6th samos conference in actuarial science and finance, samos, june 3-6 insurance guarantee schemes:...

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6

Insurance Guarantee Schemes:A credit portfolio approach to estimate potential exposures and funding needs

in Europe

Joossens E., Marchesi M., Rezessy A. and Petracco M.

EC Joint Research CentreUnit for Econometrics and Applied Statistics

The views expressed in this paper are those of the authorsand should not be attributed to the European Commission or Member States.


Background

• Recent financial crisis and insurance crisis in Greece created new interest on consumer protection mechanisms in insurance market

• Mechanism on which we concentrate is an Insurance Guarantee Scheme. i.e. provider last resort protection to policyholder in case insurance company becomes insolvent

• Within Europe currently: – 9 MS with coverage for life assurance– 8 MS with coverage for non life insurance


Aim of paper

With: – only minimal data requirements– taking into account Solvency II capital requirements– the possibility to offer applications for EU countries

What has been done in the past:– a simple point estimation of the expected value has been

provided without a more complete loss distribution

Propose a methodology to estimate the distribution of losses of an IGS


The model

IGS protect policyholders/claimants from credit risk of insurersEmploy a default risk model Merton model:

– Default process of a firm as the exercise of an option– Using a diffusion process with Gaussian underlying

BUT: does not capture sensitivity to common factors and correlation

Portfolio credit risk Vasicek (1991) model:– Incorporates single common factor and idiosyncratic factors

so the value of the asset can be written as:

1ii XYZ


The model II

Limiting distribution of losses within a homogeneous portfolio of exposures leads to :

Where X stands for the share of portfolio which defaults. This distribution only depends on:• the average unconditional default probability, PD , of each

exposure and • the correlation between the exposures and a common factor, ρ.


Extension of the model

Model assumption is infinite and homogeneous marketBUT:

– only a finite number of exposures – not all insurance companies are equally large

Inclusion of additional correction term “granularity factor” δ :– is a measure of concentration – obtained as , where are the shares of the

individual exposures in the portfolio, and – is then used to adjust the correlation coefficient by setting:

iw iw


Maximum expected loss

Inverting the equation it is possible to obtain the maximum loss (as a share of the total portfolio) which should not be exceeded in one year under any given confidence level α:

To obtain the amount in monetary losses include:–Loss given default or LGD –Total exposure at default or EAD

Leading to the maximum expected losses under confidence level α:

EADLGDVaR(αsespected losMaximum ex )


Application

Assumptions made:• Type of coverage: full coverage without exclusions• Geographic scope: home state principle (i.e. scheme covers

policies issued by domestic companies that participate in the scheme, including policies issued by the companies’ braches established in other EU MS)

• Eligible claimants: natural persons and legal entity• Type of intervention: continuation of contracts

IGS for the Life insurance sector in each EU member states


Current EU position

Used in this

paper

Life Total

LV BG UK MT FR DE RO PL ESNature of interventionPure compensation to claimants X X x x X X X X XContinuation of contracts X X(1) X X XEligible claimantsNatural persons only X XNatural persons + SMEs x x Natural and legal persons except financial institutions XNatural and legal entity X X X X XCompensation limits and reductionsCapping payouts X X X X n/a Capping payouts for non-compulsory insurance X XLevel of coverage in percentage terms 100 100 70 90 75 100 100 50 n/a Level of coverage in percentage terms (compulsory ins.) 100 100Fixed deductibleOther reduction in benefits X XGeographic scopeAn IGS in each MS with home state principle X X X X X X X XAn IGS in each MS with host state principle X x X X Other XTypes of policies coveredWithout exclusions X X X X X X XWith exclusion X X X


Calibration of parameters

Calibration of the VaR parameters– For the probability of default: PD =0.1%

• Standard and Poor’s one-year corporate default rates by rating• Credit ratings distribution (Year-end) of the leading European insurance

groups as provided by CEIOPS (Committee of European Insurance and Occupational Pensions Supervisors)

– For the correlation coefficient: ρ = 20%• In line with Basel II IRB risk model recommendations

– For the granularity adjustment: δ =country specific; based on• Number of companies per insurance sector and country• Total premium income of the insurance sector and top 5 companies• Additional available market shares of top 5, 10 and 15All from CEA (the European insurance and reinsurance federation)


Calibration of parameters: results for δ

Country delta Country deltaAustria 0.124 Latvia 0.284Belgium 0.136 Lithuania 0.125

Bulgaria 0.123 Luxembourg* 0.018Cyprus 0.183 Malta 0.2Czech Republic 0.146 Netherlands 0.115Denmark 0.066 Poland 0.181Estonia 0.327 Portugal 0.143

Finland 0.215 Romania* 0.048France 0.085 Slovakia 0.138Germany 0.052 Slovenia 0.215Greece 0.101 Spain 0.053

Hungary* 0.045 Sweden 0.103Ireland 0.083 United Kingdom 0.064Italy 0.111

For LU, RO and HU the value is only based on the number of companies available as all other information is missing


