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Philipp Keller, Federal Office of Private Insurance

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Title: Philipp Keller, Federal Office of Private Insurance


1
Supervisory Framework for Risk Assessment and
Risk-based Solvency
  • Philipp Keller, Federal Office of Private
    Insurance
  • FSI, 28 April 2006

2
Contents
  • Global Regulatory Trends
  • Global Tendencies
  • Regulatory Initiatives
  • Risk Management
  • Risk Based Solvency Models
  • Swiss Solvency Test
  • Internal Model
  • Group Effects
  • Appendix

3
Global Regulatory Tendencies
Still some loss making long-tail business in the
books (life and non-life) Smaller investment
profits Scarce capital
Reliance on investment profits Acceptance of
negative technical results to obtain cash to
invest in market Risk management often no issue
Explicit requirements on risk management,
risk-based capital requirements, transparency
Some fixed rules, limits, prudence
Self-regulation
Strengthening of supervision
Stock market boom
Crash
Today
Rule-based
Principle-based
time
Competition
Liberalization international expansion
Cartels Build-up of hidden reserves
Possibly more volatile results, better ALM,
possibly different business models
4
Global Regulatory Tendencies
There are costs and risks to a program of action,
but they are far less than the long-range risks
and costs of comfortable inaction John F. Kennedy
In the past, insurance supervisors but also
insurance companies were not sufficiently aware
of economic reality
  • The valuation of assets and liabilities were not
    adequate for an analysis of risk
  • The artificial smoothing of results often made
    companies and supervisors inclined to comfortable
    inaction
  • An adequate risk quantification was perceived by
    some to be too complex and too onerous

The financial crisis of 2000/2001 has shown to
all that the insurance industry was more exposed
than previously thought and both insurers and
regulators saw the need for a more adequate, risk
based supervisory framework ? many regulators
(UK, NL, CH,) and the EU have started
initiatives to develop more risk based
supervisory models
5
Regulatory Initiatives
Banking
1996
1988
1999
2007
1980
Market Riski Amendment
Impleme4ntation foBasel II
Basel Accord
Start of Basel II
CBOT SPAN
SEC VaR Measure
European
1947
1957
1961
1973
1979
1997
2002
2003
2001
2006
2005
Campagne publishes reports on life and nonlife
solvency assessment
KPMG Report Sharma Report
1. EU Nonlife Directive
Muller report
1. EU Life Directive
CEIOPS Established
Start of Solvency 2
CEIOPS EQIS2
CEIOPS QIS1
International
1992
2000
1985
2004
2005
2006
1953
1998
Canadian RBC System
FSA Realistic Balance Sheet
Finalnd RBC
US Life RBC
Australia RBC
Singapore RBC
UK ICA, NL DST
Swiss SST
Canada Life DST
Canada PC DST
6
Contents
  • Global Regulatory Trends
  • Prudential Supervision and Risk Management
  • Risk Management
  • Prudential Supervision
  • Risk Based Solvency Models
  • Swiss Solvency Test
  • Internal Model
  • Group Effects
  • Appendix

7
Prudential Supervision
Prudential Supervision aims to systematically
evaluate the risk profile and the risk bearing
capacity of the supervised entities. Finnish
Financial Supervisory Authority
What prudential supervision is about is helping
protect other people from the failure of the
institution by trying to ensure the institution
is adequately run. An adequately-run institution
needs to know why its in business. It need s to
have a strategy and some idea of where its
revenues will come from. It needs to know what
kind of risks it faces and, preferably, to try to
measure them. It needs to know what kinds of
risks it wants to face and take measures to
eliminate the rest. And it needs to have some way
of telling how much capital it needs to deliver
an acceptable risk-adjusted return to
shareholders Howard Davis, Chairman, Financial
Services Authority, UK
Prudential supervision is not only about
quantifying insurers risks, but to give
incentives so that the companies themselves
manage their risks appropriately, i.e. have an
adequate risk management and corporate governance
8
Risk Management
Wir müssen wissen. Wir werden wissen. David
Hilbert
Risk management is responsible for identifying,
assessing, analyzing, quantifying and then
transferring, mitigating or accepting of
risk For risk management to be effective, there
needs to be a risk culture such that senior
management wants to know and risk management is
able to tell the truth about the risks Senior
management and the board have to ensure that
there is a honest dialog and transparency
regarding risks within the company Risk
management is not solely about control but about
confronting issues and uncomfortable truths
openly and honestly
A risk based supervisory framework should be such
that it fosters a climate in the market where an
appropriate risk culture and risk management is
rewarded ? principles instead of rules ?
responsibility with senior management ?
transparency and trust in market and in regulator
9
Risk Management
Possible set-up of risk and capital management
within an insurance company many different
organizational structures are possible
Capital
Dividends
Equity
Senior
Hybrid
Contingent
Board
CFO
Capital Management
Risk Capacity
market, credit risk
Risk Appetite
Risk and capital management, reinsurance
Claims Payment
Under-writing
Assets
CRO
CIO
Reserving
ALM
Appointed Actuary
market, credit risk
Pricing Actuary
credit, insurance risk
insurance risk
Liabilities
Sales
Reinsurance
Capital Market
Insurance Market
external
internal
Securitization,
Intra Group
Portfolio Swaps
Traditional,
Premium, Future Profit
Coinsurance,
Finite
10
Risk Management
Warren Buffetts three key principles for running
a successful insurance business
  • They accept only those risks that they are able
    to properly evaluate (staying within their circle
    of competence) and that, after they have
    evaluated all relevant factors including remote
    loss scenarios, carry the expectancy of profit.
    These insurers ignore market-share considerations
    and are sanguine about losing business to
    competitors that are offering foolish prices or
    policy conditions.
  • They limit the business they accept in a manner
    that guarantees they will suffer no aggregation
    of losses from a single event or from related
    events that will threaten their solvency. They
    ceaselessly search for possible correlation among
    seemingly-unrelated risks.
  • They avoid business involving moral risk No
    matter what the rate, trying to write good
    contracts with bad people doesn't work. While
    most policyholders and clients are honorable and
    ethical, doing business with the few exceptions
    is usually expensive, sometimes extraordinarily
    so.

