1 philipp keller, federal office of private insurance brussels, 14 october 2005 swiss solvency test

1

Philipp Keller, Federal Office of Private Insurance Brussels, 14 October 2005

Swiss Solvency Test

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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

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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

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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

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Definition of Capital

Valuation

Time Horizon

Risks to Quantify

Risk Measure

Definition of Ruin

Define risk typology, decide which risks are quantified and which treated qualitatively

Define risk margin in SST: risk margin = lowest acceptable level of risk bearing capital

Decide over which time horizon risk capital needs to cover risks

Define valuation methodology of assets and liabilities

Define risk bearing capital, e.g. value of assets less best-estimate of liabilities, define which forms of capital are eligible

Define measurement of risks, e.g. Value at Risk, Expected Shortfall, etc.

Operational Implementation

In the last stage, define standard model (if necessary), details of the system, e.g. correlations vs copulas, etc.

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Implications of Principles vs Rules

Principle-based

Rule-based

Principle-based standards describe the objective sought in general terms and require interpretation according to the circumstance.

Objective

Objective

Risk Based Capital Requirement

Companies tailor approach such that clearly stated objective is attained

Rule based approach does not allow truly company specific risk assessment

Attained result depends on how well rules capture the situation of the insurer

Objective can be attained if companies interpret principles faithfully. The objective is defined by a (theoretically) correct quantification and allocation of group diversification

=

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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

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Principles Definitions

Guidelines

• Principles define concisely the objectives

• Definition of terms and concepts so that meaning and possible interpretation of principles become clear

Glossary

The SST is defined not by the Standard Model but by underlying principles

Core of the Solvency Test

Standard Model

• Guidelines help in interpretation

• Standard Model allows use of Solvency Test also by small companies

The SST Concept: Principle-Based

The more laws and order are made prominent, the more thieves and robbers there will be, Lao-tzu

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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 insurer’s 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

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Risk Measures: Expected Shortfall

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:

- ES1%=average one-in-a-hundred-years loss

- VaR1% = the loss that is in 99-out-of-a-100-years not exceeded

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]

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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 management’s 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

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The SST Concept: The economic view

Market Consistent

Assets Liabilities

Best-Estimate Provisions

Risk Margin

Market consistent provisions

Risk bearing capital

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

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

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The SST Concept: The SST in a Nutshell

TC = ES[ΔRBC] + RM

Risk MarginChange of Risk-Bearing Capital

Target Capital

Expected Shortfall

Covers risks emanating during a one-year time horizon

Risk margin should be sufficient to allow a run-off or portfolio transfer

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The SST Concept: Risk Margin

Risk Margin: to cover policyholders against risks emanating beyond 1 year

Risk Margin

Best Estimate

Provisions

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 P&C liabilities, discussed within Solvency 2.

• 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

• 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.

The Risk Margin and SCR/ES cover different risks:

There should not be double-counting between SCR and Risk Margin

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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?

-> Assumptions on the evolution of the asset portfolio are necessary

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Key Idea:

Liabilities: Assume no new business

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.

• 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.

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ES with optimally replicating asset portfolio

ES with portfolio converging from actual to replicating portfolio taking into account illiquidity of assets Sequence of Achievable Replicating Portfolios

Years

ES: 1-Period (e.g. 1 year) risk capital = Expected Shortfall of risk-bearing capital

t=1 t=2 t=3

Achievable Replicating Portfolio has converged to Replicating Portfolio


t=0

ES at t=0 does not enter calculation of the risk margin necessary at t=0 risks taken into account for 1-year risk capital and risk margin are completely disjoint and there is no double-counting

Future ES entering calculation of risk margin at t=0

t 2

TC=ES ΔRBC(1) +sp ES ΔRBC(t)

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Risk Margin

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Risk Margin / Best Estimate

Ris

k M

argi

n /

1 Y

ear

Ris

k C

apita

l

Risk Margin / Best Estimate vs Risk Margin / 1-Year Risk Capital

Nonlife

Life

Risk Margin / Best Estimate vs Risk Margin / ES[RBC], based on provisional data of Field Test 2005

Life companies writing predominately risk products

Life companies writing predominately savings products

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Change in Risk Bearing Capital

Assets Liabilities

RBC(0) RBC(1)

RBC(0) should be such that at the end of the year, even when a large loss with P<1% occurs, the insurer‘s available RBC covers (on average) still the risk margin

