Modeling of Automobile Insurance under Solvency II

Roland Voggenauer-Graf von Bothmer Group Actuarial, Allianz SE

1 Automobile Insurance in Germany The Market Modeling of Automobile Insurance under Solvency II

Pricing

Reserving Reinsurance

2

Automobile Insurance under Solvency II Solvency I & US Risk Based Capital Solvency II: Standard Model Solvency II: Internal Model

© Allianz SE 2011

Table of contents

Use Test of the Internal Model

2

Premium generated by the German insurance industry

Modeling of Automobile Insurance under Solvency II

Euro 18 x 1010

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183,000,000,000 € 3

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€ 60 bn

* Property & Casualty 4

Modeling of Automobile Insurance under Solvency II

… out of that:

… and the Non-Life Market splits up in: € 20 bn

Premium

 About 55 million vehicles Property 43%

 More than 45 million private passenger cars

Modeling of Automobile Insurance under Solvency II

Total Automobile 33%

Liability 13%

Germany

 … which is 55 cars per 100 inhabitants Accident 11%

Reserves  Around 30 million vehicles  Approximately 30 cars per 100 inhabitants  Only a quarter of the vehicles are insured

Total Automobile 41%

Property 24%

Liability 27%

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Mexico

Accident 9%

5

Automobile Insurance in Germany Lines of Business  Motor Third Party Liability (MTPL): Mandatory since 1939

Modeling of Automobile Insurance under Solvency II

 Motor Own Damage (MOD): • Voluntary cover, split up in: - Partial coverage = fire, theft & nat cat

- Full coverage = partial + accidental damage  Accidentcover for passengers and the driver  Other additional covers, like

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• Assistance, Mobility • Extended Warranty, Gap •… 6

Automobile Insurance in Germany Share of MTPL and MOD 3 out of 4 cars have an MOD cover

Motor Own Damage 4%

Premium (€ 8 bn + € 12 bn)

Reserves

MTPL 61%

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Motor Own Damage 39%

Modeling of Automobile Insurance under Solvency II

MTPL 96%

7

Automobile Insurance in Germany Legal requirements for MTPL • Bodily injury (BI):

€ 7.5 mn

• Property damage:

€ 1.0 mn

• Other damages:

€ 50,000

Modeling of Automobile Insurance under Solvency II

 Minimum coverage

 Standard coverage • Used to be “unlimited”

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• Now: € 50-100 mn, with BI limited to € 8-15 mn per person  Close co-operation between association of insurance companies, Vehicle registration offices, and the police 8

Automobile Insurance in Germany Cumulative market shares of the 14 (out of about 100) largest players 100%

80%

72%

82%

67%

70%

62% 57%

60%

52% 46%

50% 39%

40% 28%

30% 17%

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20%

76%

79%

85% 86%

Modeling of Automobile Insurance under Solvency II

90%

10% 0% 9

Automobile Insurance in Germany Consequences of a strongly fragmented market  Medium and small size insurers need support in their pricing by Modeling of Automobile Insurance under Solvency II

• German Insurance Association (GDV) • Pools  Very competitive market (small margin – if any)  Focus on distribution channels

 Innovations in tariff structures and pricing techniques

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 Cyclical market

10

90%

100%

MTPL

MOD

80%

70%

11

Modeling of Automobile Insurance under Solvency II

60% © Allianz SE 2011

2010

2008

2006

2004

2002

2000

1998

1996

1994

1992

1990

1988

1986

1984

1982

1980

Automobile Insurance in Germany The cycle: Claims(!)-ratios

120%

110%

Automobile Insurance in Germany Market shares by distribution channels

Broker 25%

Modeling of Automobile Insurance under Solvency II

Direct 15%

Agents 60%

Aggregators are gaining market share  Across all distribution channels, yet ...  ... mainly in Direct

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• 25% of new business and • >80% of this by one comparison website

12

Pricing of automobile insurance Evolution of rating criteria Type of vehicle, Type of occupation, Region, Bonus / Malus

Today:

On average almost 20 factors, such as:

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Modeling of Automobile Insurance under Solvency II

Prior to 1994:

13

Criteria to model

b

Identification of risk criteria

e.g. nationality

b

Selection of usable criteria

e.g. origin of driving license

1

Rating criteria 1

Grouping

Region

2

Rating criteria 2

Grouping

Occupation

3

Rating criteria 3

Grouping

Age*Gender

n

Rating criteria n Cube-like structure

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...