February 28, 2002, Warren E. Buffett
  • An insurance regulator should set incentives
    such, that good risk management practices are
    rewarded
  • setting transparent requirements
  • putting responsibility to the board and senior
    management
  • Enforce requirements consistently

11
Prudential Supervision Pitfalls to Avoid
A regulator has to be careful not to give
incentives for secondary risk management of
supervisors
Secondary Risk Management the preoccupation of
risk managers with managing their own risks. This
can lead to a culture of risk aversion. Symptoms
are that disclaimer paragraphs become longer than
the expert opinion, a proliferation of risks
which are considered in order to be able to cover
all bases, the perception that all risk are
unacceptable and a preoccupation with residual,
ill-defined risk. (based on The Risk Management
of Everything Rethinking the politics of
uncertainty, Michael Power, Demos 2004)
  • Symptoms of secondary risk management in
    supervision
  • The insistence on limits on investments and
    products
  • The fear of transparency, allowing comfortable
    inaction
  • An obsession with formalities rather than
    substance
  • The fear and rejection of all things new and
    unconventional

Secondary risk management has to be fought with
transparency of the economic state of the
companies but also of the regulatory requirements
and a continuing, public engagement of the
supervisors with all stakeholders
12
Prudential Supervision Pitfalls to Avoid
Risk management is crucial, however, there are
some pitfalls to avoid
The Regulation of Everything Regulation should
concentrate on relevant risks Self-regulation and
market forces should have their place The Myth of
Auditability Audits should not be used to
abrogate responsibility Over-reliance on
auditability can lead to check-box mentality both
within the industry and the regulator
Limits of Quantification Residual risks (e.g.
operational risks) can become blown up all out of
proportion Due to lack of data and clear
concepts, pseudo-quantifications are used for
capital requirements Dangers of Secondary Risk
Management Excessive reflection on risks can lead
to the perception that danger lurks everywhere
Risk management should deal with a companys
risks, not manage their own risk Excessive
Internal Control Excessive internal control can
lead to a bureaucratic, risk averse company
13
Principles vs Rules for Risk-Based Solvency
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
Principle-based
Objective
Company specific risk-based solvency assessment

Rule-based
Objective
Rule based approach does not allow truly company
specific risk assessment (or the set of rules
becomes huge and Byzantine)
Attained result deviates from true company
specific solvency requirement, depending on how
well rules capture the situation of the insurer
14
Contents
  • Global Regulatory Trends
  • Risk Management
  • Risk Based Solvency Models
  • Capital Models
  • Risk Based Solvency Frameworks
  • Scope
  • Time Horizon
  • Risk Definition, Classification, Risk Measures
  • Valuation Economic, Fair Value vs. Amortized
    Cost
  • The Market Value Margin
  • Risk Bearing Capital Risk as Change of RBC
  • Standard Models Typology
  • Swiss Solvency Test
  • Internal Model
  • Group Effects
  • Appendix

15
Capital Models
  • Most capital models and solvency models consist
    of two main parts
  • A valuation V(.) is a mapping from the space of
    financial instruments (assets and liabilities) in
    R
  • V A L ? R, where A L is the space of all
    assets and liabilities
  • A risk measure rm(.) of a random variable rm G
    ? R

Necessary capital C for risk is quantified by the
risk measure of the change of risk bearing
capital over a given time horizon (e.g. 1
year) Risk bearing capital is defined as value
of assets V(A) less value of liabilities V(L),
where value is generally market value. Let
RBC(k)V(A(k))-V(L(k)) be the risk bearing
capital at time k. Then
The mathematical set up is slightly different for
multiperiod models
Crm( RBC(t) RBC(0) )
Risk bearing capital at time t random variable
Risk bearing capital at time 0 known
16
Capital Models
  • An economic capital model should be consistent
  • between valuation and risk quantification and
  • between the valuation of assets and valuation of
    liabilities

