Solvency Assessment and Management:
Steering Committee
Position Paper 481 (v 4)
SCR Standard Formula - Correlations
EXECUTIVE SUMMARY
Solvency Assessment and Management (“SAM”) is a fundamental review of the solvency
regime for South African (re)insurers, planned to take effect from January 2016. It aims to
establish a revised set of capital requirements, disclosure and risk management standards, and
valuation techniques that will replace or enhance most of the current legislative requirements
contained in the Long-term Insurance Act (No. 52 of 1998) and the Short-term Insurance Act
(No. 53 of 1998). The new regime is expected to apply to all insurance firms and represents a
shift towards risk-based regulation for (re)insurers.
In this paper, the approach to risk aggregation under Solvency II is compared with international
standards and guidance, as well as to the existing regulatory approaches in other jurisdictions.
For non-life and life insurance the recommendation is to adopt the approach to risk aggregation
as set out in the Solvency II directive. The current life and non-life insurance regulation does
make some allowance for diversification of risk but will change to reflect the Solvency II
approach.
1. INTRODUCTION AND PURPOSE
The regulatory approach to risk aggregation can allow insurers to take advantage of
diversification effects present between different risks. Allowance for diversification in the risk
aggregation method produces a lower overall solvency capital requirement (SCR). This
document presents the approach to risk aggregation under Solvency II and selected other
regulatory regimes in order to inform the development of forthcoming South African
legislation and regulation such that they are consistent with international standards. In
particular, since the SAM project aims to produce a regulatory environment that will qualify
for Solvency II 3rd country equivalence, this paper spends more time considering the
Solvency II approach to risk aggregation than approaches of other regulatory regimes.
2. INTERNATIONAL STANDARDS: IAIS ICPs
Since its inception in 1994, the IAIS has developed a number of principles and standards in
guidance papers to help promote the global development of well-regulated insurance
markets. A further objective of the IAIS is to contribute to broader stability of the financial
system.
The IAIS is currently revising the ICPs with corresponding standards and guidance material
to be ready for adoption at the October 2011 General Meeting. ICP 17 Capital Adequacy,
standards and guidance material (from October 2010, to be included in the full set of ICPs
1
Position Paper 48 (v 4) was approved as a FINAL Position Paper by Steering Committee on 5 December 2014.
Solvency Assessment and Management: Steering Committee
Position Paper 48 (v 4) – SCR Standard Formula - Correlations
adopted in 2011) contains the following principles which inform the approach to the role of
risk aggregation in determining solvency capital:
o
17.1: The solvency regime requires that a total balance sheet approach is used in the
assessment of solvency to recognise the interdependence between assets, liabilities,
regulatory capital requirements and capital resources and to ensure that risks are
appropriately recognised.
o
17.7.2: The assessment of the overall risk that an insurer is exposed to should
address the dependencies and interrelationships between risk categories (for
example, between underwriting risk and market risk) as well as within a risk category
(for example, between equity risk and interest rate risk). This should include an
assessment of potential reinforcing effects between different risk types as well as
potential “second order effects”, i.e. indirect effects to an insurer’s exposure caused
by an adverse event or a change in economic or financial markets conditions. It
should also consider that dependencies between different risks may vary as general
market conditions change, and may significantly increase during periods of stress or
when extreme events occur. "Wrong way risk", which is defined as the risk that
occurs when exposure to counterparties, such as financial guarantors, is adversely
correlated to the credit quality of those counterparties should also be considered as a
potential source of significant loss e.g. in connection with derivative transactions.
Where the determination of an overall capital requirement takes into account
diversification effects between different risk types, the insurer should be able to
explain the allowance for these effects and ensure that it considers how
dependencies may increase under stressed circumstances.
3. EU DIRECTIVE ON SOLVENCY II: PRINCIPLES (LEVEL 1)
The Solvency II Directive contains the following article pertaining to correlations which
should be considered for input for SAM primary legislation:
Article 101: “Calculation of the Solvency Capital Requirement”
o
101.3: The Solvency Capital Requirement shall be calibrated so as to ensure that all
quantifiable risks to which an insurance or reinsurance undertaking is exposed are
taken into account. It shall cover existing business, as well as the new business
expected to be written over the following 12 months. With respect to existing
business, it shall cover only unexpected losses.
It shall correspond to the Value-at-Risk of the basic own funds of an insurance or
reinsurance undertaking subject to a confidence level of 99,5 % over a one-year
period.
Article 104: “Design of the Basic Solvency Capital Requirement”
o
104.1: The Basic Solvency Capital Requirement shall comprise individual risk
modules, which are aggregated in accordance with point (1) of Annex IV. It shall
consist of at least the following risk modules:
(a) non-life underwriting risk;
(b) life underwriting risk;
(c) health underwriting risk;
(d) market risk;
(e) counterparty default risk.
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o
104.2: For the purposes of points (a), (b) and (c) of paragraph 1, insurance or
reinsurance operations shall be allocated to the underwriting risk module that best
reflects the technical nature of the underlying risks.
o
104.3: The correlation coefficients for the aggregation of the risk modules referred to
in paragraph 1, as well as the calibration of the capital requirements for each risk
module, shall result in an overall Solvency Capital Requirement which complies with
the principles set out in Article 101.
o
104.4: Each of the risk modules referred to in paragraph 1 shall be calibrated using a
Value-at-Risk measure, with a 99,5 % confidence level, over a one-year period.
Where appropriate, diversification effects shall be taken into account in the design of
each risk module.
o
104.5: The same design and specifications for the risk modules shall be used for all
insurance and reinsurance undertakings, both with respect to the Basic Solvency
Capital Requirement and to any simplified calculations as laid down in Article 109.
o
104.6: With regard to risks arising from catastrophes, geographical specifications
may, where appropriate, be used for the calculation of the life, non-life and health
underwriting risk modules.
o
104.7: Subject to approval by the supervisory authorities, insurance and reinsurance
undertakings may, within the design of the standard formula, replace a subset of its
parameters by parameters specific to the undertaking concerned when calculating
the life, non-life and health underwriting risk modules. Such parameters shall be
calibrated on the basis of the internal data of the undertaking concerned, or of data
which is directly relevant for the operations of that undertaking using standardised
methods. When granting supervisory approval, supervisory authorities shall verify the
completeness, accuracy and appropriateness of the data used.
Article 111: “Implementing Measures”
o
111.1: 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 providing for the following:
(d) the correlation parameters, including, if necessary, those set out in Annex IV, and
the procedures for the updating of those parameters;
ANNEX IV of the Directive: Solvency Capital Requirement (SCR) standard formula
1. Calculation of the Basic Solvency Capital Requirement
The Basic Solvency Capital Requirement set out in Article 104(1) shall be equal to
the following:
Basic SCR = √∑
where
denotes the risk module and
denotes the risk module , and where
" " means that the sum of the different terms should cover all possible
combinations of and j. In the calculation,
and
are replaced by the
following:
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-
SCR non-life denotes the non-life underwriting risk module;
SCR life denotes the life underwriting risk module;
SCR health denotes the health underwriting risk module;
SCR market denotes the market risk module;
SCR default denotes the counterparty default risk module.