Investment profit (above risk-free) + known payoffs (deterministic)

New business during one year (deterministic)

Changes in value of assets (stochastic)

Changes in value of liabilities + claims during 1 year (stochastic)

Assets Liabilities

Year 0 Year 1

State 1.1 known / deterministic

State 31.12 unknown / stochastic

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

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(0)1

(0)1

( (0) )1

IE R rA UPR P K

r

(1)

(0)1

( )1

CY

CY

E DP K E S

r

)0()0(

1

)1()1(

)0(1

)1()1(

)0(1 1

][][

1

][))()0((

1

][PY

PYPYCY

CYCYII Rr

DEDSE

r

DEDKUPRPA

r

RER

RBC(0)RBC(1)

Year 0 Year 1

)0()0()0(

1

)1(

)0(1

)1(

11PYPYPY

PYCYCY

CY RdCr

DESES

r

DE

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Expected asset return over risk-free

Insurance risk (deviation of technical result from expectation)

Expected insurance (technical) result

(0)1

(1)(0)

1RBC

RBCr

CYCY SEr

DEKP

)0(1

)1(

1)(

(1) (1)

(0) (0)(0) (0)

1 11 1CY PY

CY CY PY PY PY

E D E DS E S C d R

r r

(0)1

(0)1

( (0) )1

IE R rA UPR P K

r

(1) (1) (1) (1)(0)

(0) (0) (0)1 1 1

[ ][ ] [ ]( (0) ( ) ) [ ]

1 1 1CY CYI I PY PY

CY PY

D E DR E R D E DA P UPR K E S R

r r r

ALM risk

Current Year Risk

Previous Year Risk

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Expected Shortfall of Risk Bearing Capital

Definition. An insurer satisfies the SST when:

ES[RBC(1) 0]≥ rm;

where rm denotes the risk margin.

RBC(1) = (rbc(0) + r(0) + p - k)(1 + RI ) - S(1) - R(1)

RBC(1) in function of terms known at t=0:

rbc(0)=a(0) - R(0): Risk-bearing capital at t=0, a(0): assets at t=0, R(0): liabilities at t=0 (best-estimate)

p: Expected premium during [0,1] r(0): Liabilities at t=0

(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 t=1 Notation simplified

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RBC(1) = (rbc(0) +r (0) + p - k)(1 + RI ) - S(1) - R(1)

ES[RBC(1) 0]=ES[(rbc(0) + r(0) + p - k)(1+RI) - S(1) - R(1)]

= ES[(rbc(0) + r(0) + p - k)(1 + r0-r0+RI) - S(1) - R(1)]

rbc(0)(1+r0)+ES[r(0)+p-k)(1+r0-r0+RI )

+rbc(0)(RI-r0)-S(1)-R(1)] ≥rm

rbc(0) ≥-ES[(r(0)+p-k)(1+r0-r0+RI )

+rbc(0)(I-r0)-S(1)-R(1)] ≥rm

0 0

(a(0)-upr+p-k)(1+I)-S(1)-R(1) rmrbc(0) -ES -(a(0)-upr+r(0)) +

1+r 1+r

Expected Shortfall of Risk Bearing Capital

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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

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The SST Concept: General Framework

SST Concept

Models Scenarios

Aggregation Method

Fin

anci

al

Ris

ks

Cre

dit

R

isks

Insu

rance

R

isks

Standard Models or Internal Models

Mix of predefined and company specific scenarios

Asset-Liability Model

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

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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%

•DeflationFor SST, RiskMetrics type model with given risk factors and associated volatilities and correlation matrix is used together with scenarios

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 shouldn’t force companies to disinvest totally from certain investment classes (e.g. shares, private equity)

Standard Model: Market Risk

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Standard Model: Market Risk

CHFEUR

USDGBP

Spreads•AAA•AA•A•BAA

Equity

•Shares•CHF•EUM•USD•GPB•JPY

•Real Estate•IAZI•Commercial•Rüd Blass•WUPIX A

•Hedge Funds

•Private Equityi.r. time buckets:1,…,10, 15,20,30+

75 Risk Factors:•4*13 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

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Asset Cash Flows

Liability Cash Flows

Year

Year

Netto Cash Flows A-L

Present Value von Asset - Liabilities

Change of present value of net cash flow (assets-liabilities) due to change in the 2 year CHF yield

