Solvency ii - Best Estimate
from the Solvency ii Association,
the largest Association
of Solvency ii Professionals in the world
CEIOPS Consultation Paper No. 26
Draft Advice for
Level 2 Implementing Measures on Solvency II:
Technical provisions - Elements of actuarial and statistical
methodologies for the calculation of the best estimate
1. Introduction
1.1. In its letter of 19 July 2007, the European Commission
requested CEIOPS to provide final, fully
consulted advice on Level 2 implementing measures by October
2009 and recommended CEIOPS to develop Level 3 guidance on certain
areas to foster supervisory convergence.
1.2. This consultation paper aims at providing advice with regard to
actuarial and statistical methodologies for the calculation of the
best estimate
as requested in Article 85 (a) of the General approach on the
Solvency II Directive proposal adopted by the ECOFIN Council on 2
December 2008 (herafter: “Level 1 text”).
1.3. The objective of this paper is to give draft advice on the
valuation techniques which shall be considered as appropriate
methodologies for the calculation of the
best estimate
and how these shall satisfy the requirements of the Level 1 text.
This would
include the application of approximations and simplified methods and
techniques.
1.4. CEIOPS will complement the advice with further advice on
related issues.
This includes the paper on management actions which is also being
released for consultation.
CEIOPS will continue to develop further advice relating to the
implementing measure covered by Article 85(a).
2. Extract from Level 1 Text
2.1 Legal basis for implementing measure
Article 85 - Implementing measures
“In order to ensure that the same treatment is applied to all
insurance and reinsurance undertakings calculating the Solvency
Capital Requirement on the basis of the standard formula, or to take
account of market developments, the Commission shall adopt
implementing measures laying down the following:
(a) Actuarial and statistical methodologies to calculate the
best estimate
referred to in Article 76(2) … ”
2.2 Other relevant articles for providing background to the
adviceArticle 76(2) – Calculation of the technical provisions
In particular, this Article requires that:
“[…] the
best estimate
shall be equal 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
calculation of the best estimate
shall be based upon current and credible information and realistic
assumptions and be performed using adequate actuarial and
statistical methods.
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.
The
best estimate
shall be calculated gross, without deductions of the amounts
recoverable from reinsurance contracts and special purpose vehicles.
Those amounts shall be calculated separately, in accordance with
Article 80.”
3. Advice
3.1 Explanatory text
3.1.1. Definition of “best estimate”
3.1. The Level 1 text states that the
best estimate
shall be equal to the probability weighted average of future
cash-flows taking account of the time value of money, using the
relevant risk-free interest rate term structure.
This in effect acknowledges that
the best estimate shall allow for uncertainty in the future
cash-flows.
3.2. In order to capture the above uncertainty a (re)insurance
undertaking shall ideally:
• Consider all possible future scenarios.
• Estimate the likelihood/probability of each of those scenarios.
• Calculate the cash-flows receivable/payable by the insurer in each
of those scenarios.
• Discount the projected cash-flows to reflect the time value of
money in each of those scenarios.
• Take the probability weighted average of the discounted cash-flows
from each of those scenarios.
3.3. The standard above is unlikely to be practical and the (re)insurance
undertaking shall consider how far the assumptions underlying the
valuation approach are likely to differ from this ideal.
3.4. In choosing an appropriate actuarial and statistical method to
calculate the best estimate,
the (re)insurance undertaking shall consider whether the assumptions
underlying the valuation technique appropriately reflect the nature
of their (re)insurance obligations and the element of uncertainty
inherent in the cash-flows.
3.1.2. Selection of valuation techniques
3.5. The causes of uncertainty in the
cash-flows that shall be allowed for in the application of the
valuation technique, may include the following:
• Fluctuation in the timing, frequency and
severity of claim events.
• Fluctuation in the period taken to settle claims and/or expenses.
• Fluctuation in the amount of expenses.
• Changes in the value of an index/market values used to determine
claim amounts.
• Changes in both entity and portfolio specific factors such as
legal, social, or economic environmental factors in particular in
interest rates.
• Uncertainty in policyholder behaviour.
• The exercise of discretion by the (re)insurance undertaking (which
may depend on the above-mentioned causes of uncertainty and also on
entity specific factors).
• Path dependency (as per 3.6).
• Interdependency between two or more causes of uncertainty (as per
3.7).
3.6.
