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Philipp Keller, Federal Office of Private Insurance

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Title: Philipp Keller, Federal Office of Private Insurance


1
Swiss Solvency Test
  • Philipp Keller, Federal Office of Private
    Insurance
  • Brussels, 14 October 2005

2
Contents
  • Designing a Solvency System
  • Basic Requirements
  • Principles vs Rules
  • Concept of the Swiss Solvency Test
  • The SST Standard Model
  • Experiences from the Field Tests
  • Internal Models
  • Group Aspects

3
Designing a Solvency Test
  • Basic requirements of a risk-based solvency
    system
  • Requirements and definitions have to follow from
    regulatory purpose (e.g. what is the risk margin
    for, what purpose does the solvency capital
    requirement (SCR) have, etc.)
  • If internal models are to be used, the solvency
    system should be defined by underlying principles
  • Building blocks have to fit together (SCR has to
    be linked to risk margin to avoid double counting
    of risks, the valuation of assets and liabilities
    has to be consistent, )
  • If the solvency system has to be embedded within
    insurance companies, it has to be founded on
    economic principles
  • Avoid nontransparent mix of quantification of
    risks, limited eligibility of capital, limits and
    implicit safety margins which would make
    interpretation of SCR impossible

4
Designing a Solvency Test
  • A risk based solvency system has to address the
    needs of different stakeholders
  • Regulators policyholder protection, setting
    capital requirements, incentive for risk
    management, obtaining a view on companies risk
    culture and risk awareness, achieving a
    competitive market place,
  • Policyholders, Investors, Shareholders,
    Brokers, Comparison of the financial situation
    of different companies, information on the
    efficiency of risk management, ALM etc.
  • Insurers (CEO, CRO, CFO, Actuaries) Comparison
    with peers, use of internal models, analysis of
    contribution of different risk types,

A risk based solvency system has many purposes
and needs to be a reasonable compromise to
satisfy the needs of many stakeholders
5
Designing a Solvency Test
Define risk bearing capital, e.g. value of assets
less best-estimate of liabilities, define which
forms of capital are eligible
Definition of Capital
Define valuation methodology of assets and
liabilities
Valuation
Decide over which time horizon risk capital needs
to cover risks
Time Horizon
Define risk typology, decide which risks are
quantified and which treated qualitatively
Risks to Quantify
Definition of Ruin
Define risk margin ? in SST risk margin lowest
acceptable level of risk bearing capital
Risk Measure
Define measurement of risks, e.g. Value at Risk,
Expected Shortfall, etc.
In the last stage, define standard model (if
necessary), details of the system, e.g.
correlations vs copulas, etc.
Operational Implementation
6
Implications of Principles vs Rules
Principle-based standards describe the objective
sought in general terms and require
interpretation according to the circumstance.
Companies tailor approach such that clearly
stated objective is attained
Objective can be attained if companies interpret
principles faithfully. The objective is defined
by a (theoretically) correct quantification and
allocation of group diversification
Principle-based
Objective
Risk Based Capital Requirement

Rule-based
Objective
Rule based approach does not allow truly company
specific risk assessment
Attained result depends on how well rules capture
the situation of the insurer
7
Contents
  • Designing a Solvency System
  • Concept of the Swiss Solvency Test
  • Principles
  • Quantified Risks
  • Risk Measure
  • Valuation
  • Risk Margin
  • Change in Risk Bearing Capital
  • Capital
  • The SST Standard Model
  • Experiences from the Field Tests
  • Internal Models
  • Group Aspects

8
The SST Concept Principle-Based
The more laws and order are made prominent, the
more thieves and robbers there will be, Lao-tzu
Core of the Solvency Test
Principles
Definitions
Glossary
Guidelines
Standard Model
The SST is defined not by the Standard Model but
by underlying principles
  • Principles define concisely the objectives
  • Definition of terms and concepts so that meaning
    and possible interpretation of principles become
    clear
  • Guidelines help in interpretation
  • Standard Model allows use of Solvency Test also
    by small companies

9
Principles defining the SST
  1. All assets and liabilities are valued market
    consistently
  2. Risks considered are market, credit and insurance
    risks
  3. Risk-bearing capital is defined as the difference
    of the market consistent value of assets less the
    market consistent value of liabilities plus the
    risk margin
  4. Target capital is defined as the sum of the
    Expected Shortfall of change of risk-bearing
    capital within one year at the 99 confidence
    level plus the risk margin
  5. The SST defines an insurers capital adequacy if
    its target capital is less than its risk bearing
    capital
  6. The scope of SST is legal entity and group /
    conglomerate level domiciled in Switzerland
  7. Scenarios defined by the regulator as well as
    company specific scenarios have to be evaluated
    and, if relevant, aggregated within the target
    capital calculation
  8. All relevant probabilistic states have to be
    modeled probabilistically
  9. Partial and full internal models can and should
    be used
  10. The internal model has to be integrated into the
    core processes within the company
  11. SST Report to supervisor such that a
    knowledgeable 3rd party can understand the
    results
  12. Disclosure of methodology of internal model such
    that a knowledgeable 3rd party can get a
    reasonably good impression on methodology and
    design decisions
  13. Senior Management is responsible for adherence to
    principles