The SST Concept: Cash Flow Based

0

1

2

3

CHF Yield Curve

Stressed 2Y Yield

Example: Sensitivity to 2 Year CHF Yield

- =

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Standard Model: Nonlife

Normal claims Large claims

Compound Poisson

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

Method of Moments with prescribed correlation matrix Lognormal

Reserving Risk

Discounted cash flows

Assets: bonds, equity, …

CF -> i.r. sensitivities

Asset Model: Covariance/Riskmetrics

approach

Normal

Premium risk Market risk

… …

…

Further aggregation with scenarios

Aggregation by Convolution

Lin

es

of

Bu

sin

ess

Aggregation by Convolution

First two moments of premium risk (normal claims) and reserving risk are aggregated using correlation -> two moments defining lognormal

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Standard Model: Insurance Part

(0) (0) (0)( 1)CY CY PY PY PYP K d S d C R

Assumed deterministi

c

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)

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Standard Model: CY Risk Normal Claims

Coefficient of Variation for a single claim in LoB i

22 param 2i i ,2

due to Parameter Riskdue to Stochastic Risk

Var[ ] 1CoeffVar CoeffVar ( CoeffVar( ) 1)

E[ ]

Ni

i jNi i

CY

C

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

, , ,1 , 1

2

i , , , j ,1 , 1

Var Cov ,

CoeffVar E (CoeffVar E ) (CoeffVar E )

NS NS NS NSCY CY i CY i CY j

i i ji j

NS NS NSCY i i j i CY i CY j

i i ji j

Var S S S S

S S S

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

Parameter RiskLoB i CoeffVari CoeffVar(Yi,j) CoeffVar(Yi,j)

Split at CHF 1 Mio Split at CHF 5 MioMFH 3.50% 7.00 10.00MFK 3.50% 2.50 2.50Sach 3.00% 5.00 8.00Haftpflicht 4.50% 8.00 11.00UVG 3.50% 7.50 9.50Unfall ohne UVG 3.00% 4.50 5.50Kollektiv Kranken 3.00% 2.50 2.50Einzelkranken 5.00% 2.25 2.25Transport 5.00% 6.50 7.00Luftfahrt 5.00% 2.50 3.00Finanz und Kaution 5.00% 5.00 5.00Other 5.00% 5.00 5.00

Stochastic RiskFor 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

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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

, ,1

iN

LC LCCY i i j

j

S Y

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

.1

,0

)()( ,,

yy

y

yYPyF i

GSji

GSjiY

Pareto Distribution:

Smallest large claim comsidered: β threshold parameter

Shape parameter α: The smaller , the more heavy-tailed. If ≤k, k-th moment does not exist anymore

Table with standard parameters for companies lacking sufficient data

For numerical calculations the cut-off point of the distribution is very important

LoB b=1 Mio b=5 Mio Cut off PointMFH 2.50 2.80 I llimitéMFK Marktet Share * 1.5 Mrd. CHFSach 1.40 1.50 Company specific estimation of largest possible claimHaftpflicht 1.80 2.00 Company specific estimation of largest possible claimUVG inkl UVGZ 2.00 2.00 I llimitéUnfall ohne UVG CHF 50 MioKollektiv Kranken 3.00 3.00 Company specific estimation of largest possible claimEinzelkranken 3.00 3.00 Company specific estimation of largest possible claimTransport 1.50 1.50 2 * largest possible sum at riskLuftfahrt not modeled as mostly reinsured in poolFinanz und Kaution 0.75 0.75 Company specific estimation of largest possible claimAndere 1.50 1.50 Company specific estimation of largest possible claim

α

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Current Year Risk: Large Claims

1

~ ( ), ~ , , then is compund Poisson, ~ ( , )N

i Y i Yi

N Pois Y F iid S Y S F

Aggregation: Use the property that for each LoB, the loss S is compound Poison distributed

Let ~ ( , ), indep. Then ~ , is also compound Poisson.j

Yj

j Yj

j j j jj j j

j

FS F Z S

For Compound Poisson distributions, efficient algorithms exist to numerically evaluate the distribution function, e.g. Panjer Recursion

Consider the class of claim frequency distributions N with pn/pn-1=a+b/n, n=1,2,3,.. Where pn=P (N=n). For this class with claim sizes Y defined on the positive integers, the following recursive formula for the distribution of total claims holds:

1

( ) ( ) ( ), 1,2,3,...y

S Y Sj

jf y a b f j f y j y

y

See Insurance Risk Models, Panjer&Willmot

37

Standard Model: Previous Year Risk

Assumption: CPY*RPY(0) lognormal, with

expectation RPY(0) E[CPY]=1

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.