Path-dependency
is where the cash-flows depend not only on economic conditions on
the cash-flow date, but also on economic conditions at previous
dates.
A cash-flow which has no path dependency can be valued by, for
example,
using an assumed value of the equity market
at a future point in time.
However,
a cash-flow with path-dependency would need additional assumptions
as to how the level of the equity market evolved (the equity
market's path) over time in order to be valued.
3.7. Similarly, some risk drivers may be largely independent of the
other factors which determine the cash-flows.
Alternatively, other risk-drivers may be heavily influenced by or
even determined by several other risk drivers
(interdependence).
For example, a fall in market values may influence the (re)insurance
undertaking’s exercise of discretion in future
participation, which in turn affects policyholder behaviour.
Another example would be a change in the legal
environment or the onset of a recession which could increase
the frequency or severity of non-life claims.
3.8. The valuation technique chosen shall meet
the following requirements:
• The (re)insurance undertaking shall be able to
demonstrate that the valuation
technique and the underlying assumptions are realistic and reflect
the uncertain nature of the cash-flows.
• The valuation technique shall be chosen on
the basis of the nature of the liability being valued and
from the identification of risks which materially affect the
underlying cash-flows.
• The assumptions underlying the valuation technique shall be validated
and reviewed by the (re)insurance undertaking.
• The valuation technique and its results shall be capable of being
audited.
• If policy data is grouped, (e.g. in model points or homogeneous
risk groups), the (re)insurance undertaking shall demonstrate that the
grouping process appropriately allows for the risk characteristics
of the individual policies.
• (Re)insurance undertakings shall ensure that
their capabilities (e.g. actuarial expertise, IT systems) are
commensurate with the actuarial and statistical techniques used.
• Under the proportionality principle,
the (re)insurance undertaking shall demonstrate that the assumptions
and techniques used are consistent with the nature, scale and
complexity of the risk.
3.9. The responsibility for the choice of adequate techniques for
the
calculation of the best estimate
liability rests with the (re)insurance undertaking subject to the
requirements set out in the Level 1 text and in implementing
measures.
However, the supervisor should be able to require an alternative
technique where that other valuation technique
achieves the objective of the valuation (prudent, reliable and
objective) in a better way.
3.10. The (re)insurance undertaking will be required to demonstrate
the appropriateness and robustness of the techniques, having regard
to the nature, scale and complexity of risks (principle of
proportionality).
This also applies to simplified techniques and
approximations.
When such demonstration fails, the supervisor shall have the power
to ask the insurer to develop more sophisticated techniques or
refine the assumption and parameters of the models used.
3.1.3. Valuation techniques
3.11. For many types of uncertainty, there are
a very large or possibly infinite number of possible future
scenarios.
Actuarial and statistical techniques have developed to form a
practical approach of estimating the value of (re)insurance
liabilities, including stochastic simulation (referred to hereafter
as simulation), deterministic and analytical techniques.
Examples of each technique are included in Section 3.1.4.
3.12. Rather than considering all possible future scenarios, (re)insurance
undertakings can choose a suitably large number of scenarios which
are representative of all possible futures, as for example in a
Monte Carlo simulation.
This approach is referred to as a
“simulation technique”.
3.13. A simulation technique would normally be recommended for
valuing cash flows where one or more of the following factors have a
material impact on the value of the liability:
• The cash-flows are highly path dependent.
• There are significant non-linear inter-dependencies between
several drivers of uncertainty.
• The cash-flows are materially affected by the potential future
management actions.
• Risks have a significant asymmetric impact on the value of the
cash-flows, in particular if contracts include material embedded
options and guarantees or if there are complex reinsurance contracts
in place.
• The value of options and guarantees is affected by the
policyholder behaviour assumed in the model.
3.14. Analytical and/or deterministic techniques may be applied
provided that the (re)insurance undertaking can demonstrate that the
above factors have been adequately allowed for.
Furthermore, CEIOPS recognise that this may
not be a proportionate approach for some (re)insurance undertakings.
3.15. There are particular challenges with
using a simulation approach.
As a result, a different approach may be more adequate for (re)insurance
undertakings that do not have the necessary capabilities.
• The computing time and power required
for a simulation technique can be much greater than for a closed
form solution since thousands of projections are required.