Defines Output
Defines How-to
Transpar-ency
Responsi-bility
10
Risk Measures Expected Shortfall
The Expected Shortfall of a random variable X to
the confidence level 1-? (ES?) is given by ES?X
1/ ? E max( X- VaR?X, 0 ) VaR?X
  • Expected Shortfall is a coherent risk measure

Shareholder Only default or non-default is
relevant not how bad the state of the insurer is
in case of default as shareholders have a
put-option on the insurer (Merton) ?
Value-at-Risk is appropriate Policy Holder In
case of default, it matters how much capital is
left ? Expected Shortfall is more appropriate
than VAR
  • From the perspective of an insurance regulator,
    Expected Shortfall has advantages compared to
    Value at Risk
  • For an insurer, Expected Shortfall has advantage
    of being coherent
  • Allocation of risk and risk management of
    subunits is possible
  • ES? is easier to explain to management
  • ES1average one-in-a-hundred-years loss
  • VaR1 the loss that is in 99-out-of-a-100-years
    not exceeded

11
The SST Concept The economic view
  • How to measure risks?
  • Accounting risk or economic risk?
  • Reported earnings follow the rules and
    principles of accounting. The results do not
    always create measures consistent with underlying
    economics. However, corporate managements
    performance is generally measured by accounting
    income, not underlying economics. Therefore, risk
    management strategies are directed at
    accounting, rather than economic performance.
  • Enron in-house risk-management handbook
  • For a risk-based solvency system, risks need to
    be measured objectively and consistently ?
    economic risk rather than accounting risk
  • ? Market Consistent Valuation of Assets and
    Liabilities

12
The SST Concept The economic view
Market Consistent
Assets
Liabilities
Wherever possible, market-consistent valuation is
based on observable market prices (marking to
market) If such values are not available, a
market-consistent value is determined by
examining comparable market values, taking
account of liquidity and other product-specific
features, or on a model basis (marking to
model) Market-consistent means that up to date
values are used for all parameters
Best-estimate Expected value of liabilities,
taking into account all up to date information
from financial market and from insurance. All
relevant options and guarantees have to be
valued. No explicit or implicit
margins Discounting with risk-free interest rate
Best-Estimate Provisions
Market consistent provisions
Risk Margin
Risk bearing capital
Risk Margin for inherent risk in liability
portfolio
Valuation of policyholder-options Assume
realistic behavior of policy holders, but option
exercise depends on financial market
parameters One approach to value options is using
replicating portfolio of traded financial
instruments
13
The SST Concept The SST in a Nutshell
Expected Shortfall
Target Capital
Risk Margin
Change of Risk-Bearing Capital
Covers risks emanating during a one-year time
horizon
Risk margin should be sufficient to allow a
run-off or portfolio transfer
14
The SST Concept Risk Margin
Risk Margin to cover policyholders against risks
emanating beyond 1 year
The Risk Margin and SCR/ES cover different risks
  • SCR / ES To cover risks which emanate during a
    1-year time horizon
  • Risk Margin To cover risks during the whole
    run-off of the portfolio

There should not be double-counting between SCR
and Risk Margin
  • Possible Approaches
  • Statutory Taking undiscounted reserves, using
    prudent assumptions, adding a simple factor on
    best-estimate etc.
  • Quantile Taking e.g. the 75 quantile of the
    ultimate loss distribution of the liabilities
    Used by APRA for PC liabilities, discussed
    within Solvency 2.

Risk Margin
Best Estimate
Provisions
  • Market Value Margin the additional amount on top
    of the best estimate which is required by a
    willing buyer in an arms-length transaction to
    assume the liabilities the loss reserves are held
    to meet Discussed within Fair Value Accounting,
    used (partly) within the SST.

15
The SST Concept Risk Margin
Definition The risk margin is the smallest
amount of capital which is necessary in addition
to the best-estimate of the liabilities, so that
a buyer would be willing to take over the
portfolio of assets and liabilities.
Idea A buyer (or a run-off company) needs to put
up regulatory capital during the run-off period
of the portfolio of assets and liabilities ? a
potential buyer needs to be compensated for the
cost of having to put up regulatory capital
Risk Margin cost of capital of the present
value of future regulatory risk capital
associated with the portfolio of assets and
liabilities
Problem How to determine future regulatory
capital requirement during the run-off of the
portfolio of assets and liabilities? -gt
Assumptions on the evolution of the asset
portfolio are necessary
16
The SST Concept Risk Margin
Key Idea
  • The insurer setting up the risk margin should not
    be penalized if, after the transfer, the insurer
    taking over the portfolio does not minimize the
    regulatory risk capital requirements as fast as
    possible.
  • The insurer taking over the portfolio of assets
    and liabilities should be compensated if the
    insurer setting up the risk margin invested in an
    illiquid asset portfolio.