Modeling of Automobile Insurance under Solvency II

e.g. claims frequency

a

Occupation

Interaction of criteria

Pricing of automobile insurance

Region Age*Gender 14

Pricing of automobile insurance Cube-like structure of e.g. 3 dimensions

Munich

Modeling of Automobile Insurance under Solvency II

Actuary, male, 35-40, living in Munich

Occupation

Region

Actuary

Actuary:

x

Munich:

y

male & 35-40: z

Male, 35-40

Gender*Age

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Tariff calculation uses factors:

… and derives the premium P as: P = Base Rate * x * y * z

15

Pricing of automobile insurance Multiplicative rating structure 

with classes i є (1, ... , n) and k ε (1, ... , l) respectively



producing a cube Q of tariff clusters (i,k) ε ((1, ... , n) x (1, ... , l)) =: Q Modeling of Automobile Insurance under Solvency II

Let I and K be rating criteria ...

Let v i,k be the volume and S i,k the amount of losses in (i,k), then: The pure premium in cluster (i,k) should equal Ε(S i,k / v i,k) =: P i,k In a multiplicative structure there are parameters μ, αi, βk such that for all (i,k) ε Q

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P i,k = μ αi βk

μ being a base rate and αi, βk (normalized) rating factors 16

Reserving in automobile insurance Reserving under local German GAAP requested to be prudent! Usually we see patterns like this … 150%

“Long tail”

Own Damage Known Share of Ultimate

Incurred

Incurred

Third Party Liability Modeling of Automobile Insurance under Solvency II

“Short tail” Known Share of Ultimate

100% Paid Paid

Claims Development in Years

Claims Development in Years 1

2

3

4

5

6

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50%

Thus run-off losses do occur on portfolio level, but are exceptional with regard to single known claims 17

Reserving in automobile insurance Development Factor Methods

Historical Data

Modeling of Automobile Insurance under Solvency II

(e.g. Chain-Ladder, Bornhuetter/Ferguson)

Future Development

 Historical claims development is used to predict future development

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 Apply “Tail Factor” – if need be … which most often is the case

 … subject to: data are homogeneous, no systematic changes, etc. 18

Reserving in automobile insurance DF-Methods are applied to both Incurred and Paid

Incurred

100%

Third Party Liability

Modeling of Automobile Insurance under Solvency II

In theory we would expect the two projections to converge at one “Best Estimate”

Paid

In reality this seldomly works out

0% 1

2

3

4

5

6

7

Munich Chain Ladder (by Th. Mack & G. Quarg, 2004)  Analyzing correlations between paid and incurred, we often observe

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• after a low “paid to incurred ratio” higher than average paid factors • after a high “paid to incurred ratio” lower than average paid factors

 Making use of this can reduce the gap between paid and incurred projections 19

Reserving of automobile insurance Some of the challenges we face

 Duration of BI-claims increases in MTPL (less people die after an accident)  … but in MOD claims are settled much faster (better claims management)  Court decisions change, mostly in favor of the insured or the claimant (annuity vs lumb sum payment)  … many more 20

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 … while the average cost of claims is increasing (increasing values, cost of medical treatment)

Modeling of Automobile Insurance under Solvency II

 The claims frequency in MTPL is declining over time (safety standards)

Reinsurance in automobile insurance Typical programs would be

Modeling of Automobile Insurance under Solvency II

Quota Share Risk-based Excess of Loss, e.g.: € 4 mn xs € 1 mn € 15 mn xs € 5 mn € 80 mn xs € 20 mn

MOD Quota Share Event-based Excess of Loss, e.g. € 25 mn xs € 25 mn € 50 mn xs € 50 mn Stop Loss for nat-cat perils Facultative Reinsurance

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MTPL

21

2 1

Automobile Insurance in Germany The Market Pricing Modeling of Automobile Insurance under Solvency II