The factor
denotes the correlation between the item in row i and column j of
the correlation matrix.
2. Calculation of the non-life underwriting risk module
The non-life underwriting risk module set out in Article 105(2) shall be equal to the
following:
SCR non-life = √∑
where SCRi denotes the sub-module i and SCRj denotes the sub-module j, and
where "i,j" means that the sum of the different terms should cover all possible
combinations of i and j. In the calculation, SCRi and SCRj are replaced by the
following:
- SCR nl premium and reserve denotes the non-life premium and reserve risk
sub-module;
- SCR nl catastrophe denotes the non-life catastrophe risk sub-module.
- SCR nl lapse denotes the non-life lapse risk
3. Calculation of the life underwriting risk module
The life underwriting risk module set out in Article 105(3) shall be equal to the
following:
SCR life = √∑
where SCRi denotes the sub-module i and SCRj denotes the sub-module j, and
where "i,j" means that the sum of the different terms should cover all possible
combinations of i and j. In the calculation, SCRi and SCRj are replaced by the
following:
-
SCR mortality denotes the mortality risk sub-module;
SCR longevity denotes the longevity risk sub-module;
SCR disability denotes the disability - morbidity risk sub-module;
SCR life expense denotes the life expense risk sub-module;
SCR revision denotes the revision risk sub-module;
SCR lapse denotes the lapse risk sub-module;
SCR life catastrophe denotes the life catastrophe risk sub-module.
4. Calculation of the market risk module
The market risk module, set out in Article 105(5) shall be equal to the following:
SCR market= √∑
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where SCRi denotes the sub-module i and SCRj denotes the sub-module j, and
where "i,j" means that the sum of the different terms should cover all possible
combinations of i and j. In the calculation, SCRi and SCRj are replaced by the
following:
-
SCR interest rate denotes the interest rate risk sub-module;
SCR equity denotes the equity risk sub-module;
SCR property denotes the property risk sub-module;
SCR spread denotes the spread risk sub-module;
SCR concentration denotes the market risk concentrations sub-module;
SCR currency denotes the currency risk sub-module.
Based on these texts, the basis for the allowance for correlation between risk sub-modules
within the underwriting risk and other risk modules is proposed on an aggregate risk basis
through the summation formulae. Specific correlation between different classes of
underwriting risk through frequency or severity correlation is not precluded but is not
specifically addressed either.
Allowance for correlation using the proposed formulae above complicates allowances for “tail
correlations” or specified event correlations as well as varying levels of correlations
dependent on specific outcomes. However, with the provision for parameter substitution, this
shortcoming could possibly be addressed, although such allowances would need to be made
on a lower level than at the point of aggregation as suggested by the formulae.
In order to reach the overall SCR from the Basic SCR (BSCR), undertakings need to add the
operational risk SCR to the BSCR. Adding operational risk in this way, after using correlation
matrices to aggregate the other risks, implies no diversification benefit between operational
risk and all other risks. This is consistent with the existing approach to aggregation of
operational risk and all other risks for long-term insurers in South Africa.
4. MAPPING ANY PRINCIPLE (LEVEL 1) DIFFERENCES BETWEEN IAIS ICP & EU
DIRECTIVE
There are no apparent contradictions; both bodies advocate a total balance sheet approach
that takes into account the dependence structure of the various risk components. As ICP 17
is a principle-based standard rather than a technical specification, Solvency II is far more
specific in terms of the specifying the use of correlations to aggregate SCR risk modules and
risk sub-modules.
5. STANDARDS AND GUIDANCE (LEVELS 2 & 3)
5.1
IAIS standards and guidance papers
In the IAIS Standard on the Structure of Regulatory Capital Requirements the following
standard is relevant for consideration on the topic of correlations:
1: A total balance sheet approach should be used in the assessment of solvency to
recognise the interdependence between assets, liabilities, regulatory capital
requirements and capital resources and to ensure that risks are appropriately
recognised.
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The IAIS Stress Testing By Insurers Guidance Paper adds the following detail, which is
considered useful input to the task of determining correlations:
o
63: The correlation and the interdependency among risks should be regularly
evaluated. While the frequency of such evaluation should normally be fixed in
advance, it may need to be done more frequently in times of crisis.
o
64: The correlation analyses are required to ensure that the interrelationship of risks
is taken into account. For example, if an insurer was affected by a major catastrophe,
other parties on which it is dependent may also have been affected, such as:
- reinsurers on which the insurer is reliant to meet claims
- intermediaries who generate future business
- other service providers, who may be unable to meet their contractual
obligations or provide a full service
- counterparties in the capital markets (e.g. after the 11 September 2001
terrorist attack)
o
66: Determining the extent of dependencies that exist can be complex. A degree of
prudence and pragmatism will be required when making judgment. This is particularly
the case when determining tail-dependencies.
o
67: An example of tail-dependency would be where there are two risks that are
usually uncorrelated, but where an extreme event for one risk may lead to greater
loss from the other risk than would ordinarily have occurred. For example, a major
catastrophe may coincide with a stock market collapse. The effects of the latter may
be greater than expected due to investor nervousness. The 11 September 2001
terrorist attack is an example of this, since ordinarily an airline catastrophe would not
accentuate a stock market decline.
Attention is paid to the potential shortcomings and suitable approaches to allow for nonlinear correlation on an aggregated basis. However, no specific format is described. The use
of stress testing is also recommended, although data availability may reduce the direct
usefulness of such tests in practice.
5.2
EIOPA Solvency II Final Level 2 Advice and Quantitative Impact Studies
For the purpose of clarity: the European Insurance and Occupational Pensions Authority
(EIOPA) is a European Union financial regulatory institution that replaced the Committee of
European Insurance and Occupational Pensions Supervisors (CEIOPS) on 1 January 2011.
Due to the fact that the current Solvency II Final Level 2 Advice documents were produced in
2010 by CEIOPS, before it was replaced by EIOPA, the documents still bear the CEIOPS
name and refer to the regulatory authority as CEIOPS.
In the document CEIOPS–DOC–08/07 (“Further advice to the European Commission on
Pillar 1 issues”) published in March 2007 it is stated that the use of correlation matrices is
“recommended for the aggregation of capital requirements”. The following considerations
were also provided regarding the choice of correlation parameters:
- to keep note of any dependencies that would not be addressed properly by this
treatment;
- to choose the correlation coefficients to adequately reflect potential dependencies in
the tail of the distributions;
- to assess the stability of any correlation assumptions under stress conditions.
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Level 2 advice document CEIOPS-DOC-70/10 (“Advice for Level 2 Implementing Measures
on Solvency II: SCR Standard Formula, Article 111(d) Correlations”, formerly Consultation
Paper No. 74) provides further background regarding use of the correlation matrix approach,
specifically for sub-divisions of modules specified in the Solvency II Directive:
o
3.4: According to Articles 104(1) and 105 of the Level 1 text, the aggregation of the
capital requirements for the sub-risks of at least the following parts of the standard
formula are done by means of correlation matrices:
- the Basic SCR,
- the capital requirement for non-life underwriting risk,
- the capital requirement for life underwriting risk, and
- the capital requirement for market risk.
o
3.5: Moreover, the Level 1 text does not specify the aggregation method for certain
other parts of the standard formula, for example for the health underwriting module or
regarding any further subdivision of sub-modules for the above mentioned modules.