Assets Assume that initial asset portfolio is
rebalanced such that it matches optimally the
liabilities. The speed of the rebalancing is
constrained by liquidity of assets (it takes
longer to liquidate for real estate than for
government bonds). The time until the optimal
replicating asset portfolio is achieved depends
on the asset mix.
Liabilities Assume no new business
17
The SST Concept Risk Margin
ES at t0 does not enter calculation of the risk
margin necessary at t0 ? risks taken into
account for 1-year risk capital and risk margin
are completely disjoint and there is no
double-counting
ES with portfolio converging from actual to
replicating portfolio taking into account
illiquidity of assets ? Sequence of Achievable
Replicating Portfolios
ES with optimally replicating asset portfolio
Achievable Replicating Portfolio has converged to
Replicating Portfolio
t1
t2
t3
t0
Years
ES 1-Period (e.g. 1 year) risk capital
Expected Shortfall of risk-bearing capital
Future ES entering calculation of risk margin at
t0
18
Risk Margin
Risk Margin / Best Estimate vs Risk Margin /
ESRBC, based on provisional data of Field Test
2005
Life companies writing predominately risk products
Life companies writing predominately savings
products
19
Change in Risk Bearing Capital
State 1.1 known / deterministic
State 31.12 unknown / stochastic
Assets
Liabilities
Assets
Liabilities
New business during one year (deterministic)
Changes in value of liabilities claims during 1
year (stochastic)
RBC(0)
RBC(1)
Investment profit (above risk-free) known
payoffs (deterministic)
Changes in value of assets (stochastic)
Year 0
Year 1
The SST requires the quantification of the
randomness of risk bearing capital in one year
(the probability distribution of RBC). From this
follows the determination of target capital
RBC(0) should be such that at the end of the
year, even when a large loss with Plt1 occurs,
the insurers available RBC covers (on average)
still the risk margin
20
Change in Risk Bearing Capital
RBC(0)
RBC(1)
Year 0
Year 1
21
Change in Risk Bearing Capital
ALM risk
Expected asset return over risk-free
Expected insurance (technical) result
Insurance risk (deviation of technical result
from expectation)
Current Year Risk
Previous Year Risk
22
Expected Shortfall of Risk Bearing Capital
Definition. An insurer satisfies the SST
when ESRBC(1) ? ?0 rm where rm denotes the
risk margin.
RBC(1) in function of terms known at t0
RBC(1) (rbc(0) r(0) p - k)?(1 RI ) - S(1)
- R(1)
rbc(0)a(0) - R(0) Risk-bearing capital at t0,
a(0) assets at t0, R(0) liabilities at t0
(best-estimate) p Expected premium during 0,1
r(0) Liabilities at t0
(Current year) r0 risk-free rate k
Expected costs during current year upr
unearned premium reserve S(1) Claim payments
during current year RI Asset return R(1)
Liabilities at t1
Notation simplified
23
Expected Shortfall of Risk Bearing Capital
RBC(1) (rbc(0) r (0) p - k)(1 RI ) - S(1)
- R(1)
ESRBC(1) ? ?0ES(rbc(0) r(0) p - k)(1RI)
- S(1) - R(1) ES(rbc(0) r(0)
p - k)(1 r0-r0RI) - S(1) - R(1)
rbc(0)(1r0)ESr(0)p-k)(1r0-r0RI )
rbc(0)(RI-r0)-S(1)-R(1) rm
rbc(0) -ES(r(0)p-k)(1r0-r0RI )
rbc(0)(I-r0)-S(1)-R(1) rm
24
Contents
  • Designing a Solvency System
  • Concept of the Swiss Solvency Test
  • The SST Standard Model
  • Market Risk
  • Nonlife Risk
  • Current Year Risk
  • Previous Year Risk
  • Life Risk
  • Scenarios
  • Experiences from the Field Tests
  • Internal Models
  • Group Aspects

25
The SST Concept General Framework
Standard Models or Internal Models
Mix of predefined and company specific scenarios
SST Concept
Models
Scenarios
Asset-Liability Model
Financial Risks
Insurance Risks
Credit Risks
Aggregation Method
Target Capital
SST Report
26
The SST Concept Standard Models
  • Market Risk
  • For many companies this is the most important
    risk (up to 80 of total target capital emanating
    from market risk)
  • Needs to be modeled with particular care
  • Most relevant are interest rate risk, real estate
    risk, spread risk, equity risk
  • Market risk model needs to take into account ALM
  • Credit Risk
  • Credit risk is becoming more important as
    companies go out of equity and into corporate
    bonds
  • Many smaller and mid-sized companies do not yet
    have much experience in modeling credit risk
  • Insurance Risk (Life)
  • For many life companies with predominantly
    savings product, pure life insurance risk is not
    too important
  • Life insurance risk is substantial for companies
    selling more risk products / disability
  • Model needs to capture optionalities and
    policyholder behavior
  • Insurance Risk (Nonlife)
  • Premium-, reserving- and cat risk are important
  • A broad consensus on modeling exists among
    actuaries