This is particularly true of any calculation which requires
a stochastic projection of cash-flows which is calculated using a
simulation technique as this in theory requires nested stochastic
calculations.
• Where simulation techniques are used,
economic scenario files are a key assumption.
Such scenario files could be produced by market consistent asset
models which must in turn be calibrated appropriately.
This calibration relies both on
expert judgement and the availability of market data.
The application of more sophisticated techniques is limited to cases
where sufficiently robust knowledge/data is available.
• Owing to the greater computing time and power, simulation
techniques in life (re)insurance are often
applied to model points rather than policy by policy.
The computing constraint can lead to the necessary
grouping of contracts which introduces
additional approximation error and may neglect important risk
characteristics of the portfolio.
• When the number of risk factors is high,
a holistic approach treating all the variables stochastically may
not be feasible
(because the number of required simulations would be excessively
high) and so some simplifications may have to be embedded in the
model.
Such limitations of the model shall be recognised as well as its
potential for influencing the final results.
• The (re)insurance undertaking will also need to separate
systematic influences from random influences and reflect them
accordingly within the valuation technique.
• The use of simulation techniques means that the valuation results
are based on (typically) many thousands of scenarios each with its
own assumption set.
The additional dimension in the assumption set adds considerably to
the complexity of the simulation approach and may be an
obstacle to an internal/external audit of its processes and results.
•
The model as well as the underlying assumptions may become
increasingly difficult to understand due to complexity incorporated
by the simulation technique.
This may also lead to higher potential for human or IT errors during
the implementation phase.
• The choice of technique will need to balance any expected loss of
accuracy with a range of financial and non-financial costs and
benefits.
• Where a simulation approach is used, the underlying asset
liability model (ALM) will be a vital component of the technique.
The asset liability model will apply a holistic approach which
captures all the guarantees and other costs within the portfolio
together in order to capture the interactions between different
items of cash-flows.
This is particularly important when the liability cash-flows depend
on the assets held and (re)insurance undertaking’s use of
discretion.
The following areas should be taken into account when considering
the advice on the use of simulation techniques:
•
Management actions:
The (re)insurance undertaking shall apply management actions which
are objective, reasonable and verifiable.
•
Setting assumptions:
The model may require a large number of parameters which a more
limited number of (external) people have the experience to
calibrate.
For example, a market consistent scenario file, or a list of
scenarios generated by a catastrophe modeller.
Although assumptions are based on past experience and current
conditions as far as possible, judgement shall be used for
some assumptions.
•
Validation:
Due to the additional dimension in the assumption set, it is
insufficient to check the result obtained is accurate through a
combination of summary statistics, spot checks and rough estimates
(as may be the case for some deterministic/analytical approaches).
The use of simulation approaches therefore means that the results
require different techniques/tools to audit.
•
Interpretation:
With all approaches, interpretation of the results may require a
clear understanding of the assumptions underlying the technique
where this materially affects the overall results.
With a simulation approach, particular attention shall be paid to
the behaviour of the asset-liability model in extreme scenarios
(where this materially affects the conclusions that can be drawn
from the model).
•
Model points:
The (re)insurance undertaking shall measure the potential for
additional error and review the grouping accordingly to ensure that
important risk characteristics of the portfolio are not neglected.
3.16. The (re)insurance undertaking may be able to
use a valuation technique based on closed form solutions.
Such techniques are referred to as analytical techniques and are
based on the distribution of future of cashflows.
For example:
•
Bayesian techniques
which use an assumption that future claim amounts follow a
given mathematical distribution.
These techniques calculate an undiscounted probability weighted
average set of cash-flows without explicitly considering each
potential scenario.
•
Black-Scholes
techniques which use an assumption that risk-free and risky
investment returns follow a given mathematical
distribution
3.17. The (re)insurance undertaking may also be able to use a
technique where the projection of the cash-flows is based on a fixed
set of assumptions.
The uncertainty is captured in some other way for example through
the derivation of the assumptions.
This is referred to below as a
“deterministic approach”.
3.18. In view of the criteria defined in paragraph 3.13 (re)insurance
undertakings may apply deterministic techniques in circumstances
such as:
• Where an alternative technique may require
the calibration of parameters for which only inadequate data is
available.
• Where the nature of the liability is complex but the complexity
does not materially affect the result or the complexity cannot be
captured better by other techniques.