Often V1(.) A ? R and V2(l) L ? R are used i.e.
the valuation of assets and liabilities are
different functionals, which are not necessarily
consistent.
  • Examples
  • Solvency 1 V1(.) is a mix of market value and
    book-values, V2 is basically unspecified
    (undiscounted, prudent etc.)
  • Solvency 2 V1(.) is market value, V2(.) is
    discussed to be 90 quantile of the ultimate of
    the liabilities
  • SST V1(.) is market value, V2(.) is best
    estimate cost for of future regulatory capital

Consistency requirement for valuation If a l,
a in A, l in L, then V(a) ? V(l) Bad example A
pure endowment insurance is close to a ZCB.
However, the market value of a ZCB can be far
away from its statutory value
17
Risk Based Solvency Frameworks
Solvency Framework
Quantification
Valuation
Risk Measurement
Scope
Legal Entity
Group
Risks
Risk Measure
Time Horizon SCR
Principles
Market Consistent
Prudent
1 year
Multi-year
Group Risk
Consolidated
Observable
Assets
Liabilities
VaR
Mathematical Framework
CRTs only
CRTs only
TailVaR
Market Prices
others
Unobservable
Market
Credit
Amortized cost for bonds
Undiscounted for PC
Liabilities
Assets
Insurance
Internal Models
Standard Models
Prudent discount rate at time of sale
Operational?
Mix of book value, market value
Mark to Model
MVM
Others?
Proxy
Scope
Prudent assumptions
No recognition of derivatives etc.
Scope
Type
Cost of Capital
LoB
Parallel run with standard models
Quantile (?)
Quantile?
Legal Entity
Life
Factor
Group
Others?
Stand-alone run
PC
RBC
Mandatory vs facultative
Health
Scenario
RI?
18
Risk Based Solvency Frameworks
There are some unique challenges when developing
regulatory capital models
  • They need to be applicable to a wide range of
    companies
  • They should be flexible in order to allow
    adaptation to new risks
  • They should be close to companies internal
    models
  • Their underlying principles should be transparent
  • They should be easily recalibrated if risk
    factors change (e.g. financial market risk)
  • They should not be so complex as to inhibit use
    of internal models
  • They should not be so simple as to not allow the
    use of partial model as a stepping stone for
    smaller companies to full internal models

The art of defining a regulatory capital model is
to find an optimal solution fitted to the
specific insurance market
19
Scope of Regulatory Models
Subsidiaries Can be in all parts of the world,
home country regulator cannot 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
Branch
Parent Company
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 cannot 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.
20
Time Horizon
The time horizon of 1 year used by most internal
models and supervisory frameworks is not natural
but a compromise
  • A time horizon of one year is short enough that
    asset and business strategy need not necessarily
    be modeled assume that asset and liability
    composition at the end of one year is more or
    less as at the beginning of the year
  • Since solvability requirements (in theory) have
    to be fulfilled at each point in time a time
    horizon of one year is short enough so that
    satisfying the solvency requirement only at the
    end of each year is a reasonable approximation to
    a continuous model
  • However, the are also disadvantages to a one year
    time horizon
  • Diversification over time is limited
  • During one year many things can happen
    (strategies can change, assets rebalanced etc. ?
    SST requires to do a recalculation if risk
    situation has changed substantially

21
Risk
Risk In the abstract, used to indicate a
condition of the real world in which there is a
possibility of loss also used by insurance
practitioners to indicate the property insured or
the peril insured against. IAIS Glossary of Terms
An investors initial portfolio consists of
positions Ai, 1iI, (possibly with some
institutional constraints such as the absence of
short sales and a congruence for each currency
between assets and liabilities). The position Ai
provides Ai(T) units of currency i at date T. We
call risk the investors future net worth sum
eiAi(T) (ei denotes the random number of units
of currency 1 which one unit currency i buys at
time T.) Coherent Measures of Risk, Artzner,
Delbaen, Eber, Heath
Risk is the chance of something happening that
will have an impact upon objectives. It is
measured in terms of consequences and likelihood.
Australian and New Zealand Standard on Risk
Management
22
Risk Regulatory Treatment of Risks
Relevant for Regulatory Risk Capital
Relevant for Reserving
Irrelevant for Capital Requirements
23
Risk Classification (Example SST)
Total Risk
Liquidity Risks
Group Risks
Insurance Risks
Operational Risks
Financial Risks
quantitatively
Credit Risks
Market Risks
qualitatively
PC
Life
Interest Rates
Defaults
Capital Mobility
Equity
Migration
Group Internal Risk
Premium Risk
Biometric
Reinsurers
Shares
Group Behavior Risk
Real Estate
Mortality
Concentration
Small Claims
Regulatory Risks
Alt Invest.
Longevity
Large Claims
Model
Morbidity
Catastrophes
FX
Reactivation
Spreads
Policyholder
Reserve Risk
Concentration
Lapse
Other options
Model
24
Risk Measures Expected Shortfall vs VaR
The Expected Shortfall of a random variable X to
the confidence level 1-? (ES?) is given by ES?X
1/a 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 might be 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