More information under www.sav-ausbildung.ch
27
Standard Model Market Risk
  • Scenarios
  • Historical
  • Share crash (1987)
  • Nikkei crash (1990)
  • European FX-crisis (1992)
  • US i.r. crisis (1994)
  • Russia crisis / LTCM (1998)
  • Share crash (2000/2001)
  • Default of Reinsurer
  • Financial Distress
  • Equity drop
  • Lapse 25
  • New business -75
  • Deflation

Financial market risk often dominates for
insurers ? adequate modeling of interest rate-,
equity-,.. risks is key Interest rate risk can
not be captured solely by a duration
number Financial instruments have to be segmented
sufficiently fine else arbitrage opportunities
might be created Regulatory requirements
shouldnt force companies to disinvest totally
from certain investment classes (e.g. shares,
private equity)
For SST, RiskMetrics type model with given risk
factors and associated volatilities and
correlation matrix is used together with scenarios
28
Standard Model Market Risk
  • 75 Risk Factors
  • 413 interest rate
  • 4 spreads
  • 4 FX
  • 5 shares
  • 4 real estate
  • 1 hedge fund
  • 1 private equity
  • 1 participations
  • 3 implied volas
  • FX
  • EUR
  • USD
  • GBP
  • JPY
  • Spreads
  • AAA
  • AA
  • A
  • BAA

CHF
EUR
USD
GBP
  • Equity
  • Shares
  • CHF
  • EUM
  • USD
  • GPB
  • JPY
  • Real Estate
  • IAZI
  • Commercial
  • Rüd Blass
  • WUPIX A
  • Hedge Funds
  • Private Equity

i.r. time buckets1,,10, 15,20,30
29
The SST Concept Cash Flow Based
Example Sensitivity to 2 Year CHF Yield
Asset Cash Flows
-

Year
Present Value von Asset - Liabilities
Liability Cash Flows
Year
Netto Cash Flows A-L
3
Change of present value of net cash flow
(assets-liabilities) due to change in the 2 year
CHF yield
Stressed 2Y Yield
2
CHF Yield Curve
1
0
30
Standard Model Nonlife
Premium risk
Market risk
Normal claims
Large claims
Discounted cash flows
Assets bonds, equity,
Lines of Business
For each LoB, Pareto distribution with specified
or company specific parameters
For each LoB, moments are derived by parameter-
and stochastic risks (coefficients of variation)


Method of Moments with prescribed correlation
matrix
CF -gt i.r. sensitivities
Asset Model Covariance/Riskmetrics approach
First two moments of premium risk (normal claims)
and reserving risk are aggregated using
correlation -gt two moments defining lognormal
Compound Poisson
Normal
Reserving Risk
Method of Moments with prescribed correlation
matrix

Further aggregation with scenarios
Aggregation by Convolution
Aggregation by Convolution
Lognormal
31
Standard Model Insurance Part
Assumed deterministic
Current Year Risk
Previous Year Risk
  • Claims which occur during 1 year
  • Within each Line of Business
  • Normal claims and large claims
  • Catastrophes which affect different LoBs
    simultaneously
  • Reserving risks due to
  • Randomness (stochastic risk)
  • Reassessment of reserves (parameter risk)

32
Standard Model CY Risk Normal Claims
  • Normal Claims High frequency claims, different
    for each LoB.
  • Split Normal / Large claims is in standard-model
    defined, companies can adjust to their specific
    situation
  • For each LoB
  • Estimate Parameter Stochastic Risk due to
    normal claims
  • Then aggregate using correlation matrix ( ? first
    two moments define a Gamma distribution for
    normal claims )

For each LoB i
Expected number of claims Yi,j in LoB j
33
Standard Model CY Risk Normal Claims
Within the Standard Model CoeffVari for
parameter risk and coeffvar(Yi,j) for single
normal claims for two different splits normal /
large claims is given
  • For each LoB, each company has to
  • Define a split into normal and large claims
  • Estimate the expected number of normal claims
  • Estimate the expected normal claim amount
  • If split normal/large is 1 or 5 Mio, then
    standard values can be used

