used after benchmarking against such a calculation on a model point level.

    For reinsurers the parameter is 150% for all durations.

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