PY Risk: Reserving Risk, due to uncertainty of run-off result

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:

MFH 3.50%MFK 3.50%Sach 3.00%Haftpflicht 4.50%UVG 3.50%Unfall ohne UVG 3.00%Kollektiv Kranken 3.00%Einzelkranken 5.00%Transport 5.00%Luftfahrt 5.00%Finanz und Kaution 5.00%Andere 5.00%

38

Volatility: Describes changes of risk factors within one year due to parameter-uncertainty

Stochastic risk will be included using company specific data if relevant

The volatilities have been set during discussions with specialist and represent a best-guess

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

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


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

Einzel Gruppen

Ste

rblic

hkei

t

Lan

gleb

igke

it

i(x)

r(x)

Sto

rno

Opt

ions

ausü

bung

Ste

rblic

hkei

t

Lan

gleb

igke

it

i(x)

r(x)

Sto

rno

Opt

ions

ausü

bung

Sterblichkeit 1 0 0 0 0 0 1Langlebigkeit 0 1 0 0 0 0 1i(x) 0 0 1 0 0 0 1r(x) 0 0 0 1 0 0 1Storno 0 0 0 0 1 0.75 1 0.5Optionsausübung 0 0 0 0 0.75 1 0.5 1Sterblichkeit 1 1 0 0 0 0 0Langlebigkeit 1 0 1 0 0 0 0i(x) 1 0 0 1 0 0 0r(x) 1 0 0 0 1 0 0Storno 1 0.5 0 0 0 0 1 0.75Optionsausübung 0.5 1 0 0 0 0 0.75 1

40


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

,

,,

,

M IG

I GTM IG T

I G

M C

I CC

C G

Correlations between market risk factors and insurance risk factors (individual and group business)

For field test 2005, CM,IG=0, but in future correlation between market risk and insurance risk can easily be included (e.g. correlation between lapse and interest rate)

Correlations between market risk factors

Correlations between life insurance risk factors (within individual (I), within group (G) and between individual and group CI,G

41

The SST Concept: Scenarios

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.

Current state of the world

Alternate states of the world

“Ersatz experience is a better guide to the future than the real past and present”, Hermann Kahn in On Thermonuclear War

42

Standard Model: Aggregation with Scenarios

00 0

( ) ( ) ( )n n

i i i ii i

F x p F x p F x c

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, i=1,…,n occurs with probability pi and causes an additional loss of ci (ci<0)

The probability of a normal year is p0=1-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), i=1,…,n, where c0=0.

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 < 45 lapse

Collapse of a dam (Swiss specific)

Terrorism

Global Scenarios (for groups&reinsurers)

Property Cats (earthquake, windstorm)

Special Line Cats: Aviation (2 planes collide, marine event, energy event, credit&surety 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

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 …’

Some have a somewhat reluctant attitude:

We would like to thank Andreas Kull (Ernst&Young) for the permission to use this slide

47


‘…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…’

Some see it in a positive light:

We would like to thank Andreas Kull (Ernst&Young) for the permission to use this slide

48


„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

Implementation of the SST for small to midsized companies:

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 ES[RBC]: 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

Effect of scenarios

Expected technical &

financial result

Diversification between market and insurance risk

Insurance Risk, taking into account diversification between risk factors and lines of business and branches

Market risk, taking into account diversification between different asset classes Risk

Margin

1 year risk capital

Target capital

Relative length of bars correspond approximatively to actual median values

51

Results of Field Tests: Market Risk

Relative length of bars correspond approximatively to actual median values

Scenarios

Expected Result

Diversification between Market and

Insurance Risks

Insurance Risk

Market riskRisk

Margin

1 year risk capital

Target capital

Credit Risk

Interest Rates (CHF, EUR, USD, GBP)

Spreads

Real Estate

FX

Shares

Others

Diversification between market risk factors

Market risk

Diversification effect between different asset classes

52

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

1.2

1.4Results 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

Nonlife Best Estimate

Statutory Reserves (=100%)

Market Consistent Reserves (best estimate + risk margin)

Nonlife Life

Nonlife Risk Margin

Life Best Estimate

Life Risk Margin

53

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

1.2

1.4

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

Nonlife Best Estimate

Statutory Assets (=100%)

Market Consistent Valued Assets

Nonlife Life

Nonlife Risk Margin

Life Best Estimate

Life Risk Margin

54

0 1 2 3 4 5 6 7 8-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Results of Field Tests: Diversification

Diversification between Market and Insurance Risk

Figure shows 1 year risk capital due to market and insurance risk (normalized with total 1 year capital requirement) and diversification.