34
Standard Model CY Risk Large Claims
Large claims Large single claims and
accumulation of claims due to a single event
For each LoB j Total amount due to large claims
is modeled as Compound Poisson with single claims
Yi,j being Pareto distributed and number of claim
Nj being Poisson. Then
Further assumption SCYj are independent ? Total
amount due to large claims over all LoB is again
Compound Poisson
35
Standard Model CY Risk Large Claims
Pareto Distribution
Smallest large claim comsidered ß ? threshold
parameter Shape parameter a The smaller ?, the
more heavy-tailed. If ?k, k-th moment does not
exist anymore
For numerical calculations the cut-off point of
the distribution is very important
Table with standard parameters for companies
lacking sufficient data
36
Current Year Risk Large Claims
Aggregation Use the property that for each LoB,
the loss S is compound Poison distributed
Consider the class of claim frequency
distributions N with pn/pn-1ab/n, n1,2,3,..
Where pnP (Nn). For this class with claim sizes
Y defined on the positive integers, the following
recursive formula for the distribution of total
claims holds
For Compound Poisson distributions, efficient
algorithms exist to numerically evaluate the
distribution function, e.g. Panjer Recursion
See Insurance Risk Models, PanjerWillmot
37
Standard Model Previous Year Risk
PY Risk Reserving Risk, due to uncertainty of
run-off result
Assumption CPYRPY(0) lognormal, with
expectation RPY(0) ? ECPY1 Randomness of CPY
due to parameter and stochastic risk Stochastic
Risk due to randomness of single claims ?
company specific estimation from historical
run-off result. Determine for each LoB (where all
historical data is on best-estimate
basis) Parameter Risk Estimates of parameters
are uncertain which affect all provisions of a
LoB ? level of total provisions incorrectly
chosen.
For parameter risk predefined values are given
For stochastic risk company has to determine
based on experience, e.g. using Mack
Parameter Risk Parameters given for standard
model

38
Standard Model Life
Assumptions The risk factors are normal
distributed with given volatilities. Change of
risk bearing capital in function of the risk
factors is linear ? The distribution over all
risk factors is again (multivariate) normal
distributed
Volatility Describes changes of risk factors
within one year due to parameter-uncertainty Stoch
astic risk will be included using company
specific data if relevant The volatilities have
been set during discussions with specialist and
represent a best-guess
  • Risk Factors Volatility
  • Indiv. Group
  • Mortality 5 5
  • Longevity (trend) 10 10
  • Disability 10 20
  • Reactivation 10 10
  • Lapse 25 25
  • Option Exercise 10 10

39
Standard Model Life
Correlations between risk factors for field test
2005 Split into individual and group business.
Full correlation between individual and group
business risk factors, except for lapse
40
Standard Model Life
The model is simple and transparent the company
has to determine sensitivities with respect to
life insurance risk factors and then can use
correlation matrix and volatilities to arrive at
distribution for life insurance risk The
normality assumption allows easy aggregation with
market risk
Correlations between market risk factors
Correlations between market risk factors and
insurance risk factors (individual and group
business) For field test 2005, CM,IG0, but in
future correlation between market risk and
insurance risk can easily be included (e.g.
correlation between lapse and interest rate)
Correlations between life insurance risk factors
(within individual (I), within group (G) and
between individual and group CI,G
41
The SST Concept Scenarios
Ersatz experience is a better guide to the
future than the real past and present, Hermann
Kahn in On Thermonuclear War
Scenarios can be seen as thought experiments
about possible future states of the world.
Scenarios are not forecasts, in that they need
not predict the future development, but rather
should illuminate possible but perhaps extreme
situations. Scenarios are also different from
sensitivity analysis where the impact of a
(small) change of a single variable is evaluated.
Alternate states of the world
Current state of the world
42
Standard Model Aggregation with Scenarios
Assumption During normal years, analytical
models without scenarios are valid (described by
a probability distribution F0), during
exceptional years, additional losses due to
events described in scenarios occur, causing a
shift in the pre-scenario distribution. Scenario
i, i1,,n occurs with probability pi and causes
an additional loss of ci (cilt0) The probability
of a normal year is p01-p1--pn The probability
distribution of the risk during a year with
aggregated scenarios is
F(x) is the weighted mean of shifted
distributions F0(.-ci), i1,,n, where c00.
43
The SST Concept Scenarios
Historical Scenarios Stock Market Crash 1987,
Nikkei Crash 1989, European Currency Crisis 1992,
US Interest Rates 1994, Russia / LTCM 1998, Stock
Market Crash 2000 Financial Distress Increase of
i.r., lapse, no new business, downgrading of
company, Deflation decrease of i.r. Pandemic
Flu Pandemic with given parameters (e.g. number
of death, sick-days, etc.) Longevity Reserving
Provisions have to be increased by 10 Hail
(Swiss specific) Given footprints
Default of Reinsurer Reinsurer to which most
business has been ceded defaults Industrial
Accident Accident at chemical plant Personal
Accident large accident during company outing or
mass panic in soccer stadium Anti-selection for
Health Insurers all insured with age lt 45 lapse
Collapse of a dam (Swiss specific) Terrorism Glob
al Scenarios (for groupsreinsurers) Property
Cats (earthquake, windstorm) Special Line Cats
Aviation (2 planes collide, marine event, energy
event, creditsurety event
44
Contents
  • Designing a Solvency System
  • Concept of the Swiss Solvency Test
  • The SST Standard Model
  • Experiences from the Field Tests
  • Experiences
  • Comments
  • Some Results
  • Internal Models
  • Group Aspects