Correlation matrices could also be used for these aggregation tasks.
o
3.6: The selection of the correlation parameters has a significant influence on the
result of the SCR calculation. For example, if five capital requirements of equal size
are aggregated, the result is 55% lower if the correlation parameter 0 instead of the
parameter 1 is used to describe the relation between each pair of risks. Hence, the
choice of correlation parameters has an impact on the level of diversification to be
obtained within the SCR standard formula.
The document CEIOPS-SEC-40/10 (“Solvency II Calibration Paper”), published for use in
QIS 5, provides mathematical background for the correlation matrix approach and also
highlights the limitations of the approach:
o
3.1244: In the mathematical science, correlation matrices are used to aggregate
standard deviations of probability distributions or random variables. In this case, the
entries of the matrix are defined as linear correlation coefficients, i.e. for two random
variables X and Y, the entry is:
ov
√ ar
ar
o
3.1245: The capital requirements that are aggregated in the standard formula are,
from a mathematical point of view, not standard deviations but quantiles of probability
distributions. However, this does not imply that it is an abuse of the concept of
correlation matrices to apply it in the context of the standard formula. This is because
it can be shown that for multivariate normal distributions (or more general: for elliptic
distributions), the aggregation with correlation matrices produces a correct aggregate
of quantiles.
o
3.1246: On the other hand, only for a restricted class of distributions the aggregation
with linear correlation coefficients produces the correct result. In the mathematical
literature a number of examples can be found where linear correlations in themselves
are insufficient to fully reflect the dependence between distributions and where the
use of linear correlations could lead to incorrect aggregation results, i.e. to either an
under- or an over-estimation of the capital requirements at the aggregated level.
o
3.1247: Two main reasons can be identified for this aggregation problem:
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-
The dependence between the distributions is not linear; for example there are
tail dependencies.
The shape of the marginal distributions is significantly different from the
normal distribution; for example the distributions are skewed.
o
3.1248: Unfortunately, both characteristics are shared by many risks which an
insurance or reinsurance undertaking is exposed to. Tail dependence exists both in
underwriting risks (e.g. catastrophe events) and in market and credit risks. The
current financial crisis is a good example of this. Market parameters (like credit
spreads, property prices and equity prices) which have revealed no strong
dependence under benign economic conditions simultaneously showed strong
adverse changes in the last two years. Moreover, it became apparent that a change
in one parameter had a reinforcing effect on the deterioration of the other
parameters.
o
3.1249: As to the second characteristic, it is known of the relevant risks of an
insurance or reinsurance undertaking that the underlying distributions are not normal.
They are usually skewed and some of them are truncated by reinsurance or hedging.
o
3.1250: Because of these shortfalls of the correlation technique and the relevance of
the shortfalls to the risks covered in the standard formula, the choice of the
correlation factors should attempt to avoid misestimating the aggregate risk. In
particular, linear correlations are in many cases not an appropriate choice for the
correlation parameter.
o
3.1251: Instead, the correlation parameters should be chosen in such a way as to
achieve the best approximation of the 99.5% VaR for the aggregated capital
requirement. In mathematical terms, this approach can be described as follows: for
two risks X and Y with E(X)=E(Y)=0, the correlation parameter ρ should minimise the
aggregation error
a
o
a
a
a
a
3.1252: This approach is a consequence of Article 104 of the Level 1 text. According
to paragraph 3 of Article 104,
“the correlation coefficients for the aggregation of the risk modules
referred to in paragraph 1, as well as the calibration of the capital
requirements for each risk module, shall result in an overall Solvency
Capital Requirement which complies with the principles set out in
Article 101.”
Article 101 stipulates that the SCR corresponds to the Value-at-Risk with a
confidence level of 99.5%.
o
3.1253: CEIOPS acknowledges that achieving this overall conceptual aim is likely to
present a number of practical challenges:
-
In most cases the standard formula does not set out explicit assumptions on
the type or shape of the risk distributions of X and Y, nor on the dependence
structure between X and Y. In these cases the risk distribution of the
aggregated risk X + Y will not generally be known, so that its Value-of-Risk
cannot be estimated or observed directly;
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-
-
In the scenario-based sub-modules, the standard formula prescribes shocks
to the underlying risk drivers of the sub-risk considered. The risk variables X
and Y – representing the change of the level of own funds of the insurer
resulting from a change of the underlying risk driver – then also depend on
the risk characteristics of the insurer’s individual portfolios. Hence in these
cases the relationship between the Value at Risk for the aggregated risk X+Y
in respect to the Value at Risk for the individual risks X and Y would likely be
different across different insurers: and
Where more than two risks are aggregated, the minimisation of the
aggregation error has to go beyond only considering individual pairs of risks.
o
3.1254: As was observed in the above, where it can be assumed that the considered
risks follow a multivariate normal (or elliptical) distribution, minimising the aggregation
error can be achieved by calibrating the correlation parameters in the standard
formula as linear correlations. Hence in this special case, the challenges described
above could be met in case linear correlation coefficients can be reliably derived.
o
3.1255: However, where such a simplifying assumption cannot be made - for
example, where there is tail-dependency between the risks or where the shape of the
marginal risk distributions is significantly different from the normal distribution - the
use of linear correlations may not be adequate for the purpose of minimising the
aggregation error. In these cases, it may be necessary to consider other dependence
concepts for deriving the correlation parameters in the standard formula.
o
3.1256: For example, in this case it may be more adequate to derive the standard
formula correlation parameter for two risks X and Y as the coefficient of (upper) tail
dependence of X and Y, which is defined as:
|
where FX and FY are the distribution functions of X and Y, respectively. Note that this
coefficient measures the asymptotic degree of dependence in the “tail” of the risk
distributions of X and Y, i.e. the likelihood of simultaneous occurrences of extreme
events in both risks.
This section attempts to address the area of tail correlations as a sub-set of non-linear
correlations. The VaR method attempts to create a correlation matrix calibrated to the
correlations effectively expected in the tails of the distributions. However, significant lack of
data in extreme observations as well as the added complexity, along with loss of
correspondence throughout the remainder of the distributions may create a difficult
environment in which to execute such an approach directly.
The next section of the document considers the calibration of correlation parameters
between risks which are thought to be independent. It is noted that for aggregations of nonnormally distributed risks, risks where the distribution is not known or risks where the
distribution is altered in a company-specific way by reinsurance or hedging, the assumption
of a zero correlation can misestimate the aggregated variance. A mathematical example is
provided and then the section concludes by stating:
o
3.1263: Hence where a standard formula correlation parameter has to be specified
between two risks which can be assumed to be independent but such uncertainties
exist, it appears to be acceptable to choose a low correlation parameter, reflecting
that model risk may lead to an over- or under-estimation of the combined risk.