25
Valuation 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

26
Valuation Market Value vs. Amortized Cost
  • Economic Consequences of Amortized Cost
  • Amortized cost only makes (marginally) sense when
    bonds are truly held to maturity, but then
  • investment opportunities vanish
  • if market value of bonds is below amortized cost,
    any selling of a bond leads to realization of a
    loss
  • if assets have to be sold, recently bought bonds
    or equities have to be used to keep realized
    losses under control
  • if business decreases, cash outflow might have to
    be served by bonds, leading to a realization of
    losses
  • In an amortized cost world, companies have an
    incentive to write loss making business in order
    not to be forced to sell bonds, exacerbating
    thereby underwriting cycles, in particular when
    interest rates rise
  • In addition, the amortized cost framework is
    difficult if not impossible to extend to
    derivatives, making it impossible to take into
    account sophisticated hedging strategies
  • If a company becomes insolvent, the portfolio
    cannot be sold to second insurer if economic
    worth of the company is negative under market
    consistent valuation even if under an amortized
    cost the valuation looks fine

Amortized cost framework for assets gives
incentives for perverse risk management
  • Foreclosing of investment opportunities
  • Cash flow underwriting
  • Downward spiral when business contracts

Amortized cost framework for assets is difficult
to extend to derivatives and more complex
instruments
27
Valuation Market Value vs. Amortized Cost
Economic Consequences of Amortized Cost (cont.)
  • Under an amortized cost framework, insurance
    liabilities should be valued consistently
  • Liabilities then cannot depend on (current)
    interest rates
  • valuation undiscounted or
  • discounted at time of product sale
  • implicit prudence can vanish quickly, e.g. when
    interest rates decrease
  • discounted using the expected asset return
  • making liability values depend on assets held was
    called by M. Taylor, Chairman of WM Smith, one
    of the weirdest emanations of the human mind
  • Use of prudent assumptions (e.g. on mortality,
    morbidity etc.)
  • again, implicit prudence tends to vanish quickly
    without anyone realizing it
  • The amortized cost framework generally does not
    take into account embedded options, giving
    incentives to add optionalities indiscriminately
    to increase sales without valuing them

Amortized cost framework for liabilities gives
incentives to add optionalities without
provisioning and implicit prudence vanishes
quickly
Achieving internal consistency between asset and
liability valuation is difficult if not impossible
Amortized cost framework often gives conflicting
signals to market consistent view
  • Hedging is punished
  • Incentives to have huge duration gap rather than
    proper ALM

28
Market Value Margin
  • Asset valuation Market consistent
  • Market price if traded
  • Marked to Model if not traded

Liability valuation How to define if liability
valuation has to be consistent with asset
valuation?
Problem Most liabilities are not actively traded
? Marked to Model
Asset Valuation Fair Value the price at which
an asset or liability could be exchanged in a
current transaction between knowledgeable,
unrelated willing parties. The price is an
estimate in the absence of an actual exchange
(FASB)
At what price could an insurance liability be
transferred to a willing buyer (e.g. to an
insurer)?
Definition The market value margin is the
smallest amount 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.
29
Market Value Margin Cost of Capital Approx.
What is a good proxy for the Market Value
Margin? Proposals Quantile and Cost of Capital
Approach
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
Market Value Margin the present value of future
regulatory risk capital costs 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?
30
Market Value Margin Cost of Capital Approx.
Risks considered in the MVM
t1
t2
t3
t0
Years
Risks emanating during year 2 are covered by the
cost of setting up SCR(2) CoCSCR(2) compensates
for having to finance SCR(2) during one year
Risks emanating during year 1 are covered by the
cost of setting up SCR(1) CoCSCR(1) compensates
for having to finance SCR(1) during one year
Risks emanating during year 0 are covered by the
SCR(0)
Note This approach for calculation the cost of
capital margin assumes that the portfolio
transfer occurs at the end of year 0, hence
SCR(0) does not enter calculation
31
Market Value Margin Cost of Capital Approx.
SCR(0)
Premium risk
Run-off risk
Market and credit risk
SCR(1)
Market and credit risk assuming asset portfolio
corresponds to the optimal replicating portfolio
SCR(2)
SCR(1)
SCR(T)
t1
t2
t3
t0
Years
Future SCR entering calculation of MVM at t0
32
Market Value Margin Cost of Capital Approx.
Calculation of the Cost of Capital Margin
1. calculate the capital requirement SCR(t) for
all years t until the run-off of the portfolio,
assuming no new business and assume that asset
portfolio equals to optimal replicating portfolio
(i.e. only unhedgeable risks remain for
SCR(t)). 2. calculate the capital charge, i.e.
the cost of holding the required capital, for
each projection year as the required amount of
capital multiplied by a cost of capital. 3. the
cost of capital margin is then determined as the
present value of the (discounted) capital charges
as projected over the full time horizon of the
liabilities
Step 1 is the difficult one. In theory, one needs
to do a full solvency test for each year until
the portfolio has run-off. In practice
simplifications can be employed
  • Determine a proxy p(t) for future SCR(t) which is
    easier to calculate than SCR(t), i.e. the
    best-estimate of liabilities at time t.
  • Then approximate SCR(t) using the proxy p(t).
  • Show to the supervisor that the proxy is
    reasonable