45
Results of Field Test
  • It is a challenge to stay principle-based, since
    explicit rules are desired by some of those who
    have to implement the SST
  • The possibility of analyzing the contributions of
    different risks to required capital are seen as a
    big advantage in particular for companies not yet
    using a full internal model
  • A risk based solvency framework entails close
    cooperation and communication of different
    sections within insurance companies
  • Substantial simplification are not perceived to
    be feasible if explanatory power of SST is to be
    kept
  • Solvency 1 (statutory view) and SST are not yet
    compatible ? Solvency 1 will have to be made more
    consistent so as not to send out conflicting
    signals
  • Modelling of participations and contingent risk
    and capital transfer solutions will be
    challenging

46
Impressions from the Industry
Some have a somewhat reluctant attitude
  • SST will favour large companies that have already
    sophisticated risk-based management systems in
    place
  • Small companies without internal model will be
    punished by the Standard Approach of SST
  • SST may call for a complete overhaul of risk
    management
  • Technical implementation can become a problem
  • transparency and fair values will further
    increase the volatility of earnings
  • complexity of internal models will allow
    companies to game the system
  • SST leads to complexity where simplicity is
    required
  • SST will increase the minimum Solvency level

We would like to thank Andreas Kull (ErnstYoung)
for the permission to use this slide
47
Impressions from the Industry
Some see it in a positive light
  • facilitates more efficient use of risk capital
  • Facilitates company wide risk culture and
    dialogue
  • will reward companies that have a
    comprehensive risk management in place
  • internal models are an excellent management
    tool and can be a competitive advantage
  • Rating dependent premiums will gain acceptance.
  • Increased transparency in the insurance sector
    may reduce cost of capital for the sector as a
    whole
  • will lead to increased transparency in an
    insurer's financial strength/weakness
  • is an effective regulatory instrument to
    prevent insolvencies

We would like to thank Andreas Kull (ErnstYoung)
for the permission to use this slide
48
Impressions from the Industry
Implementation of the SST for small to midsized
companies
Wir haben diesen Sommer viel gelernt über unser
Versicherungsgeschäft und über die Bedeutung von
einzelnen Zahlen. Es gab viele Diskussionen über
Kennziffern usw. welche zu einem Wissensaufbau in
unserer Geschäftsführung führten und dazu
beitragen werden, dass wir die Gesellschaft mit
noch besseren Entscheidungsgrundlagen führen
können. Die Ergebnisse aus dem SST-Testlauf
nutzen wir auch für Diskussionen mit dem
Verwaltungsrat (es gibt eine zusätzliche Sicht
auf den Vermögensstand und den Geschäftsverlauf).
Ich bin überzeugt, dass der SST die Führung von
unserer Gesellschaft zukünftig unterstützen wird.
Die Aufsicht lieferte uns dementsprechend ein
weit ausgebautes Führungshilfsmittel.
Comment by Martin Rastetter from the
Metzgerversicherung a small-to-midsized nonlife
company
Days of worked used approximately Internal
40-50 days, External 15-20 days
49
Results of Field Tests
  • Market risk is often dominating (50-80)
  • The risk margin is between 10-40 of target
    capital rsp. 1-8 of best-estimate provisions
  • Diversification Effect between Insurance and
    Market Risk between -5 and -30
  • Effect of Scenarios on ESRBC Between 5 and
    50
  • Seems too high and some scenarios will be
    adjusted
  • Market consistent value of assets / Statutory
    value of assets between 90 and 120 but in
    most cases market consistent value is higher than
    statutory
  • Market consistent value of liabilities /
    Statutory value of liabilities between 70 and
    100
  • While SCR/Target Capital requirement is in many
    cases higher than statutory capital requirement,
    the economics solvency ratio can be better or
    worse than the statutory solvency ratio (Solvency
    1), since economic capital is in most cases
    substantially higher than statutory capital