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The document then proceeds to consider the approach for calibration of the correlations for
each sub-module, starting with market risk. Due to industry concerns about a lack of
empirical justification for the correlation coefficients suggested in the draft advice, the
Solvency II Calibration Paper mentions that CEIOPS (as the authority was still known at the
time) undertook another statistical analysis. This analysis aimed to:
- determine the overall level of diversification implied by the correlation matrix
proposed, and to assess its appropriateness; and
- statistically assess the correlation between individual pairs of risks in the market risk
module using historical data.
The following detail on the analysis is provided:
o
3.1273: To test the overall appropriateness of the correlation matrix proposed in its
draft advice, CEIOPS has carried out a statistical “top down” modelling analysis to
assess whether the overall diversification benefit implied by the matrix is consistent
with the 1:200 year confidence level targeted for the determination of the capital
charge for market risk as a whole.
o
3.1274: The diversification benefit implied by the matrix can be measured as
∑
where SCRmkt denotes the capital charge for market risk, Mktr denote the capital
charges for the individual market risks, and where
√∑
is derived from the capital charges for the individual sub-risks by using the proposed
correlation matrix CorrMktr,c.
o
3.1275: This diversification benefit as implied by the aggregation matrix is consistent
with the targeted confidence level of 99.5% for market risk if it coincides with the risktheoretic diversification benefit which is given as
∑
where VaRmkt denotes the Value-at-Risk 99.5% capital charge for market risk as a
whole and VaRr denotes the Value-at-Risk capital charges for the individual sub-risks
of market risk.
o
3.1276: Assuming that the calculation of the capital charges Mktr of the individual
sub-risks are commensurate with the 99.5% Value-at-Risk confidence level, it follows
that the diversification benefit implied by the matrix is consistent with the 99.5%
confidence level if the capital charge SCRmkt derived from aggregating the individual
charges with the correlation matrix coincides with the risk-theoretic 99.5% Value-atRisk capital charge VaRmkt for market risk as whole, i.e. if the aggregation error
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|
√∑
|
is zero.
The market risk correlation matrix is then calibrated by considering the correlations of each
pair of components, and using judgment to decide on a value of low, medium or high.
Further detail on the model used to empirically validate the calibration of the market risk
correlation matrix provided in the appendix running from section 3.1335 to section 3.1407 of
CEIOPS-SEC-40-10. As a result of this empirical investigation, the correlation matrix
proposed was found to be consistent with a 1-in-200 VaR level.
Following this, the paper discusses difficulties in empirically deriving correlations for the subcomponents of life underwriting risk and health underwriting risk due to lack of data. The
paper also states that until further data is available, it is difficult to calibrate the correlation
matrix of the sub-components of non-life underwriting risk. The correlations for these
underwriting risk components are thus based on expert judgment for the time being.
5.3
QIS 5 Report
The document EIOPA-TFQIS5-11/001 (The EIOPA Final Report on the fifth Quantitative
Impact Study (QIS5) for Solvency II) published by EIOPA on 14 March 2011 adds the
following on the topic of risk aggregation:
o
5.4: SCR Aggregation and operational risk
The aggregation methodology was generally well received, with no major or
widespread complaints. A minority of undertakings were concerned that the
correlation matrix approach would not adequately capture the effects of non-linearity
and tail dependence. It was noted by supervisors that though there are a number of
limitations to the SCR aggregation approach (see CP74), they still feel it appropriate
for the purposes of the standard formula, and that its calibration is fitting for a 99.5
VaR measure.
A few undertakings commented that the “tiered” aggregation structure was
inappropriate. For example, the method is unable to accurately reflect the interactions
between sub-modules belonging to separate risk modules (the method implicitly
assumes the same correlation between equity and lapse as between equity and
mortality), although again supervisors considered the application as it stands
adequate. A minority of undertakings complained about the two-sided correlation
matrix for market risk (for interest rate risk) since there would be increased
complexity due to additional volatility of results over time. Only a few individual
undertakings which provided internal model input made comments on parameters
used in their correlation matrixes.
5.4
The Australian Prudential Regulation Authority (APRA)
In Australia, as per the AP A‟s Prudential Standard GPS 101, insurers are required to
determine their capital either by using a prescribed method or by using an internal model
that adheres to the guidance. The standard model includes the following risk modules:
- Insurance risk – sum of outstanding-claims risk and premium-liability risk.
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- Investment risk – including market (or mismatch) risk, liquidity risk and credit risk.
- Concentration risk.
For investment risk, capital charges are determined using capital factors for different asset
classes, and the investment risk capital requirement is the sum of the capital charges for all
classes. Concentration risk is calculated as the addition of the insurer‟s Maximum Event
Retention (MER) after taking into account acceptable reinsurance arrangements, plus the
cost of one reinstatement of those reinsurance arrangements.
The MCR is then calculated as the sum of the insurance risk, investment risk and
concentration risk capital requirements.
5.5
The Office of the Superintendant of Financial Institutions (OSFI) - Canada
Life insurance companies in Canada are subject to the capital requirements contained in the
OSFI‟s Minimum Continuing Capital and Surplus Requirements (MCCSR) guideline of
December 2009. Non-life insurers (referred to as property and casualty insurers in the
regulation) are subject to the requirements of the Minimum Capital Test (MCT) guideline of
March 2008. The MCT is a factor-based requirement, which aggregates risks additively. It
does not allow for explicit measurements of, or assumptions about, diversification of risks.
The MCCSR, in comparison, allows for diversification of risks in some areas.
The MCCSR specifies capital requirements for the following five risk categories:
-
asset-default risk;
mortality, morbidity and lapse risks;
changes in interest rate environment risk;
segregated funds risk (risk of loss arising from guarantees embedded in segregated
funds); and
- foreign exchange risk.
There is allowance for diversification of risk within mortality risk, morbidity risk and
segregated funds risk components. There is, however, no allowance for diversification of risk
over the risk components. As such, the MCCSR is the sum of the capital requirements for
each of the risk components.
5.6
Federal Office of Private Insurance (FOPI) - Switzerland
The capital requirement for all insurers in Switzerland is determined via the Swiss Solvency
Test (SST), which was published in 2008 by the FOPI. The regulation includes a standard
model as well as principles for the development of internal models. Within the standard
model the following risks modules are included:
-
market risk,
credit risk (counterparty default),
non-life insurance risk,
life insurance risk, and
health insurance risk.
Operational risk is not included in the current SST. To aggregate risks under the SST, life
companies use a correlation matrix approach which allows for diversification benefits
between modules. For non-life business, undertakings make use of a distribution-based
approach using copulas, as well as performing FPOI-prescribed scenario analyses. The
results of both approaches are then aggregated to determine the capital requirement.
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5.7
Mapping of differences between above approaches (Level 2 and 3)
There is no contradiction between EIOPA and IAIS guidance. The EIOPA Level 2
documentation is more specific about the methods that should be used to aggregate subcomponents of each risk category and provides formulae. IAIS Level 2 documentation
provides guidance on how and when insurers/regulators should apply stress testing to check
their models, but gives little advice on the specification of the models or the correlation
structures.
Both the Australian and Canadian approaches offer little in the way of inter-risk aggregation
benefits, although the Canadian approach does offer some intra-risk diversification benefits.
The Swiss regulation allows for risk aggregation benefits in a similar way to Solvency II for
life insurers, i.e. use of correlation matrices, and allows a distribution-based approach for
non-life risks.
