1. 22nd November 2012 Alex Summers
ASSAL-IAIS Training Seminar: Insurance Risks in the Swiss Solvency Test
22nd November 2012
Alex Summers

2. 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

3. 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

4. Risk based framework for calculating SST
Market Consistent Data and Best Estimate Assumptions
Standard Models or Internal Models
Mix of predefined and company specific scenarios
Risk Models
Valuation Models
Scenarios
Market Risk
Market Value Assets
Credit Risk
Life
Best Estimate Liabilities
P&C
Health
Risk margin
Output of analytical models (Distribution)
Aggregation Method
Target Capital
SST Report
Source: FOPI, 2007

5. Risk measure is 99% expected shortfall
Year 0:
known
Best estimate of liabilities
Available Capital
Market value of assets
Economic balance sheet at t=0 (deterministic)
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
Probability density of the change in available capital
Average value of available capital in the 1% “bad” cases = Expected shortfall
Probability < 1%

6. Coverage of life risks in the SST Standard Model Expected Shortfall risk calculations
Life liability risks
Life business risks
Mortality
Longevity
Morbidity – inception
Morbidity – recovery
Lapses – increase
Lapses – decrease
Expenses
Option take-up
In 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 principle
Separate modelling of reinsurance is often needed for assessment of corresponding credit risk
Scenarios allow for separate consideration of catastrophe risk and combinations of risks

7. Insurance risk is not typically the dominant risk in SST for Swiss life insurers
Source: FINMA SST report 2012

8. 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

9. 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

10. 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

11. Settlement risk (Reserve risk)
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
Catastrophes
Compound Poisson - Pareto
In 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 principle
Separate 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

12. Insurance risk is often the dominant risk in SST for Swiss non-life insurers
Source: FINMA SST report 2012

13. 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

14. Models for life risks can be broken down into components
Choice of risk drivers
Risk driver distributions
Choice & parameterisation of distribution
Loss function
Loss in available capital for a given value of the risk driver
Aggregation between losses for different risk drivers

15. 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

16. 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 paid
Impact of latest experience through changes to assumption as to future experience over the remaining lifetime of the business

17. 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

18. Calibrating risk driver distributions seeks to answer several questions
What is the functional form of the distribution?
What are the parameters / key percentiles?
What is the quality of the fit to data i.e. how confident can we be in answers to questions 1 and 2?

19. Calibrating risk driver distributions is challenging
Calibration is needed for each component of the risk driver
1 year volatility vs. longer term assumption change risk
Maintenance expense level vs. inflation
Morbidity 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 choice
Asymmetric 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

20. Some considerations in treatment of data in calibration of risk driver distributions
Different sources
Population data
Industry data
For insurers, own experience data
Weighting
Amounts vs. lives
Grouping
Underling assumption that observations of the risk driver are independent and identically distributed
Consistency vs. specific local calibration
Important to keep in mind how data will eventually be used

21. 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, cubic
Extrapolation needs care
More fitting points are needed
Treatment of composite risk drivers can be challenging
Out of sample testing helps give confidence in quality of fit

22. 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 used
Easier understanding and communication

23. 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
Simple model
Risk driver distribution
Normal
Loss function
N(1,(5%)2)
Loss distribution
f(X) = -100.(X-1)
Average loss
Standard deviation of losses 5
Expected shortfall 99%
13.3
Extended model
Lognormal
LogN(0,(5%)2)
f(X) = -15(X-1)3+15(X-1)2 -100(X-1) 5
13.9

24. 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

25. 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 alternative
Choices of risk driver
Risk driver distribution and stress levels
Loss functions
Aggregation techniques

26. Thank you for your attention
Any further questions?

27. 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

28. 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 measures
Companies 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

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

30. The SST Principles in full
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 insurer’s capital adequacy is defined if its target capital is less than its risk bearing capital
The scope of the 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
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
Regulatory 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 the adherence to principles
Defines How-to
Defines Output
Transparency
Governance
Source: FOPI, 2007