50
Results of Field Tests Target Capital
Credit Risk In the standard model additiv
add-on based on Basel II, but portfolio models
can be used
Diversification between market and insurance risk
Target capital
1 year risk capital
Market risk, taking into account diversification
between different asset classes
Effect of scenarios
Risk Margin
Expected technical financial result
Insurance Risk, taking into account
diversification between risk factors and lines of
business and branches
Relative length of bars correspond
approximatively to actual median values
51
Results of Field Tests Market Risk
Diversification effect between different asset
classes
Diversification between market risk factors
Others
Real Estate
Diversification between Market and Insurance Risks
Credit Risk
1 year risk capital
Target capital
Shares
Scenarios
Spreads
Risk Margin
Market risk
Expected Result
FX
Insurance Risk
Market risk
Interest Rates (CHF, EUR, USD, GBP)
Relative length of bars correspond
approximatively to actual median values
52
Results of Field Tests Valuation
The following graph shows how market consistent
liabilities compare to statutory liabilities. In
most cases, market consistent valuation releases
substantial amounts of hidden reserves to risk
bearing capital
Statutory Reserves (100)
Market Consistent Reserves (best estimate risk
margin)
Nonlife Risk Margin
Nonlife Best Estimate
Life Risk Margin
Life Best Estimate
Nonlife
Life
53
Results of Field Tests Valuation
The following graph shows how market consistent
assets compare to statutory assets. In most
cases, market consistent valuation releases
substantial amounts of hidden reserves to risk
bearing capital
Statutory Assets (100)
Market Consistent Valued Assets
Nonlife Risk Margin
Nonlife Best Estimate
Life Risk Margin
Life Best Estimate
Nonlife
Life
54
Results of Field Tests Diversification
Diversification between Market and Insurance Risk
100
Figure shows 1 year risk capital due to market
and insurance risk (normalized with total 1 year
capital requirement) and diversification.
Nonlife Insurance Risk
Nonlife Market Estimate
0
Life Insurance Risk
Life Market Risk
-30
Diversification
Nonlife
Life
55
Results of Field Tests Scenarios
Effect of Scenarios Expressed as Fraction of RBC
Equity Drop -50
Real Estate Crash 1987
Crash 1987
Nikkei Crash 1990
European FX Crisis 1992
US i.r. crisis 1992
Russia Crisis/LTCM 1998
Crash 2000/2001
Global Deflation
Longevity
High Impact
No Impact
Medium Impact
56
Results of Field Tests Sensitivities
Sensitivities of life companies to different
insurance risk factors, expressed as fraction of
risk bearing capital (normalized with volatility
of risk factors)
Option Exercise
Option Exercise
Reactivation
Lapse
Reactivation
Lapse
Longevity
Longevity
Morbidity
Morbidity
Mortality
Mortality
Individual Business
Group Business
Example shows 4 different life companies
57
Results of Field Tests Sensitivities
  • Relative influence of stand-alone market risk
    factors
  • Interest rates (CHF,EUR,USD,GBP)
  • Spreads
  • FX
  • Shares
  • Real Estate
  • Others
  • Shown are standard deviations (in arbitrary
    units)
  • Correlations between above risk factors not taken
    into account

58
Contents
  • Designing a Solvency System
  • Concept of the Swiss Solvency Test
  • The SST Standard Model
  • Experiences from the Field Tests
  • Internal Models
  • Definition of an Internal Model
  • The Scientific Method
  • Acceptable and Unacceptable Models
  • Review of Internal Models
  • Group Aspects

59
Internal Models
A model is a framework to discuss economic
capital The point of the model is not (solely)
the calculation of economic capital but to have a
common framework for discussion of risks, of
dependencies, of links between different areas of
the business etc.
  • A model consists of
  • Methodology Assumptions, models, mathematics,
    mapping of the real world to a conceptual
    framework,
  • Parameters estimates, mortality tables, claim
    size estimates,
  • Data Position data, data on financial
    instruments, insurance policies,
  • Implementation Software code, IT platforms, data
    warehouses,
  • Processes Testing, back-testing, falsification,
    plausibilisation, estimation,

60
Internal Models Problems
When allowing internal models for target capital
calculation, the problems a regulator faces are
  • How to ensure that the results are comparable
    between different companies
  • How to ensure, that a company is not punished if
    it models risks more conscientiously than its
    peers
  • How to be able to distinguish between acceptable
    and not acceptable models
  • How to be certain that a model is deeply embedded
    within a company

61
Acceptable Models The Scientific Method
There are limits on what a regulator can demand
  • Model verification is impossible
  • Falsification is in many cases unpractical
  • The scientific method can not be formalized.
    There can be no set of guidelines codifying the
    model approval process
  • We need to accept that some properties of a model
    can not be proven statistically (e.g. some
    dependency structures, some parameters)
  • Models can, however, be persuasive

Therefore
  • Develop a set of model requirements any internal
    model needs to satisfy to be accepted by the
    regulator
  • Supplement the model requirements by guidelines
    encouraging a process within a company so that
    models go through an appropriate internal review
    process (Pillar 2 and 3)

62
Internal Models
Even worse than having a bad model is having any
kind of model good or bad and not
understanding it
The review of internal models will focus strongly
on how internal models are embedded within
companies and how they are understood on
different levels
  • Understanding of the underlying methodology,
    assumptions and limitations by the board, the
    CEO, the CRO, the actuaries etc.
  • Quality of documentation, reports etc
  • Use of the internal models by the company, e.g.
    for capital allocation, performance measurement
    etc.

63
Internal Models Public Transparency
The public disclosure requirements on internal
models should be principles based. The amount of
information to be disclosed should be based on
the principle that a knowledgeable person can get
a reasonably good impression on the basic
methodology of the internal models as well as on
the major design decisions. In particular a
description of the following main features should
be provided
  • valuation methods (for assets and liabilities)
  • risk measure
  • criteria for the choice of parameter values and
    distribution functions
  • major scenarios and risk factors and the
    assumptions on their dependencies
  • aggregation methods
  • embedding into the company's risk management
    processes
  • scope of the model and which relevant risks are
    not quantified.