33
Market Value Margin Cost of Capital Approx.
Example
  • Assume that the best estimate of liabilities
    BE(t) is a good proxy for future SCR(t)
  • Determine SCR(0) without current year risk
    (premium risk) and assume assets are optimal
    replicating liabilities ? only unhedgeable
    financial market risk needs to be considered.
  • Call this value SCR(0)
  • Then set SCR(t)SCR(0)/BE(0)BE(t), t1,,T

SCR(3)SCR(0)/BE(0)BE(3)20/20077
34
Market Consistent Valuation Definition
  • Advantages of the Cost of Capital Margin
    Approach
  • The CoCM is defined as a proxy for the MVM,
    therefore it fits into a market consistent
    valuation framework
  • It can be defined consistently for both life and
    PC companies
  • It allows a range of calculation methods, from
    very sophisticated to simplified
  • It is congruent to the margins used by many
    companies internally (e.g. for pricing, for
    EEV,)
  • It forces companies to think about long term risk
    and capital requirements
  • For supervisors, the CoCM is easy to review

35
Economic Balance Sheet
Building blocks Market consistent (economic)
balance sheet
Free capital
SCR Required capital for 1-year risk
Risk bearing capital
Target capital
Market value of assets
Market Value Margin
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
Market consistent value of liabilities
Best estimate of liabilities
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
36
Risk as Change of Risk Bearing Capital
Building blocks
Year 0
Year 1
Probability density of the change of risk bearing
capital
Risk bearing capital
Revaluation of liabilities due to new information
Market Value Margin
Probability lt 1
New business during one year
Claims
Change in market value of assets
Average value of RBC in the 1 bad cases
Expected Shortfall SCR
Catastrophes
Market consistent value of liabilities
Smallest value of RBC in the 1 bad cases
Value at Risk
Market value of assets
Best estimate of liabilities
Economic balance sheet at t0 (deterministic)
Economic balance sheet at t1 (stochastic)
37
Regulatory Models Typology
A rough typology
Factor Models Linear combination of volume
measures
RBC Models Risk charges C1,C2, are combined
Scenario Based Models
Hybrid Models A mix of several types of
approaches
Internal Model based
38
Regulatory Models Typology
Factor Models
RBC
Scenario Based
Internal Model Based
Basel 1
GDV
SPAN
Solvency 1
MCT
CEA
Basel 2
MCCRS
FFSA
RBC (US)
CEIOPS
RBC (JP)
Lloyds RDS
RiskMetrics
MCR, APRA
ICAS
DST
ECR, FSA
SST
DCAT
39
Outlook
  • There have been great improvements in risk based
    solvency frameworks during the last years, many
    problems however are still unsolved
  • A regulator developing a risk based solvency
    framework should have in view not only the
    current knowledge and modeling capabilities but
    should base the framework on what will be
    available in a few years time
  • Risk-based solvency systems will co-evolve with
    insurance market
  • There is not one best risk based solvency system,
    but mix of rules and principle, level of
    sophistication etc. depends on the culture of
    the market
  • One should never forget that the point of a risk
    based solvency system is not only the calculation
    of target capital (or SCR) but to foster a risk
    awareness in the market (and in the regulator)

40
Contents
  • Global Regulatory Trends
  • Risk Management
  • Risk Based Solvency Models
  • Swiss Solvency Test
  • Principles
  • Standard Models Financial Market, PC
  • Cost of Capital Margin
  • Scenarios
  • Experiences from Field Test 2005
  • Internal Model
  • Group Effects
  • Appendix

41
The SST Concept Requirements
SST models and all parameters are published and
are in the public domain
  • Transparent methodology
  • The model should correspond to the ideas of the
    users
  • Easy to adjust to changing risk landscape
  • Easy integration of internal models
  • To give incentives for risk management
  • As simple as possibly, as complex as necessary

SST is modular, partial modules can easily be
changed or improved
Calculation is responsibility of management, SST
is clear and understandable for management
Not a simple factor model but a model which needs
to be adapted by each insurer to its specific
situation
42
The SST Concept
Solvency Framework
Valuation
Risk Measurement
Scope
Quantification
Legal Entity
Group
Risks
Risk Measure
Time Horizon SCR
Principles
Market Consistent
Prudent
1 year
Multi-year
Group Risk
Consolidated
Observable
Assets
Liabilities
VaR
Mathematical Framework
CRTs only
CRTs only
TailVaR
Market Prices
others
Unobservable
Market
Credit
Amortized cost for bonds
Undiscounted for PC
Assets
Liabilities
Insurance
Internal Models
Standard Models
Prudent discount rate at time of sale
Operational?
Mix of book value, market value
Mark to Model
MVM
Others?
Proxy
Scope
Prudent assumptions
No recognition of derivatives etc.
Scope
Type
Cost of Capital
LoB
Parallel run with standard models
Quantile (?)
Quantile?
Legal Entity
Life
Factor
Group
Others?
Stand-alone run
PC
RBC
Mandatory vs facultative
Health
Scenario
RI?
43
The SST Concept Principle-Based
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 desired
    objectives
  • Definition of terms and concepts so that meaning
    and possible interpretation of principles become
    clear
  • Glossary with terms and concepts
  • Guidelines help in interpretation
  • Standard Model allows use of Solvency Test also
    by small companies