• Where the nature of the liability is sufficiently simple or for
other reasons of nature such that
best estimate assumptions
result in a best estimate liability and this can be demonstrated.
3.19. An insurer may use a
combination of approaches when calculating the best estimate.
For example:
• The (re)insurance undertaking may use a valuation technique which
fails to include one or more causes of uncertainty.
The excluded/additional cause of uncertainty could then be valued
accurately as a separate set of cash-flows or measured through the
use of validation tools and appropriate adjustments made.
• The (re)insurance undertaking may identify that much of the
cause of uncertainty arises from one or more
risk (e.g. investment returns) with the remaining risks making a
much smaller contribution to the uncertainty (e.g. mortality
experience).
In this example, the (re)insurance undertaking may choose to use a
valuation technique which
combines
a simulation approach for investment returns with either a
deterministic or analytical approach for mortality experience
provided the loss of accuracy
is sufficiently small.
3.1.4. Examples of valuation techniques
3.20. Examples of simulation techniques:
•
Monte-Carlo simulations:
the value of the liabilities is calculated in a large number of
scenarios where one or more assumptions are changed in each
scenario.
By simulating the behaviour of the random variable(s) in a very
large number of scenarios, the model produces a distribution
of possible outcomes.
The mean of the distribution of scenarios may be considered a
“probability weighted average”.
• For example, the nature of the financial options and guarantees
embedded in some life (re)insurance contracts, particularly those
with profit sharing features, is such that a set of deterministic
best estimate assumptions
may not be sufficient to produce a
best estimate liability.
The application of
closed form analytical solutions
to value the options and guarantees may also be limited, if it is
difficult to find market hedges that replicate the cash-flows under
the contract, for example to reflect the use of management actions
or the effects of path dependency.
A deterministic or an analytical technique may therefore not be
suitable for valuing such contracts, and a simulation technique
may be needed.
• Stochastic variation in non-market
assumptions such as lapses and option take-up rates can have
significant influence on options and guarantees.
One possible approach used is to assume that they are 100%
correlated with interest rates/market value which allows the
insurer to include the relationship within the liability models
without an additional stochastic variable.
• Bootstrapping: one of the most extended uses
of bootstrap within actuarial work is associated with estimation of
claims provisions.
Starting from a model that explains how losses are paid, it consists
of resampling residuals from that model and obtaining a large sample
of estimated provisions required to pay future outstanding losses.
• Simulating losses above a certain threshold and up to a certain
limit is also a frequently used technique by (re)insurers to
calculate an estimated expected loss in respect of a given excess of
loss programme.
3.21. Examples of analytical techniques:
• Stochastic variation in non-market assumptions (such as mortality)
• The time value of options and guarantees may be captured by
reference to the market costs of hedging the option or guarantee; if
the market price is not directly observable, it may be approximated
using option pricing techniques, for example closed form solutions
such as the Black-Scholes formula.
• The Mack method, also known as the distribution free chain ladder.
• Bayesian approaches, where one combines expert knowledge or
existing prior information with observations resulting in an
estimate for the ultimate claim.
3.22. Examples of deterministic techniques:
•
Stress and scenario testing;
for example, adjusting data for inflation and allowing inflation to
vary, thus producing sensitivities around this parameter.
• Influential observations or outliers have been allowed for
appropriately, for example via case by case reserving.
• Systematic as well as other random features are being captured
through sensitivity testing, diagnostics or other techniques (this
could be stochastic).
• Where a calculation relies on assumptions of an even spread of
risk over the policy year and this is not the case (e.g. seasonality
such as due to weather or hurricane season) the proportions shall be
adjusted.
• The use of relevant assumptions or other external/portfolio
specific data as an input to the calculation when there is lack of
data or as a benchmark for comparison..
• Applying different techniques and allowing for any volatility
within the results.
• Embedded options may be captured by considering different
scenarios chosen to capture, as far as possible, the full range of
future scenarios.
An appropriate average or worst-case technique could be used to
derive an initial estimate of the value of options embedded in the
life insurance portfolio.
A deterministic-to-stochastic adjustment could then be applied. This
adjustment may be derived from any standardised method including
flat benchmarked percentages.
3.2 CEIOPS’ advice
3.23. The Level 1 text states that the
best estimate
shall equal to the probability weighted average of future cash-flows
taking account of the time value of money, using the relevant
risk-free interest rate term structure.