6. ASSESSMENT OF AVAILABLE APPROACHES GIVEN THE SOUTH AFRICAN
CONTEXT
6.1
Discussion of inherent advantages and disadvantages of each approach
The correlation approach is specified for many components of the Solvency II standard
model, i.e. the Basic SCR, the capital requirement for non-life underwriting risk, the capital
requirement for life underwriting risk, and the capital requirement for market risk. It is also
suggested that this approach can be used for all other parts of the standard formula. The
correlation approach is used to aggregate the risk sub-modules of all risk modules in the
QIS5 model, and also for aggregating the risk modules to quantify the Basic SCR.
The issues of data insufficiency which exist in the European context are likely to be
comparable (or worse) in South Africa. It might be difficult (or impossible) to justify choices of
correlations empirically. This is further exacerbated when non-linear correlations are
considered; something that not even stress-testing might be able to compensate for.
Application of correlation to aggregate amounts is supported not only by the amount of
available data, but also the likely format of the data available for the calibration.
Despite the difficulty of calibrating the matrices, the correlation matrix approach is far simpler
to implement than the use of copulas. The calibration based on the tail correlations would
also be more difficult to implement due to the potential lack of credible data in a suitable
format. A copula approach is likely to have the same difficulties in calibration, along with
added complexity, potentially resulting in less reliable and more volatile results.
As mentioned above, linear correlations only produce the correct dependence structure
when marginal distributions are elliptical. For skewed or truncated distributions it is worth
considering the use of tail correlations in the matrices as these reflect the dependence
behaviour during periods that correspond to 1-in-200 VaR shocks. The use of copulas would
allow more accurate modelling of the dependency structure on the case of skewed or
truncated distributions and where tail dependencies exist, but the complexity of
parameterisation of the copulas could be significantly more difficult and prone to estimation
error than the use of correlation matrices.
From a proportionality point of view correlation matrices are thus the most suitable approach
as the implementation is far simpler than more complex alternatives to model non-linear
correlations.
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EU and IAIS documentation both recommend the use of stress testing to check the suitability
of correlation matrices under those conditions. Although the format of stress-testing is not
described, pragmatic approaches could give a sensible indication of the impact.
While the use of correlation matrices is not a perfect solution, it seems unlikely that South
Africa could hope to implement a more technically intensive correlation structure in its
standard model if this approach is considered unfeasible in the EU. However, the possibility
of reviewing this approach at a future stage should not be excluded.
6.2
Impact of the approaches on EU 3rd country equivalence
There is no evidence that the adoption of a correlation matrices would impact 3rd country
equivalence, since Solvency II itself is using and suggests the same approach.
6.3
Comparison of the approaches with the prevailing legislative framework
Current South African life insurance regulation aggregates the capital requirements arising
from various risks using a square-root of sum-of-squares. A correlation of zero is thus
implied between most components, with the exception of: market risk and credit risk; and
operational risk with all other risks. Operational risk is implied to possess no diversification
benefit at all. This approach bears some resemblance to the Solvency II approach,
especially in the treatment of operational risk.
Short-term insurance regulation in South Africa is currently not risk-driven and as such
makes no allowance for risk aggregation.
6.4
Conclusions on preferred approach
The preferred approach is that of correlation matrices. This approach is specified for many
component of the Solvency II standard model and it is also suggested that the approach can
be used for all other parts of the standard formula.
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7. RECOMMENDATION
7.1 Methodology
The recommendation is to adopt the correlation matrix approach to define the
dependency structure for all risk modules and sub-modules of the standard SCR
model because:
- This approach is consistent with IAIS standards and guidance, Solvency II Level 1
and Level 2 text, and QIS 5 approach.
- EU 3rd country equivalence would not be impacted.
- The approach does not unfairly burden smaller insurers with overly complex technical
requirements, i.e. it meets the criteria of proportionality.
- Tail dependencies can be used for skew/truncated distributions or other cases when
the correlation relationship is poorly described by linear correlation.
- This is a less technically demanding approach compared to more complex methods
such as the use of copulas. The calibration of the matrices would be the responsibility
of the SAM Capital Requirements Task Group, via quantitative impact studies. The
Risk Aggregation Working Group will calibrate the correlations between risk modules,
i.e. between the non-life, life, health, market and counterparty default risk modules.
The correlations within the individual risk modules will be calibrated by the relevant
Working Groups. The matrices can be updated as data becomes available.
- The possibility of using a more complex approach to defining dependency structures
at a future stage of SAM implementation should not be excluded.
Weaknesses of recommended approach
Some issues regarding the use of linear correlations to describe the dependency structure
for risks are covered in section 6.1 above, and some further weaknesses are noted here:
- The use of sub-correlation matrices can lead to non-sensical correlations between
sub-elements of different risk modules
- This approach does not model the possibility of the non-linear correlation between
risk modules. The existence and extent of tail-dependency is therefore not reflected
by this approach.
- Correlations are often set at a risk level, e.g. the correlation between a catastrophic
claim event and movements in market values. It is important to note however that
correlation factors are applied to capital figures of the respective risk modules and
risk sub-modules. The risk that leads to the highest capital amount might be in a
different „direction‟ for risk module outcomes from one company to the next. For
example, for one company a drop in interest rates might lead to a higher capital
requirement under market risk whereas for another company an increase in interest
rates might determine the market risk capital. The same correlations will then be
used to aggregate capital requirements from other risk modules for both these
companies.
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7.2 Correlation parameters
This section proposes correlation parameters for use within the Standard Model of the SAM
regime to aggregate risk capital across the respective SCR risk modules (inter-risk
correlation parameters).
Firstly in section 7.2.1, the latest correlation matrix, and background to this, under the
Solvency II regime is considered. These are the same correlation parameters that were
used within the SAQIS1 exercise. Comments from the SAQIS1 exercise regarding risk
aggregation are then considered in section 7.2.2, with sensitivity analysis and further
consideration of the SAQIS1 technical specification and Solvency II text shown in response
to comments received. The approach to inter-risk correlations for SAQIS2 is then
recommended in section 7.2.3 with the final approach to SAQIS2 shown in section 7.2.4.
SAQIS2 feedback on inter-risk correlation parameters and the approach taken is given in
section 7.2.5, and a recommended approach for SAQIS3 shown in section 7.2.6.
7.2.1 Solvency II correlations (EUQIS5)
The parameter values for correlations as used in EUQIS5 (and SAQIS1) are shown in the
table below:
j
Market
Default
Life
Health
Non-life
i
Market
1
Default
0.25
1
Life
0.25
0.25
1
Health
0.25
0.25
0.25
1
Non-life
0.25
0.5
0
0
1
The SCR is determined as follows:
SCR = BSCR + Adj +SCROp
where :
BSCR
=
Basic Solvency Capital Requirement
SCRop
=
The capital requirement for operational risk
Adj
=
Adjustment for the risk absorbing effect of technical
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provisions and deferred taxes
The Basic Solvency Capital Requirement (BSCR) is the Solvency Capital Requirement
before any adjustments, combining capital requirements for the above five major risk
categories with the above correlation matrix, and an addition for the Capital requirement for
intangible assets risk.