Reserving Reinsurance

2 Automobile Insurance under Solvency II Solvency I & US Risk Based Capital Solvency II: Standard Model

© Allianz SE 2011

Solvency II: Internal Model

Use Test of the Internal Model

22

Solvency I – The old world Local German Regulation for Solvency I in Non-Life

Premium index

Modeling of Automobile Insurance under Solvency II

Solvency Margin = max (Premium index; Claims index) = 18% * Premium of up to € 50 mn * Self Retention + 16% * Premium above € 50 mn * Self Retention = 26% * Incurred Claims of up to € 35 mn * Self Retention + 23% * Incurred Claims above € 35 mn * Self Retention

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Claims index

23

US Risk Based Capital for P/C (NAIC) The first “Factor-Model” in insurance Define:

R0 := Asset Risk - subsidiary insurance companies Modeling of Automobile Insurance under Solvency II

R1 := Asset Risk - fixed income investment R2 := Asset Risk - Equity R3 := Asset/Credit risk – Recoverables, Reinsurance

R4 := Reserve Risk

and put: Total Risk Based Capital :=

R0

2 1

R

2 2

R

2 3

R

R4

2

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R5 := Premium Risk

R52 24

Europe wants „A new drug ...“ To achieve ...  consumer protection  focus on risk-management & risk-steering

... in 2009 the Directive stipulated  Principle based approach to supervision  Market consistent approach for valuing assets and liabilities  Capital requirements linked to the company„s risk profile

... to come into force in 2013!? 25

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Modeling of Automobile Insurance under Solvency II

 higher transparency on underlying risks

Solvency II Directive A three-pillar structure

Pillar 1 Risk Quantification

Pillar 2 Risk Management

Pillar 3 Risk Disclosure

Model

Governance

Supervisory and public reporting

Technical provisions

Use Test

Capital required

ORSA

Modeling of Automobile Insurance under Solvency II

Solvency II

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Transparency

Originally focused on adequate risk management systems 26

Solvency II Directive Pillar 1: Quantitative requirements Limit worst case (financial ruin) within one year to a 0.5% probability

Modeling of Automobile Insurance under Solvency II

 Availability of free own funds to cover losses of current business (premium risk) and runoff losses (reserve risk)  Market Value Balance Sheet (“Fair Value”) • Minimum Capital Required (MCR) similar to Solvency I

• Use of approved internal models to evaluate the Solvency Capital Required (SCR) - Reduction in required capital is estimated to be 20%, yet … - …only a minority of insurers will apply for the usage of an internal model • Individual evaluation of risks with standard formula, allowing for diversification

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• Stepwise intervention of the regulator in case MCR < Own Funds < SCR

27

Solvency II Capital Requirement

Modeling of Automobile Insurance under Solvency II

Based on Monte-Carlo simulations

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Expected Value

28

Solvency II Directive Pillar 2: Governance & Risk management Adequate and transparent assessment of all risks  Principle based approach to allow for individual implementations at company level  Principle of “Proportionality”: Medium and small sized insurers should not be overburdened  Extensive audits and evaluations by the supervisor, e.g. of strategies, processes, governance systems etc.  Far-reaching authorization of the supervisor, e.g. in case of outsourcing

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 Germany: Introduction of “MaRisk” in 2009 already anticipates much of that

Modeling of Automobile Insurance under Solvency II

 Risk oriented approach: All material risks need to be included

29

Solvency II Directive Pillar 3: Disclosure & transparency Disclosure of information regarding the risk situation – both public and to the supervisor only Modeling of Automobile Insurance under Solvency II

 Uniform supervisory reporting within the EEC  Public disclosure of the solvency situation following the „Solvency and Financial Condition Report“ including e.g.

• Business policy, corporate structure, market environment, strategies, … • Governance structure and compliance statement • Principles of evaluation of assets and liabilities

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• Internal governance • Required MCR / SCR

• Disclosure and justification in case the capital requirements are not meet 30

The Standard Model Solvency Capital Required (SCR)

Intangable Assets

Health Business

Modeling of Automobile Insurance under Solvency II

Life Business

Non-Life

Non-Life Business

Market Risk

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Credit Risk

Credit Risk

Life

Intangibles

Health Market 31

31

The Standard Model – Non-Life Risk

Premium Risk

Modeling of Automobile Insurance under Solvency II

Non-Life Business Non-Life

Reserve Risk

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Nat Cat Risk

32

The Standard Model Correlation:

Premium Risk

Modeling of Automobile Insurance under Solvency II

How likely is it to have a major hurricane and to increase reserves for prior years at the same time?