Nonlife Market Estimate

Nonlife Insurance Risk

Life Market Risk

Life Insurance Risk

Diversification

Nonlife Life

0

100%

-30%

55

Results of Field Tests: Scenarios

Equity Drop -50%

Longevity

Global Deflation

US i.r. crisis 1992

Crash 2000/2001

Russia Crisis/LTCM 1998

European FX Crisis 1992

Nikkei Crash 1990

Crash 1987

Real Estate Crash 1987

Effect of Scenarios Expressed as Fraction of RBC

High ImpactNo Impact Medium Impact

56

Results of Field Tests: Sensitivities

Mort

alit

y

Longevit

y

Morb

idit

y

React

ivati

on

Lapse

Opti

on E

xerc

ise

Mort

alit

y

Longevit

y

Morb

idit

y

React

ivati

on

Lapse

Opti

on E

xerc

ise

Individual Business

Group Business

Sensitivities of life companies to different insurance risk factors, expressed as fraction of risk bearing capital (normalized with volatility of risk factors)

Example shows 4 different life companies

57

CHF EUR USD GBP Spread FX Shares Real Estate Others0

0.5

1Insurer 1


0.5

1Insurer 2


0.2

0.4Insurer 3


0.5

1Insurer 6

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 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,…

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.

60

Internal Models: Problems

• 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

When allowing internal models for target capital calculation, the problems a regulator faces are:

61

Acceptable Models: The Scientific Method

• 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

There are limits on what a regulator can demand:

• 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

• 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)

Therefore:

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

Parent Company: Standard model can be calibrated using local, country specific statistics and models

Scope of Regulatory Models: Group

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

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.

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.

Risk specific standard model is feasible

Risk specific standard model for legal entity is very difficult to develop

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

Parent CompanyLegal Entity

Group

Branch

Branch Branch

Branch

SubsidiarySubsidiary Subsidiary

66

Group Diversification

Legal Entity 2

Legal Entity 3Group Level DiversificationIntra-group risk and capital

transfer instruments allow group-level diversification to be realized and allocated to legal entities

Intra-Group Capital and Risk Transfer Instruments:

• Intra-group Retrocession

• Guarantees

• Participations

• Dividends

• Loans

• Issuance of surplus notes

A group is defined not only by its legal structure but also by its web of intra-group capital and risk transfer instruments

Legal Entity 1

• securitization of future cash flows / earnings

• sale / liquidation of a business

Limited fungibility of capital due to regulatory restrictions have to be considered

Capital and risk transfer instruments can only be considered if they are legally binding and acceptable to the regulators involved

Group

Risk reduction due to group effects

67

Group Diversification: Possible Approaches

“One group one balance sheet”

“Rational” Group “Darwinistic” Group

= SST Approach

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

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

68

Group Diversification

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

Within the SST, group diversification is the effect, legally enforceable group risk and capital transfer instruments have on required and available capital

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 (>1 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: [email protected]+41 31 324 9341 / +41 76 488 3141

Thomas Luder: [email protected]+41 31 325 0168

Mark Stober: [email protected]+41 31 323 5419

Web-Links:www.bpv.admin.chwww.sav-ausbildung.ch (-> documents)

71

Notation

A(0) market value of assets at t=0

UPR unearned premium reserve (at t=0)

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 t=1 for the CY claims (r.v)

r1(0) risk free interest for one year duration at t=0

SCY claims during year (Current Year), r.v.

DPY(1) discount factor for PY-claims at t=1, r.v.

dPY(0) discount factor at t=0

RPY(0) best estimate of PY liabilities at t=0

CPY* RPY(0) re-evaluation of RPY

(0) at t=1 (r.v.),

( (1 - CPY) * RPY(0) = run-off result)

1 philipp keller, federal office of private insurance brussels, 14 october 2005 swiss solvency test

Documents

objective risk

risk margin

riskbased solvency system

risk awareness

risk typology

companies risk culture

different risk types

efficiency of risk management