The QIS5 technical specifications follow the Level 2 advice on correlations. All correlations,
apart from Non-Life and Default, Non-Life and Health and Non-Life and Life, are set at 0.25.
The correlation between Non-Life and Default is set at 0.5 and that between Non-Life and
Health and Non-Life and Life is set at 0.
The EU CRO forum recommendations comment on these parameters, but do not investigate
their appropriateness.
These parameters are prescribed in the Solvency II Directive. They first appeared in the
technical specifications to EUQIS3. However, the EUQIS3 calibration paper does not
discuss how they were calibrated (neither does the Solvency II Level 2 advice on
correlations). They relate closely to the ranges suggested in the EUQIS2 technical
specifications, the first to include aggregation by correlations.
The EUQIS2 technical specifications provided a guideline for the correlations – low, mediumlow, medium, medium-high, high – but allowed participants to decide on the values.
Correlations between most risk modules were suggested to be medium-low. This is
consistent with the correlation of 0.25 used between most risk modules from EUQIS3
onwards. EUQIS2 suggested a medium correlation between Non-Life and Default risk; this
too is consistent with EUQIS3, which prescribed a correlation of 0.5. EUQIS2 suggested a
low correlation between Non-Life and Life and Non-Life and Health; and this too is consistent
with EUQIS3, which prescribed a correlation of 0.
EUQIS3 appears to have deviated from EUQIS2 in the setting of two correlations – that
between market and default and that between operational and all other risks. EUQIS2
suggests a medium-high correlation between market and default risk, whereas EUQIS3 only
prescribed a correlation of 0.25. EUQIS2 suggested medium to medium-low correlations
between operational and all other risks, but EUQIS3 assumes perfect correlation by taking
operational risk out of the square-root-of-sum-of-squares formula and adding it as a separate
term.
7.2.2 SAQIS1 feedback on correlation parameters
Specific feedback on SAQIS1 correlation parameters, as reflected in section 7.2.1 above,
was gained through the qualitative questionnaire. One specific criticism was received
through question 10:
QS.10. If you are not convinced by the SA QIS1 methodology, what are your most important
points of discrepancy?
SCR aggregation Response A: The correlation between Market risk and Life risk is 0.25.
The main Life underwriting risk factors are lapses, withdrawals and expenses and these are
mainly influenced by Market risks. I expect the correlation to be higher than 0.25. (Life
Insurer)
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SCR aggregation Response B: The SCR is very sensitive to the correlation structures
considered in sub-modules and for final aggregation, which adds emphasis to finding an
appropriate correlation matrix. (Life Insurer)
SCR aggregation Response C: The SCR and its components are very sensitive to the
correlation parameters used in the aggregation. If these correlation parameters have been
underestimated, the SCR will be insufficient if adverse events occur simultaneously. We
think it is imprudent to assume that this cannot happen. (Life Insurer)
Consideration of SCR aggregation Response A
The following graph shows the sensitivity of the SAQIS 1 result for Life Insurers to changing
the correlation parameter between Market risk and Life risk from 0.25 to 0.5 across all
individual insurers. 0.5 has specifically been suggested as an alternative assumption and is
the next level up in the low, medium-low, medium, medium-high, high scale:
Number of companies
Graph 1: Changing Life and Market Risk correlation from
0.25 to 0.5
6
5
4
3
2
1
0
Change in SCR
A change in the correlation assumption between Market risk and Life risk would result in a
simple average increase in SCR of 6.3%, with a maximum increase of.24.6% () and
minimum increase of 0% across all Life Insurers.
The following graph shows the sensitivity of the SAQIS 1 result for Life Reinsurers to
changing the correlation parameter between Market risk and Life risk from 0.25 to 0.5 across
all individual re-insurers:
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Graph 2: Changing Life and Market Risk correlation from
0.25 to 0.5
Number of companies
3
2
1
0
<1%
1-2%
2-3%
3-4%
4-5%
5-6%
6-7%
7-8%
>8%
Change in SCR
A change in the correlation assumption between Market risk and Life risk would result in a
simple average increase in SCR of 4.9%, with a maximum increase of 7.7% , and minimum
increase of 0% across all Life Reinsurers.
Further to this, the following extracts from the SAQIS1 technical specification are
considered:
SAQIS 1 SCR 1.7:
The scenario should be interpreted in the following manner:

The recalculation of technical provisions to determine the change in NAV should allow
for any relevant adverse changes in option take-up behaviour of policyholders under
the scenario.
Latest Solvency II developments recommend that, in the calculation of a module or submodule of the Basic Solvency Capital Requirement, recalculation of technical provisions
arising as a result of considering the impact of a scenario be applied. Any material adverse
impact of the scenario on the likelihood that policy holders will exercise contractual options
be taken into account in the recalculation of technical provisions.
Consideration of SCR aggregation Response B&C
The following graphs show the sensitivity of the SAQIS 1 result for all companies, split
between Life and Non-life Insurers (Insurers and Re-insurers were consolidated for
convenience) to changing the correlation parameter between each of the following risk
modules:





Default risk and Market risk
Life risk and Market risk
Non-life risk and Market risk
Life risk and Default risk
Non-life risk and Default risk
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
Non-life risk and Life risk
The approach used in formulating the sensitivities of the SCR (measured as a percentage of
the SCR given the original correlation parameter values) to changes in the various
correlation parameters was to change each parameter individually from values of 0.01 to 1,
while keeping the remaining parameters fixed at their original values.
For all sensitivity testing graphs, the change in SCR indicated on the y-axis for each value of
the correlation parameter considered on the x-axis is the simple average change in SCR
across all Companies considered. The SCR is 100% at the value of the correlation
parameters used for SAQIS1.
Life Companies and Life Reinsurers
The correlations that produced meaningful results when changed were those between
Default and Market risk, Life and Market risk, and Life and Default risk.
For the scenarios where the correlations between Non-life and Market risk,
Non-life and Default risk, and Non-life and Life risk, only one company produced any
changes in SCR. These scenarios were thus not graphed.