Nat Cat Risk Reserve Risk

Measurement of the Risk Exposure:

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 Volume * Factor

 Based on volatility & 99,5% percentile  For reserves and future business

 Allow for diversification by line of business and country

33

The Standard Model

Modeling of Automobile Insurance under Solvency II

Concept for Nat Cat  Scenario based

 Geographical exposure and insured volume  Add manual Cat if needed

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 Allow for diversification

34

Solvency II – Internal model for P/C business Ultimate premium risk (non-cat) Gross Model (Sub-LoB Level) 2

Distribution fitting Large Losses

Attritional Losses



Exposure adjustment



Inflation Adjustment



Historical data (Premium/Exposure/Losses)



IBNR/IBNER adjustment



Individual Large Losses



Best Estimate Ultimate by AY



Inflation Indices

Dependencies



Sub-LoB aggregation



Frequency & Severity

Premium Cycle

Frequency

Frequency

Planning data (Premium/Expenses/ Exposure/Losses)

4

3

Adjusted Data

Raw Data



Data Adjustment

Modeling of Automobile Insurance under Solvency II

Data Input

Severity

Severity

Net Model (LoB Level) 5 Reinsurance 

6 Levels of reinsurance 1 - QS & Surplus 2 – Risk XoL 3 – Event XoL 4 – Multi-Line XoL 5 – Stop Loss 6 – Net QS

Severity

UW Result (LoB & LE Level) 6

Dependencies



LoB aggregation



Low/Medium/High

7

UW result gross/net

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1

35

35

Solvency II – Internal model for P/C business Assessing the reserve risk by bootstrapping techniques A Parameterisation

(1) Data triangle

(2) Fit a CL model to your data

What would have been the historical data given the latest loss information and under the assumption the CL model is the true model?

(3) Fitted triangle

- Residuals can be used for sampling with replacement

- Pearson residuals - for incremental losses (ODP) - for individual development factors (Mack) - deviation from fitted to original triangle - need to be standardised

- Fitted triangle plus different sets of residuals result in pseudo triangles

(4) Calculate residuals

B Simulation Pseudo Reserves

- Process error is included when forecasting

0,016

0,014

Probability Density

0,012

0,010

0,008

Modeling of Automobile Insurance under Solvency II

Reserve Estimates

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0,006

0,004

0,002

0,000 750.000

800.000

850.000

900.000

950.000

1.000.000

1.050.000

Reserve

… (5) Generate pseudo triangles

… (6) Refit the same CL model

1.100.000

1.150.000

1.200.000

1.250.000

1.300.000

1.350.000

- Also provides stochastic cash flow

(7) Distribution of reserves 36

Solvency II – Use Test In order to prove the quality of the internal model

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Modeling of Automobile Insurance under Solvency II

Solvency II requires it to be used for daily business decisions!

37

Solvency II – Use Test Example The large loss model & hence the purchase of reinsurance  Large losses very much depend on the individual insurer Modeling of Automobile Insurance under Solvency II

 No standard model is able to reflect this appropriately  The internal model is simulating empirical large losses

 The reinsurance program should provide appropriate protection against them

Hence:

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The large loss model should match the reinsurance program

38

Solvency II – Use Test Linking Risk Models and Business Management Business Management

Technical Pricing

NatCat Limit Controlling Reinsurance Optimization

Modeling of Automobile Insurance under Solvency II

Capital Assessment

Strategic Planning

ALM Underwriting

RC Calculation

Reporting Reserving MVM Calculation

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Claims Analysis

Plan Year‟s Exposure A. Loss Ratio A.

39

Future Development

Incurred

Historical Data Occupation

Paid

Pillar 2

Pillar 1 Third Party Liability

100%

Model 0% 2

3

4

5

Pillar 3

6

Risk Manage ment 7

Region

Reporti 90% ng

Age*Gender76%

80%

82%

85% 86%

72%

67%

70%

62% 57%

60%

52% 46%

50% 39%

40% 28%

30% 20%

79%

© Allianz SE 2011

Solvency II

100%

1

Modeling of Automobile Insurance under Solvency II

Any Questions?

17%

10% 0%

40

Thank you for your attention!

Roland Voggenauer-Graf von Bothmer [email protected] +49 (0) 89 3800 13480