assal-iais training seminar: insurance risks in the swiss solvency test

Global Life Actuarial

INTERNAL USE ONLY

ASSAL-IAIS Training Seminar: Insurance Risks in the Swiss Solvency Test

22nd November 2012Alex Summers

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Important note

The views expressed in this presentation are the presenter’s own and do not necessarily represent the views of either Zurich Insurance Group (Zurich), or FINMA

I am very grateful to colleagues within Zurich and at FINMA for their assistance in preparation

Further information from FINMA on the Swiss Solvency Test can be found on FINMA’s website at http://www.finma.ch

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Agenda

Life Insurance Risks framework in the SST

Non-Life Risks framework in the SST

Case study: practicalities of implementing an SST internal model for life risks

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Risk based framework for calculating SST

Scenarios

Standard Models or Internal Models

Mix of predefined and company specific scenarios

Target Capital SST Report

Market Consistent Data and Best Estimate Assumptions

Market Risk

Credit Risk

Life

P&C

Market Value Assets

Risk Models Valuation Models

Best Estimate Liabilities

Risk margin

Output of analytical models (Distribution)

Health

Aggregation Method

Source: FOPI, 2007

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Risk measure is 99% expected shortfall

Probability density of the change in available capital

Average value of available capital in the 1% “bad” cases = Expected shortfall

Probability < 1%

Economic balance sheet at t=1 (stochastic)

Year 1: uncertain

Catastrophes

Claims

Revaluation of liabilities due to new information

New business during one year

Change in market value of assets

Available capital changes due to random events

Year 0:

known

Best estimate of liabilities

Available Capital

Market value of assets

Economic balance sheet at t=0 (deterministic)

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Coverage of life risks in the SST Standard Model Expected Shortfall risk calculations

Life liability risks Life business risks

MortalityLongevityMorbidity – inceptionMorbidity – recovery

Lapses – increaseLapses – decreaseExpensesOption take-upIn each case need to consider parameter risk, “random risk”,

and accumulations of riskAlternative decompositions can be considered for Internal Models

Net of reinsurance in line with holistic balance sheet principleSeparate modelling of reinsurance is often needed for assessment of corresponding credit risk

Scenarios allow for separate consideration of catastrophe risk and combinations of risks

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Insurance risk is not typically the dominant risk in SST for Swiss life insurers

Source: FINMA SST report 2012

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Treatment of life risks in SST standard formula is similar to market risks, but without cross-terms

Individual stresses to available capital for each risk driver

Simplifying assumptions of linear impact, underlying multivariate normal distribution

FINMA supply standard deviation and correlation parameters based on historical analysis

Covariance model for aggregation to overall analytic distribution for insurance risk

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Several standard SST scenarios cover extreme life insurance risks

Extreme scenarios include pandemic, terrorism, longevity, lapse

Often a link between different types of risk under a single scenario

Granular treatment

For example, pandemic scenario can incorporate not only an extreme increase to mortality rates, but also falling interest rates, widening credit spreads and generally falling share prices - except for pharmaceuticals

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Agenda




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Coverage of non-life insurance risks in the SST Standard Model Expected Shortfall risk calculations

Risk driver Subcategory

Distribution

Health Normal

Settlement risk (Reserve risk)

Lognormal

Risk of new claims(Premium risk)

Small claims Gamma

Large risks Lognormal

Catastrophes Compound Poisson - ParetoIn each case need to consider parameter risk, “random risk”, and accumulations of risk

Alternative decompositions can be considered for Internal Models

Net of reinsurance in line with holistic balance sheet principleSeparate modelling of reinsurance is often needed for assessment of corresponding credit risk

Scenarios allow for separate consideration of extreme events such as catastrophe risk, and combinations of risks

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Insurance risk is often the dominant risk in SST for Swiss non-life insurers

Source: FINMA SST report 2012

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Models for life risks can be broken down into components