Graph 3: Sensitivity of Default and Market risk correlation (Life Companies)
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106%
105%
104%
103%
102%
101%
100%
99%
98%
97%
96%
95%
Average SCR (Default and Market
risk)
0.01
0.07
0.13
0.19
0.25
0.31
0.37
0.43
0.49
0.55
0.61
0.67
0.73
0.79
0.85
0.91
0.97
SCR (%)
Average SCR
Correlation value
Graph 4: Sensitivity of Life and Market risk correlation (Life Companies)
Average SCR
120%
115%
105%
100%
Average SCR (Life and Market
risk)
95%
90%
85%
80%
0.01
0.07
0.13
0.19
0.25
0.31
0.37
0.43
0.49
0.55
0.61
0.67
0.73
0.79
0.85
0.91
0.97
SCR (%)
110%
Correlation value
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Graph 5: Sensitivity of Life and Default risk correlation (Life Companies)
Average SCR
105%
104%
103%
SCR (%)
102%
101%
100%
Average SCR (Life and default
risk)
99%
98%
97%
0.01
0.07
0.13
0.19
0.25
0.31
0.37
0.43
0.49
0.55
0.61
0.67
0.73
0.79
0.85
0.91
0.97
96%
Correlation value
Non-life Insurance Companies and Non-Life Reinsurers
Graph 6: Sensitivity of Default and market risk correlation (Non-Life Companies)
Average SCR
104%
103%
101%
100%
Average SCR (Default and market
risk)
99%
98%
97%
0.01
0.07
0.13
0.19
0.25
0.31
0.37
0.43
0.49
0.55
0.61
0.67
0.73
0.79
0.85
0.91
0.97
SCR (%)
102%
Correlation value
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Graph 7: Sensitivity of Non-life and Market risk correlation (Non-Life Companies)
Average SCR
115%
SCR (%)
110%
105%
100%
Average SCR (Non-life and
market risks)
95%
0.01
0.06
0.11
0.16
0.21
0.26
0.31
0.36
0.41
0.46
0.51
0.56
0.61
0.66
0.71
0.76
0.81
0.86
0.91
0.96
90%
Correlation value
Graph 8: Sensitivity of Non-life and Default risk correlation (Non-Life Companies)
Average SCR
110%
100%
95%
Average SCR
90%
85%
0.01
0.06
0.11
0.16
0.21
0.26
0.31
0.36
0.41
0.46
0.51
0.56
0.61
0.66
0.71
0.76
0.81
0.86
0.91
0.96
SCR (%)
105%
Correlation value
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7.2.3 Recommendation for SAQIS2
It is recommended to have a base case and to test an alternative scenario for SAQIS2.
Base case: The SAQIS2 technical specification should require the impact of policyholder
actions for Life (Re)insurance Companies to be included in SCR main Market risk scenarios
(being equity, interest rates and property), keeping inter-risk correlations unchanged
compared to SAQIS1. Any material adverse impact of the Market Risk scenarios on the
likelihood that policy holders will exercise contractual options should be taken into account in
the recalculation of technical provisions.
Alternative: Quantification of the main Market stresses (being equity, interest rates and
property) where policyholder behaviour is unchanged. These values will be considered
together with the use of correlation parameter between Market risk and Life risk of 0.5.
7.2.4 Final recommendation for SAQIS2
The SCR structure of SAQIS2 is changed in that the Counterparty Default risk module does
not appear on its own as it did in SAQIS1. The risk mitigation impact of risk
mitigating instruments such as reinsurance contracts, special purpose vehicles
and derivative hedges should now be impaired in each of the modules in which
risk mitigation is used.
In contrast to SAQIS1, instruments with original term of less than 1 year and other
instruments previously covered in the counterparty default module (including
everything classified in QIS1 as type 2 exposures in the counterparty default risk
module) are now also covered in Spread/Credit Default risk sub-module within the
Market risk module of SAQIS2.
The SAQIS2 SCR model structure is as follows:
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SCR
Adj
Market
BSCR
Health
Default
CAT
Non-SLT
Health
Op
Life
Non-life
Mortality
Premium
Reserve
Interest
rate
SLT
Health
Equity
Mortality
Property
Longevity
Spread
Disability
Morbidity
Lapse
Currency
Lapse
Expenses
Concentration
Expenses
Revision
Illiquidity
Revision
CAT
Premium
Reserve
SCRPart
Longevity
Intang
Lapse
Disability
Morbidity
Lapse
CAT
= included in the
adjustment for the lossabsorbing capacity of
technical provisions
under the modular
approach
NL Health
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The SCR is determined as follows in SAQIS2:
SCR = BSCR + Adj + SCROp + SCRPart
 Corr

where BSCR
ij
 SCRi  SCR j  SCRintangibles
ij
and for BSCR The following input information is required:
SCRmkt
=
Capital requirement for market risk
SCRlife
=
Capital requirement for life underwriting risk
SCRnl
=
Capital requirement for non-life underwriting risk
SCRintangibles
=
Capital requirement for intangible assets risk
The inter-risk correlation matrix is chosen as follows. This follows the same correlation
factors used in SAQIS1:
j
Market
Life
Non-life
i
Market
1
Life
0.25
1
Non-life
0.25
0
1
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A potential higher correlation between the Life risk module and Market risk module has been
identified as part of the SAQIS1 results. This is due to the significant Lapse Risk component
within the Market Risk module in SAQIS1. However, it is also commented that addressing
this relationship using a higher correlation between Life Risk and Market Risk has an issue
for Life companies where most of Life Risk is made up of Mortality/Morbidity risk.
To inform the ultimate approach to be taken in the Standard Model to address this challenge,
three different approaches are being tested for SAQIS2 in the Market risk module with
regard to the impact of policyholder behaviour within the interest rate and equity risk submodules:



The base approach assumes expected future policyholder behaviour allowed for in
the stressed technical provision in unchanged from that assumed in the base
technical provisions,
the first alternative specifies changes to the assumed policyholder behaviour (within
the interest rate and equity risk modules);
and the second alternative follows the Solvency II methodology which specifies that
each participant must make allowance in the calculation of technical provisions for
relevant adverse policyholder behaviour in each risk module, but does not specify
what that behaviour might be nor the extent of the behaviour.
The second alternative is voluntary (at the discretion of the participant to include or not).
The approach to specifying the impact on policyholder behaviour in the first alternative has
been criticised as this might impact different companies in different ways. Depending on the
specific situation of a Life Insurance company, the specified change in policyholder
behaviour could have either a positive of negative impact on the solvency position.
The second alternative is anticipated to yield useful results, and will be informative to
analyse the actual change in demographic assumptions that are proposed by companies.
7.2.5 SAQIS2 feedback on correlation parameters
No specific commentary was raised regarding the inter-risk correlation parameters from the
SAQIS2 qualitative questionaires submitted.
Per the SAQIS2 report produced by the FSB, the following feedback regarding to the impact
of policyholder behaviour within the interest rate and equity risk sub-modules was given:
“Some insurers preferred insurer-specific modelling of policyholder behaviours over standard
stresses defined for policyholder behaviour. There was also a concern that it would not be
possible to find an appropriate definition of policyholder behaviours that would be suitable for
all lines of business and all insurers.
One view was raised that the policyholder behaviours were very complex to model, and thus
should only be allowed under an approved internal model that has been subjected to the
internal model approval process of the FSB.
Other insurers highlighted that there is a risk of double-counting the lapse risk, as lapses are
already allowed for in the lapse stresses performed under the life underwriting risk module,
with the interaction between market risk and lapse risk implicitly allowed for within the
correlation structure.
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A further view was that this should form part of the ORSA process under Pillar 2, and that it
was not appropriate to allow for dynamic policyholder behaviour under the Pillar 1
calculation.
This alternative was generally not material for non-life and pure linked insurers.”
7.2.6 Recommendation for SAQIS3
The approach to SAQIS 3 will be to allow for any material adverse impact of scenarios
considered within a module or sub-module of the Basic Solvency Capital Requirement on
the likelihood that policy holders will exercise contractual options. In this regard, the link
between market and non-market risks between causal and non-causal effects will be split.