44
The SST Concept Principle-Based
  • All assets and liabilities are valued market
    consistently
  • Risks considered are market, credit and insurance
    risks
  • Risk-bearing capital is defined as the difference
    of the market consistent value of assets less the
    market consistent value of liabilities, plus the
    market value margin
  • 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 market value margin
  • The market value margin is approximated by the
    cost of the present value of future required
    regulatory capital for the run-off of the
    portfolio of assets and liabilities
  • Under the SST, an insurers capital adequacy is
    defined if its target capital is less than its
    risk bearing capital
  • The scope of SST is legal entity and group /
    conglomerate level domiciled in Switzerland
  • Scenarios defined by the regulator as well as
    company specific scenarios have to be evaluated
    and, if relevant, aggregated within the target
    capital calculation

Defines Output
45
The SST Concept Principle-Based
  • All relevant probabilistic states have to be
    modeled probabilistically
  • Partial and full internal models can and should
    be used. If the SST standard model is not
    applicable, then a partial or full internal model
    has to be used
  • The internal model has to be integrated into the
    core processes within the company
  • SST Report to supervisor such that a
    knowledgeable 3rd party can understand the
    results
  • Disclosure of methodology of internal model such
    that a knowledgeable 3rd party can get a
    reasonably good impression on methodology and
    design decisions
  • Senior Management is responsible for adherence to
    principles

Defines How-to
Transpar-ency
Responsi-bility
46
The SST Concept Standard Models
SST Standard Model Standard Algorithm rather
than Standard Formula
The standard algorithm is similar to companies
internal model
  • gives incentives for risk management
  • corresponds closely to the thinking of the user
    of the model (e.g. actuaries, investment
    specialists, CROs,)
  • Allows easy use of partial internal models
  • allows easy and consistent mapping of reinsurance
    (business ceded)

Financial market Risk RiskMetrics type approach
(Covariance matrix of market risk factors) Credit
Risk Basel 2 or Credit risk portfolio models,
credit risk of reinsurers via scenario PC
Insurance Risk Distribution based (small, large
and cat claims) Life Insurance Risk Covariance
approach for life insurance risk factors
  • Companies have to determine sensitivities of
    assets and liabilities to financial market risk
    factors
  • Analyze life and PC insurance risk, determine
    company specific parameters
  • Aggregate risk using convolutions etc.

47
The SST Concept General Framework
Market Consistent Data
Mix of predefined and company specific scenarios
Standard Models or Internal Models
SST Concept
Scenarios
Asset-Liability Model
Financial Risks
Insurance Risks
Credit Risks
Aggregation Method
Target Capital
SST Report
48
The SST Concept Standard Models
  • Financial Market Risk
  • For many companies this is the most important
    risk (up to 80 of total target capital emanating
    from financial market risk)
  • Most relevant are interest rate risk, real estate
    risk, spread risk, equity risk
  • Financial market risk model does take into
    account assets and liabilities simultaneously
  • Interest rate risk is captured not via simple
    duration but over different (13) time buckets
  • 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 and
www.bpv.admin.ch
49
The SST Concept Cash Flow Based
Example Sensitivity to 2 Year CHF Yield
Asset Cash Flows
Change of present value of net cash flow
(assets-liabilities) due to change in the 2 year
CHF yield
Year
Liability Cash Flows
Year
Netto Cash Flows A-L
3
Stressed 2Y Yield
2
CHF Yield Curve
Present Value von Asset - Liabilities
1
0
50
Standard Models Asset-Liability Model
  • 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 cannot
be captured solely by a duration number Financial
instruments have to be segmented sufficiently
fine else arbitrage opportunities might be
created Modeling should be such that 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 scenarios
51
Standard Models Nonlife Model
Premium risk
Financial 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
52
The SST Concept Market Value Margin
For the SST, liabilities have to be valued market
consistently, defined as the Best Estimate
Market Value Margin The MVM is approximated using
the cost of capital approach
Reasoning for the first component The insurer
setting up the market value 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 Cost of Capital Margin (CoCM) consists of two
    components
  • a first part depending on insurance risk and
    unhedgable market risk
  • a second part depending on the illiquidity of the
    assets of the insurer

Reasoning for the second component The insurer
taking over the portfolio of assets and
liabilities should be compensated if the insurer
setting up the market value margin invested in an
illiquid asset portfolio.
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
duration for achieving the optimal replicating
asset portfolio depends on the asset mix.
53
The SST Concept Market Value Margin
CoC 6 over risk free
ES at t0 does not enter calculation of the
market value margin necessary at t0 ? risks
taken into account for 1-year risk capital and
market value margin are completely disjoint and
there is no double-counting
SCR with portfolio converging from actual to
replicating portfolio taking into account
illiquidity of assets ? Sequence of Achievable
Replicating Portfolios
SCR with optimally replicating asset portfolio
Achievable Replicating Portfolio has converged to
Replicating Portfolio
t1
t2
t3
t0
Years
SCR 1-Period (e.g. 1 year) risk capital
Expected Shortfall of risk-bearing capital
Future SCR entering calculation of MVM at t0
54
SST Concept Cost of Capital Margin
For the SST, the risk margin is defined as the
market value margin which can be approximated by
the cost of capital approach
The cost of capital margin can be simplified
using the following proxies
  • Best Estimate as proxy for residual (unhedgeable)
    financial market risk
  • Best Estimate as proxy for credit risk
  • Best Estimate for nonlife insurance risk
  • Best Estimate for savings products (for life)
  • Square Root of Best Estimate for stochastic risk
    (for life and PC)
  • Sum at Risk or PV of future claims for mortality
    and disability risk
  • Incremental effect of scenarios proportional to
    approximated SCR(t)