Choice of risk drivers

Risk driver distributionsChoice & parameterisation of distribution

Loss functionLoss in available capital for a given value of the risk driver

Aggregation between losses for different risk drivers

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Choice of risk driver needs careful thought

Risks modeled should be relevant to nature of business

Risk drivers can typically be expressed in terms of ratio ACTqx /

EXPqx of actual experience over base best estimate expected experience

For example, if best estimate expected mortality rate for a 60 year old EXPq60 is 1%, then under a 1 in 100 stress the rate might be 1.1%

Ratio is then 110%, or a shift of 10% compared to base 100%This is a helpful simplification to keep the number of risk drivers manageable e.g. allowing for different mortality rates to be applied for different ages

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Alternative approaches to decomposition of risks in choice of risk drivers

It’s not always necessary to split

SST standard model starting point is mathematically motivated parameter vs. random fluctuations risk

An alternative split considering sources of impact to available capital can be useful in practice:

1 year volatility of actual experience impact on policyholder benefits paidImpact of latest experience through changes to assumption as to future experience over the remaining lifetime of the business

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Worked example splitting out components of risk drivers

Beginning of the year expectations• Sum at risk USD 1bn• Expected mortality rate 1%

Actual experience• Mortality rate 1.1%

How this impacts available capital at end of year• Mortality loss of 0.1% x 1bn = USD 1M• New best estimate mortality rate = 1.04%• Suppose impact of changing assumption is to increase BEL by

USD 4M• Then total reduction in available capital is 1+4 = USD 5M

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Calibrating risk driver distributions seeks to answer several questions1. What is the functional form of

the distribution?

2. What are the parameters / key percentiles?

3. What is the quality of the fit to data i.e. how confident can we be in answers to questions 1 and 2?

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Calibrating risk driver distributions is challenging

Calibration is needed for each component of the risk driver1 year volatility vs. longer term assumption change riskMaintenance expense level vs. inflationMorbidity incidence vs. recovery

Key challenge is finding a sufficient volume of data to give confidence of an appropriate fit

Quality of fit in the tail of the distribution is important

In many cases Normal distribution is natural choiceAsymmetric distributions or distributions with higher kurtosis (fatter tails) could also be considered e.g. lognormal

Standard statistical fitting and validation techniques can be applied e.g. maximum likelihood estimation

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Some considerations in treatment of data in calibration of risk driver distributions

Different sourcesPopulation dataIndustry dataFor insurers, own experience data

WeightingAmounts vs. lives

GroupingUnderling assumption that observations of the risk driver are independent and identically distributed

Consistency vs. specific local calibrationImportant to keep in mind how data will eventually be used

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Fitting loss functions

Key questions are choice of fitting points, and functional form

Linear loss function is often good enough

Extensions to higher order polynomials could be considered, particularly for persistency risks

Quadratic, cubicExtrapolation needs careMore fitting points are needed

Treatment of composite risk drivers can be challenging

Out of sample testing helps give confidence in quality of fit

Example of a loss function (cubic polynomial)

-50,000,000

-40,000,000

-30,000,000

-20,000,000

-10,000,000

-

10,000,000

20,000,000

30,000,000

40,000,000

50,000,000

60,000,000

-100% -80% -60% -40% -20% 0% 20% 40% 60% 80% 100%

Persistency lapse down - stress levels

Chan

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VL

Calibration points Change in MVL

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Using scenarios to allow for combinations of risks simplifies required capital calculations

The simplest approach is to consider loss functions in terms of one risk driver at a time

SST standard model for life insurance risk expected shortfall follows this approach

However this does not allow for the theoretical situation in which losses resulting from stresses to more than one risk factor at the same time differ from the sum of the losses across the standalone stresses

“Cross-terms” in the loss function can allow for this In many cases, cross-terms are not necessarily material

Combined scenarios as used in the SST can be usedEasier understanding and communication

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Combining the loss function with the risk driver distribution gives the marginal loss distribution for each risk driver