Causal links are where there is a direct link between a market stress and policyholder
behaviour. This is typically where a change in market conditions changes the value of
benefits a policyholder receives, and this change in benefits is expected to result in a change
in behaviour. An example is where a market fall results in a guaranteed maturity value biting,
which we would expect to result in a reduction in surrender rates in policies close to maturity.
These dynamic policyholder behaviours will be considered in the calculation of the base
technical provisions –in the SCR this principle is applied following a market stress.
Non-causal effects will be allowed for in the correlations. Non-causal effects typically have a
much looser link between market and non-market risk, and represent potential changes in
policyholder behaviour as a result of changes in the economy as a whole. Examples include
potential higher lapses when the economy is in a downturn (which may be characterised by
a depressed stock exchange and large changes to interest rates). As these effects are not
directly related to a specific market stress and the effects can vary by policy type, it is much
more difficult to link them to specific policyholder behaviour, and hence it is preferable to
allow for them using the correlation factors.
Based on the proposed SAQIS3 approach where policyholder behaviour relating to causal
links within the SCR stresses will be allowed for, the following recommendation is made for
the inter-risk correlation matrix for SAQIS3:
j
Market
Life
Non-life
i
Market
1
Life
0.25
1
Non-life
0.25
0
1
The above recommendation for inter-risk correlations, together with an allowance for
dynamic policyholder behaviour in the relevant SCR modules and sub-modules, would seem
to be consistent with the standard model in Solvency II.
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7.2.7 SAQIS3 feedback on correlation parameters
Specific feedback on SAQIS3 inter-risk correlation parameters, as reflected in section 7.2.6
above, was gained through the qualitative questionnaire. Specific criticism was received
through question 14. Only criticisms regarding aggregation of risk modules are raised in this
document. Aggregation of sub-risk components within risk modules are addressed in
discussion documents dealing specifically with these risk modules.
QS.14. If you are not convinced by the SA QIS3 methodology, what are your most important
points of discrepancy?
SAQIS3 SCR aggregation Response A:
Some of the correlation assumptions are regarded as high, e.g. between market risk and
non-life insurance risk, between Cat and non-Cat insurance risk. (Non-Life Niche Insurer)
Consideration of SCR aggregation Response A
Per the Solvency II deliberations recorded in this document, a correlation parameter of 0.25
between market risk and non-life insurance risk is regarded as medium-low.
SAQIS3 SCR aggregation Response B:
As a pure risk reinsurer we do not feel there is material correlation between the market risk
in our BS and the insurance risk and therefore the 0.25 used in the Standard Model is an
overstatement. (Life Reinsurer)
Consideration of SCR aggregation Response B
Per the Solvency II deliberations recorded in this document, a correlation parameters of 0.25
between market risk and non-life insurance risk is regarded as low.
SAQIS3 SCR aggregation Response C:
The standard correlation matrix approach to capital aggregation applies when a number of
conditions are satisfied. It is extremely unlikely except by chance that any company‟s risks
and risk drivers meet the conditions underlying the standard formula. Where risks are not
drawn from centered elliptical distributions we have demonstrated in our own investigations
that the capital estimate can be wildly incorrect. In addition in the case of the insurer, the
standard formula does not make any allowance for non-linearities or offsets between interest
rate and lapse risk. (Life Typical)
Consideration of SCR aggregation Response C
The possibility of non-elliptical distributions of risks and the challenges of allowing for the
aggregation such risks are raised in this document. From a proportionality point of view
correlation matrices are regarded as the most suitable approach as the implementation is far
simpler than more complex alternatives to model non-linear correlations.
EU and IAIS documentation both recommend the use of stress testing to check the suitability
of correlation matrices under those conditions. Although the format of stress-testing is not
described, pragmatic approaches could give a sensible indication of the impact.
Page 29 of 31
Solvency Assessment and Management: Steering Committee
Position Paper 48 (v 4) – SCR Standard Formula - Correlations
While the use of correlation matrices is not a perfect solution, it seems unlikely that South
Africa could hope to implement a more technically intensive correlation structure in its
standard model if this approach is considered unfeasible in the EU.
SAQIS3 SCR aggregation Response D:
The SCR correlation assumptions are more conservative than we believe are appropriate. In
particular the addition of operational risk to the BSCR implies that whenever any loss occurs
it will be accompanied by another loss due to operational causes. This is clearly an
inappropriately conservative assumption, as it is easy to construct examples where a loss
caused by another risk factor will not necessarily trigger an operational risk event.
In addition, many of the correlations have a magnitude of 0.75. These assumptions are also
arguably too conservative, as it implies that the incidence of risk factor A will be
accompanied by the incidence of risk factor B close to 90% of the time. (It should be borne in
mind that a correlation of 0.0 implies that an incidence of risk factor A will be accompanied
by an incidence of risk factor B half of the time.) While it is easy to imagine circumstances
where, for example, equities fall and credit spreads widen simultaneously, it is also quite
plausible that there are circumstances where they will not. We therefore suggest that the
correlations of 0.75 be moderated to 0.50. (This can roughly be interpreted to mean that the
two risk factors will coincide 75% of the time.)
Furthermore, the use of a tiered structure of correlation matrices can, and does, lead to
mathematical inconsistencies. For example, longevity risk has a negative correlation with
other life risks. Most life risks have a positive correlation with market risks. Therefore, by
implication longevity risk should have a negative correlation with market risks. However all
life risks are assumed to have a positive correlation with market risks. Aside from the
inconsistency, this structure of correlation matrices produces a significantly different result
compared to the same correlations used in a flat matrix. We estimate the difference to be
around 10% of the standalone risk.
Finally, the deterministic approach of the standard formula means that it is not easy to take
into account the mitigating effect of risk factors occurring simultaneously. In other words, the
loss arising from risk factor A and B occurring simultaneously is not the same as the sum of
the individual losses caused by risk factors A and B. Frequently the combined loss is lower,
for example in the case of mass lapse. If a mass lapse occurs either just before or just after
an equity shock, the combined loss is less than the sum of the individual losses. If the mass
lapse shock occurs first, there are fewer policies exposed to the subsequent equity shock. If
the equity shock occurs first, the loss arising from a policy lapsing is lower (mainly because
the expectation of future profits is lower following an equity shock). Because mass lapse will
tend to be one of the larger risk types, and because the effect involving mass lapse will
always be a mitigating one, we expect this shortcoming to cause the SCR to be overstated
for most insurers.
We do not expect SAM to remedy this issue explicitly, but it is worth bearing in mind that the
structure of the SCR means that the diversification effect is being inherently understated
because it does not allow for the mitigating effect of simultaneously occurring risk factors..
(Life Typical)
Consideration of SCR aggregation Response D
Page 30 of 31
Solvency Assessment and Management: Steering Committee
Position Paper 48 (v 4) – SCR Standard Formula - Correlations
Per the Solvency II deliberations recorded in this document, a correlation parameter of 0.25
between market risk and life insurance risk is regarded as medium-low.
It is suggested that the criticism of the aggregation of operational risk module with the BSCR
should be addressed together with any other criticisms of the operational risk module.
SAQIS3 SCR aggregation Response E:
Correlation coefficients may not well for business as ours (Non-Life niche)
Consideration of SCR aggregation Response E
The issue raised is not clear
Page 31 of 31