Companies need to show that the proxies for the
different components of SCR are reasonable
55
SST Concept Cost of Capital Margin
56
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
57
The SST Concept Scenarios
The formulation and evaluation of the scenario
should not be a compliance exercise but will
entail a detailed and comprehensive discussion
not only of primary but also of secondary and
tertiary effects.
Example A scenario Earthquake in Tokyo should
not only specify the financial impact due to loss
of life and to the collapse of buildings, but
also discuss the implication on the financial
markets (e.g. the collapse of the global
financial market for a given duration, the effect
on global markets of Japan having to rebuild the
infrastructure, etc.). Example A scenario
Dirty Bomb in European City should not only
specify the financial impact due loss of life but
should in addition discuss the impact on real
estate prices, airline travel, financial markets,
consumer confidence, long term effects on
mortality and morbidity,
  • The formulation of the scenario should comprise
  • the event occurring during the following year
  • the effects of the scenario in the future

58
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
59
Standard Models Calculations
  • Company specific calculations necessary for the
    SST are
  • Market consistent valuation of assets and
    liabilities with valuation of relevant options
    and guarantee
  • The cash flows of assets and liabilities
  • Sensitivities to different risk factors
  • Financial market risks
  • Biometric risks and Option Exercise
  • Estimation of reserving risk
  • Estimation of stochastic risk for current and
    previous year risk
  • Estimation of parameter risk for certain LoBs
  • Probability distributions of large claims for
    different lines of business
  • Aggregation (using correlations, convolutions
    etc.)
  • Evaluation of pre-specified scenarios and
    definition and evaluation of company specific
    scenarios

Company-specific parameters have to be used if
the values supplied by the regulator do not
reflect the company situation, e.g. equity
volatilities.
60
Experiences from Field Test 2005
The SST is not simple but was perceived by most
participating in the field test 2006 to be
doable. Many commented that a simplification
would make the results less relevant. The SST was
done by 45 companies, ranging from very small
insurers to large groups.
  • Skandia assesses the adequacy of its available
    economic capital annually by carrying out an
    analysis of its main risk exposures and resulting
    required capital levels according to the Swiss
    Solvency Test.
  • Skandia, Annual Report 2005

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 Metzger-versicherung
a small-to-midsized nonlife company with approx
CHF 160Mio tech. provisions
For our risk and investment strategy we need to
be able to quantify the cash flow structure and
the risk bearing capacity of our portfolios. For
this the SST is a good (although in many aspects
still to be modified and enhanced) basis. In
addition, we can use the SST to test capital
requirements for alternative investment
strategies. As we have not yet an equally well
suited internal model, the SST is for us of great
benefit. We see it as an integral part within our
ALM process. Comment by René Bühler from the
National Versicherung, a mid-sized insurance
group.
61
Results of the Field Tests Hidden Reserves
In most cases, market consistent valuation
releases substantial amounts of hidden reserves
to risk bearing capital
Nonlife
Statutory Assets (100)
Statutory Reserves (100)
Life
Market Consistent Reserves (discounted best
estimate market value margin)
Market Consistent Valued Assets
62
Results of the Field Tests Solvency Ratios
The Statutory Solvency Ratio is only a weak
predictor for the SST Solvency Ratio For nonlife
companies, Spearmans Rank Correlation is approx
0 and for life companies Spearmans Rank
Correlation is approx 0. 5
Life
Nonlife
63
Results of the Field Tests MVM
Market Value Margin / Best Estimate vs Market
Value Margin / ESRBC, based on provisional data
of Field Test 2005
0.7
MVM / Best Estimate vs MVM / 1-Year Risk Capital
Nonlife
X-axis MVM divided by best estimate of
liabilities Y-axis MVM divided by 1-year risk
capital (SCR)
Life
0.6
Life companies writing predominately risk products
0.5
0.4
0.3
0.2
Life companies writing predominately savings
products
0.1
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Market Value Margin / Best Estimate
64
Contents
  • Global Regulatory Trends
  • Risk Management
  • Risk Based Solvency Models
  • Swiss Solvency Test
  • Internal Model
  • Challenges for Supervision
  • Definition
  • Internal Models Acceptable vs Unacceptable
  • Review
  • Transparency
  • Group Effects
  • Appendix

65
Internal Models Definition
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.
  • It 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,