In the simple case that the risk driver distribution is Normal, and the loss function is linear, the loss distribution will also be Normal

The same approach applies for more complex risk driver distributions and loss functions, but simulation may be needed in the absence of a straightforward analytical formula

Extended model

Lognormal

LogN(0,(5%)2)

f(X) = -15(X-1)3+15(X-1)2 -100(X-1)

0

5

13.9

Simple model

Risk driver distribution Normal

Loss function N(1,(5%)2)

Loss distribution f(X) = -100.(X-1)

Average loss 0

Standard deviation of losses

5

Expected shortfall 99% 13.3

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It can be simpler to calibrate the dependency between risk drivers rather than dependency between loss distributions

Correlation matrix approaches help aggregate capital requirements between different risk drivers

Copula approaches can be used to aggregate either marginal loss distributions for different risk drivers into an overall loss distribution, or define dependency structure between underlying risk drivers

It’s not always easy to parameterise a suitable dependency structure between loss amounts

It can be easier to think through the dependency between underlying risk drivers rather than losses

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Overview of insurance risks in SST

SST allows a decomposition of required capital into different drivers

Scenarios play a key role in correcting tails of the distribution and aiding communication and understanding of risks

Treatment of life insurance risks in standard model follows a simple approach based on an assumption of linear loss functions, normal distribution of risk drivers and covariance matrix aggregation

Extension of the standard model approach can consider alternativeChoices of risk driverRisk driver distribution and stress levelsLoss functionsAggregation techniques

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Overview of SST

• Risk based

• Principles based

• Holistic market consistent balance sheet giving economic view of both assets and liabilities

• Available capital = market value of assets – best estimate liabilities

• Required capital based on risk margin + potential change in available capital over 1 year time horizon, using 1 in 100 expected shortfall as a risk measure, incorporating scenarios

• Applies both to legal entities and groups

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The SST has established itself as an essential supervisory tool for FINMA

Introduction of SST motivated Swiss insurers to address their solvency situation

Companies took necessary capital increasing and risk reducing measuresCompanies improved their risk management

With the SST, FINMA has access to an effective solvency testing instrument

Solvency problems are identified in a timely fashion

Conservative measures can be taken based on a ladder of intervention

Source: FINMA 2012

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Despite a baptism of fire, the SST has given a clear and helpful view in tough times

SST Solvency Position of Swiss Non-Life Insurers, SST 2009-2012

80%

82%

84%

86%

88%

90%

92%

94%

96%

98%

100%

2008 2009 2010 2011 2012

% T

ota

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sse

ts Excess Capital

Expectedshortfall SCR

Market ValueMargin

Best estimateliabilities

SST Solvency Position of Swiss Life Insurers, SST 2009-2012

80%

82%

84%

86%

88%

90%

92%

94%

96%

98%

100%

2008 2009 2010 2011 2012

% T

ota

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t va

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of a

sse

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Excess Capital

Expectedshortfall SCR

Market ValueMargin

Best estimateliabilities

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The SST Principles in full

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 market value 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 market value margin

5. 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

6. Under the SST, an insurer’s capital adequacy is defined if its target capital is less than its risk bearing capital

7. The scope of the SST is legal entity and group / conglomerate level domiciled in Switzerland

8. Scenarios defined by the regulator as well as company specific scenarios have to be evaluated and, if relevant, aggregated within the target capital calculation

Defi

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9. All relevant probabilistic states have to be modeled probabilistically

10. 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

11. The internal model has to be integrated into the core processes within the company

12. SST Report to supervisor such that a knowledgeable 3rd party can understand the results

13. Regulatory disclosure of methodology of internal model such that a knowledgeable 3rd party can get a reasonably good impression on methodology and design decisions

14. Senior Management is responsible for the adherence to principles

Defi

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Source: FOPI, 2007

Govern

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assal-iais training seminar: insurance risks in the swiss solvency test

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