This in effect acknowledges that the
best estimate calculation
shall allow for the uncertainty in the future cash-flows.
3.24. (Re)insurance undertakings shall reflect all future cash-flows
making due allowance for the sources of uncertainty within their
cash-flow projection used to calculate the
best estimate.
In particular, the causes of uncertainty in the cash-flows that
shall be identified and taken into account may include the
following:
• Fluctuations in the timing, frequency and
severity of claim events.
• Fluctuations in the period needed to settle claims.
• Fluctuations in the amount of expenses.
• Changes in the value of an index/market value used to determine
claim amounts.
• Changes in both portfolio and entity specific factors, such as
legal, social, or economic environmental factors.
• Uncertainty in policyholder behaviour.
• The exercise of discretion by the (re)insurance undertaking (which
may depend on the above-mentioned causes of uncertainty and also on
entity specific factors).
• Path-dependency – where the cash-flows depend not only on economic
conditions on the cash-flow date, but also on economic conditions at
previous dates.
• Interdependency between two or more causes of uncertainty.
3.25. The responsibility for the choice of
adequate techniques for the calculation of the
best estimate liability
rests with the (re)insurance undertaking
subject to the requirements set out in the Level 1 text as well as
those
requirements set out in paragraph 3.23 below.
3.26. The valuation technique chosen shall
meet the following requirements:
• The (re)insurance undertaking will be required to demonstrate the
appropriateness and robustness of the techniques, having regard to
the nature, scale and complexity of risks (principle of
proportionality).
• The (re)insurance undertaking shall be able to demonstrate that
the valuation technique and the underlying assumptions are realistic
and reflect the uncertain nature of the cash-flows.
• The valuation technique shall be chosen on the basis of the nature
of the liability being valued and from the identification of risks
which materially affect the underlying cash-flows.
• The assumptions underlying the valuation technique shall be
validated and reviewed by the (re)insurance undertaking.
• The valuation technique and its results shall be capable of being
audited.
• If policy data is grouped, the (re)insurance undertaking shall
demonstrate that the grouping process appropriately allows for the
risk characteristics of the individual policies.
• (Re)insurance undertakings shall ensure that their capabilities
(e.g. actuarial expertise, IT systems) are commensurate with the
actuarial and statistical methodologies that are required to be
used.
• The (re)insurance undertaking shall demonstrate that the
assumptions and techniques used are consistent with the nature,
scale and complexity of the risks.
3.27. Valuation techniques considered to be appropriate actuarial
and statistical methodologies to
calculate the best estimate
as required by Article 85(a) includes: simulation, deterministic and
analytical techniques or a combination thereof.
3.28. A simulation approach would normally be required for valuing
cash-flows where one or more of the following factors have a
material impact on the value of the liability:
• The cash-flows are highly path dependent.
• There are significant non-linear inter-dependencies between
several drivers of uncertainty.
• Risks have a significant asymmetric impact on the value of the
liabilities e.g. if contracts include material embedded options and
guarantees or if there are complex reinsurance contracts in place.
• The liability cash-flows are materially affected by the potential
future management actions.
• The value of liability cash-flows is materially affected by the
policyholder behaviour assumed in the model.
3.29. (Re)insurance undertakings may apply other appropriate
valuation techniques (e.g. a range of deterministic scenarios with
suitable adjustments) provided that the undertaking can demonstrate
that the above factors are adequately taken into account.
3.30. The supervisor shall be able to require an alternative
technique where that other valuation technique achieves the
objectives of the valuation (prudent, reliable and objective) in a
better way
CEIOPS’’
Advice for Level 2 Implementing Measures on Solvency II:
Technical
provisions -
Elements of actuarial and statistical methodologies for
the calculation of the best estimate
Consultation Paper No. 26.
Draft CEIOPS Advice for
Level 2 Implementing Measures on Solvency II:
Technical provisions - Elements of actuarial and statistical
methodologies for the calculation of the best estimate
Solvency
ii Best Estimate - CEIOPS Consultation Paper No.
26
Consultation Paper No. 41.
Draft CEIOPS’
Advice for Level 2 Implementing Measures on Solvency II:
Technical
Provisions - Article 85 c, Circumstances in which technical
provisions shall be calculated as a whole
CEIOPS Consultation Paper No. 41 - Level 2, Circumstances in which
technical provisions shall be calculated as a whole
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