64
Contents
  • Designing a Solvency System
  • Concept of the Swiss Solvency Test
  • The SST Standard Model
  • Experiences from the Field Tests
  • Internal Models
  • Group Aspects
  • Diversification
  • Modelling of Groups

65
Scope of Regulatory Models Group
Subsidiaries Can be in all parts of the world,
home country regulator can not calibrate easily
(if at all) a standard model to different risk
profiles. Mix of legal entity risk to risks
emanating from subsidiaries is widely varying
from group to group. Capital flow between
subsidiaries and parent is restricted.
Risk specific standard model for group is
extremely difficult to develop since in addition
to legal entity model restrictions on fungibility
of capital need to be taken into account
Group
Subsidiary
Subsidiary
Subsidiary
Parent Company Standard model can be calibrated
using local, country specific statistics and
models
Legal Entity
Branch
Parent Company
Branch
Risk specific standard model for legal entity is
very difficult to develop
Risk specific standard model is feasible
Branch
Branch
Branches Can be in all parts of the world, home
country regulator can not calibrate easily (if at
all) a standard model to different risk profile.
Mix of parent country risk to risks emanating
from branches is widely varying from company to
company
Capital can flow (nearly) freely between branches
and parent company and legal entity can be
considered to be one risk-entity. Diversification
between parent and branches.
66
Group Diversification
A group is defined not only by its legal
structure but also by its web of intra-group
capital and risk transfer instruments
Risk reduction due to group effects
Intra-group risk and capital transfer instruments
allow group-level diversification to be realized
and allocated to legal entities
Group Level Diversification
Legal Entity 3
Limited fungibility of capital due to regulatory
restrictions have to be considered
Group
Legal Entity 1
Legal Entity 2
Intra-Group Capital and Risk Transfer Instruments
  • Intra-group Retrocession
  • Guarantees
  • Participations
  • Dividends
  • Loans
  • Issuance of surplus notes
  • securitization of future cash flows / earnings
  • sale / liquidation of a business

Capital and risk transfer instruments can only be
considered if they are legally binding and
acceptable to the regulators involved
67
Group Diversification Possible Approaches
Darwinistic Group SST Approach
One group one balance sheet
Rational Group
The group is assumed to support or let go of
legal entities based on legally enforceable risk
and capital transfer instruments and, where those
not exist, according to some rational strategy,
amenable to modeling. Rational behavior has to be
modeled using some utility function based on cost
or benefit of legal entities going into run-off
or being supported in case of financial problems
The group is assumed to always support its legal
entities even if no formal guarantees or
obligations exist The risk that a group will not
support its legal entities or that a legal entity
has to support the group is captured by
regulators via group risk
The group is assumed to transfer capital only via
legally enforceable capital and risk transfer
instruments. Diversification is transported to
and from legal entities only via formal, legally
enforceable risk and capital transfer instruments
Regulator assumes that capital flows only via
existing guarantees and obligations Group risk is
to a large part taken into consideration in
assumptions
68
Group Diversification
Within the SST, group diversification is the
effect, legally enforceable group risk and
capital transfer instruments have on required and
available capital
Change due to risks ceded
Change due to contingent capital issued
Change due to contingent capital received
Change due to risks assumed
Allocated group diversification
Target capital net
Target capital gross
Target capital after allocation of group
diversification
69
Interesting Problems for Actuaries
  • Group issues
  • How to model the rational strategy of a group
  • Optimizing structure of a group
    (branches/subsidiaries and web of risk and
    capital transfer instruments. How to set risk
    and capital transfer?
  • Internal Models
  • Improving on methodology of internal models
    develop consistent firm-wide economic models
  • Modelling the strategy and risk during a longer
    (gt1 year) time horizon
  • Allocation of capital
  • Other issues
  • Optimizing ALM using sophisticated financial
    products
  • Integrating different fields (mathematics,
    finance, capital management, accounting, IT, risk
    management,)
  • Increased need to be able to communicate with
    different stakeholders (CEO, CRO,CFO, analysts,
    regulators, )

70
For More Information
  • Philipp Keller Philipp.Keller_at_bpv.admin.ch
  • 41 31 324 9341 / 41 76 488 3141
  • Thomas Luder Thomas.Luder_at_bpv.admin.ch
  • 41 31 325 0168
  • Mark Stober Mark.Stober_at_bpv.admin.ch
  • 41 31 323 5419
  • Web-Links
  • www.bpv.admin.ch
  • www.sav-ausbildung.ch (-gt documents)

71
Notation
A(0) market value of assets at t0 UPR unearned
premium reserve (at t0) P estimate for premiums
earned during year K estimate for costs during
year RI Asset returns during year
(r.v.) DCY(1) discount factor at t1 for the CY
claims (r.v)
r1(0) risk free interest for one year duration at
t0 SCY claims during year (Current Year),
r.v. DPY(1) discount factor for PY-claims at t1,
r.v. dPY(0) discount factor at t0 RPY(0) best
estimate of PY liabilities at t0 CPY RPY(0)
re-evaluation of RPY(0) at t1 (r.v.), (
(1 - CPY) RPY(0) run-off result)
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