Some supervisors show reluctance for the use of
internal models. However, internal models have
been used since the beginning of insurance for
valuing technical provision. The difference of
calculating provisions to an internal model used
for economic capital calculation is only that the
former is often done without a formalized
algorithmic process.
66
Internal Models Challenge
  • Internal models for the SST have to be used by
  • Reinsurers (20)
  • Captives (those which have to do the SST)
    (10-15)
  • Groups and conglomerates (10-15)
  • Legal entities with substantial amount of
    business written by foreign branches (10-15)
  • Insurers, for which the SST standard model is not
    applicable (?)
  • Life insurers writing substantial options and
    guarantees linked to financial market (in
    discussion) (5-10)

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

Some small and mid-sized companies already
indicated that they will develop partial- and
full internal models in order for the SST
calculations to be better integrated within the
companies processes In addition, the
determination of technical provisions is done via
a internal model
67
Internal Models Challenge
  • For some type of insurers, models are often
    assumption driven Up to 90 of the economic
    capital requirement due to insurance risks
    emanates from assumptions and only 10 from
    historical data
  • models can often not be back-tested
  • The review has to rely less on formalized
    requirements as for VaR market risk engines
  • The assessment of models has to rely more on
    experience, comparison with similar models and
    embedding of the model within the company

The regulatory review of models will rely heavily
on discussions with quants and actuaries,
assessment of companys know-how of the model and
its limitations and public transparency
There are limits on what a regulator can demand
from internal models of insurers and reinsurers
  • Model verification is impossible
  • Falsification is in many cases unpractical
  • The scientific method cannot be formalized. There
    can be no set of guidelines codifying the model
    approval process
  • We need to accept that some properties of a model
    cannot be proven statistically (e.g. some
    dependency structures, some parameters)
  • Models can, however, be persuasive

68
Acceptable and Unacceptable Models
Acceptable Models
Unacceptable Models
  • Theory is misapplied
  • Pure statistics, no explanation
  • Hidden and unclear assumptions
  • Too many simplifications
  • The model is not tested against the real world
  • Inappropriate or stale parameters
  • The model is not sufficiently understood within
    the company
  • Clearly stated and understood assumptions
  • Clear on idealizations and simplifications
  • Transparent on which effects are neglected
  • All relevant risk factors are taken into account
  • The model relies not purely on historical data
    but aims to model the future risks using theory,
    scenarios, expert opinion etc.
  • The model is tested
  • The model is regularly challenged, and compared
    against industry best-practice

69
Internal Models Review
Even worse than having a bad model is having any
kind of model good or bad and not
understanding it
If internal models are used for regulatory
purposes, it will be unacceptable if the model is
not understood within the company
Senior management is responsible for internal
models and the review process. The review of
internal modes will be based on 4 pillars
  • Internal Review
  • External Review
  • Review by the Supervisor
  • Public Transparency.
  • There needs to be
  • deep and detailed knowledge by the persons tasked
    with the upkeep and improvement of the model
  • Knowledge on the underlying assumptions,
    methodology and limitations by the CRO, appointed
    actuary etc.
  • Sufficient knowledge to be able to interpret the
    results and awareness of the limitations by
    senior management and the board

The regulator is responsible for ascertaining
that the review process is appropriate Companies
using internal models have to disclose publicly
the methodology, valuation framework, embedding
in the risk management processes etc.
70
Internal Models Public Transparency
A little light dispels a lot of darkness. Rabbi
Schneur Zalman
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 parameters 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.

71
Internal Models
Further Development of Internal Capital Models
  • Modeling of intra-group risk and capital transfer
    instruments, allowing analysis of group structure
    on capital requirement of group and legal
    entities
  • True multi-year models, taking into account
    business and asset allocation strategy
  • Modeling of underlying, relevant risk factors on
    assets and liabilities, dependency structure will
    emerge naturally via dependency between risk
    factors rather than via correlation matrices
    between risk types
  • Set-up to allow more flexibility to analyze
    results for sub-portfolios (e.g. lines of
    business, risk types, legal entities, management
    units, sub-groups,)

72
Contents
  • Global Regulatory Trends
  • Risk Management
  • Risk Based Solvency Models
  • Swiss Solvency Test
  • Internal Model
  • Group Effects
  • Group Level Diversification
  • Consolidated View
  • Group vs. Solo Requirements
  • Group Unconsolidated
  • Appendix

73
Group Effects
Increasing Organizational Level
Different levels of diversification
Group Level
Diversification benefit similar as for branches
but reduced fungibility of capital has to be
taken into account
Subsidiaries
Legal Entity Level
Diversification benefit between different
branches geographical diversification but
interdependencies due to cats, economic drivers
and financial risks
Branches
Company Level
Diversification benefit between different LoBs
due to independence of losses but
interdependencies due to common economic drivers,
common claim events
Lines of Business
Portfolio Level
Diversification benefit within portfolios driven
predominantly by the law of large numbers
Single Risks
Increasing relative diversification benefits
Product Level
74
Group Effects
What is diversification? Consider two
portfolios A and B. Let R(A) and R(B) be the risk
capital necessary for portfolio A and B
respectively. Assume R(.) is a risk measure.
Then, if R(AB) lt R(A)R(B), i.e. if the
necessary risk capital for the combined portfolio
is less than the sum of the risk capitals
necessary for portfolio
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