Calibration of parameters: LGD and EAD

– For the loss given default: LGD = 15% • the 30-days and emergence recovery rates on loans to insurance

companies are, respectively, 65% and 100% (Fitch Ratings 2009)• also in line with the choice made in the Oxera report (Oxera 2007)• Extension: can be considered to depend on α or even to be stochastic

– The total exposure at default: EAD • Can be considered to be the best available estimate of liabilities

towards policyholders, claimants and beneficiariesThis can be put equal to the Technical Provisions (TP)

• BUT: we should include the fact that, in case of default this could be due to a miscalculation of the risk margins

• Include additional terms proportional to the Solvency capital requirements


Calibration of EAD

Result:

Where: – : are the adjusted technical provisions at the current date– : is the solvency capital requirement at the current date– : is the ratio of the solvency capital requirement for

market risk to the total of all components (Operational risk, Counterparty risk, Market risk, and underwriting risk in the non-life, life and health sector) of the SCR

Data used is obtained from CEIOPS and CEANote: adjusted TP refers to correction from Solvency I to Solvency II


EAD- home state principle, full coverage

The results depends heavily the market covered, types of contracts covered and size of coverage

Country

EADTotal gross premiums

written

Country

EADTotal gross premiums

written

(m€) (m€) (m€) (m€)

Austria 58,188 7,141 Latvia# 83 53

Belgium 168,163 22,179 Lithuania# 525 204

Bulgaria# 203 120 Luxembourg 76,571 10,093

Cyprus# 2,717 358 Malta# 1,293 214

Czech Republic 6,544 2,034 Netherlands 266,317 26,437

Denmark 118,090 13,190 Poland 17,059 6,743

Estonia# 509 118 Portugal 40,297 9,205

Finland 37,099 2,784 Romania# 781 415

France 1,189,627 136,528 Slovakia 2,299 848

Germany 765,180 75,170 Slovenia# 2,041 443

Greece# 7,630 2,504 Spain 164,938 23,455

Hungary 5,282 2,017 Sweden 191,510 12,985

Ireland 147,444 37,563 United Kingdom 2,034,005 305,184

Italy 389,126 61,438


Results I: Share of portfolio lost

Expected 75.0% 95.0% 99.0% 99.5% 99.9%

Min 0.1% 0.02% 0.36% 1.16% 1.61% 3.05%

Median 0.1% 0.06% 0.44% 1.49% 2.22% 4.71%

Max 0.1% 0.09% 0.44% 1.98% 3.39% 8.85%


Results II: Losses as share of total premium

Expected 75% 95% 99% 99.50% 99.90%Min 0.02% 0.01% 0.09% 0.35% 0.50% 0.99%Median 0.09% 0.04% 0.39% 1.31% 1.91% 3.77%Max 0.22% 0.14% 0.98% 3.49% 5.52% 12.80%

Weighted average 0.10% 0.08% 0.50% 1.52% 2.21% 4.47%


Position of an historical loss

Insolvency of Mannheimer Lebenversicherung 2003, Germany

amounted to €100m or 0.13% of the total premiumsGerman, life insurance, Mannheimer (€100m)

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0.00% 0.01% 0.10% 1.00% 10.00%

Loss as share of premiums

α

PD=0.1% ρ=0.20 Failure


Comparison with existing funds

Life

Latvia Malta(#) France Germany Romania

Actual fund size (OXERA, latest available figures) (in m€) 0.8 (1) 2.33 (2) 569 (4) 640 (2) 136 (3) 17.1 (3)

The model used in this study would produce results identical to the actual fund size with the following parameters:

ρ=0.2, LGD=15%, PD= 0.1% then α = 99.85% 98.36% 92.80% 96.33% 81.64% 100.00%

ρ=0.2, LGD=15%, PD=0.5% then α = 98.55% 89.93% 67.99% 77.15% 44.24% 99.97%

ρ=0.2, LGD=45%, PD= 0.1% then α = 99.15% 94.62% 81.38% 63.32% 63.32% 99.96%

ρ=0.2, LGD=45%, PD= 0.5% then α = 94.49% 77.39% 45.94% 53.99% 24.00% 98.96%

ρ=0.2, α =90%, LGD=15% then PD = 2.35% 0.50% 0.14% 0.05% 0.05% 6.11%

ρ=0.2, α =90%, LGD=45% then PD = 0.89% 0.19% 0.05% 0.02% 0.02% 1.91%

ρ=0.2, α =90%, PD=0.1% then LGD = 662.41% 95.84% 20.97% 7.52% 7.52% 922.67%

ρ=0.2, α =90%, PD=0.5% then LGD = 89.32% 14.88% 3.77% 1.40% 1.40% 172.03%

Notes: (#)IGS funding needs for Malta are estimated based on the host state principle, as Malta employs a pure-host IGS, (1) 2006 data; (2) target fund size as given for 2008; (3) actual funds: 2008 data; (4) 2007 data


Conclusions

• Simple single factor model to assess loss distribution of IGS is presented

• Propose calibration of parameters using public data• Take into account Solvency II capital requirements• Apply it to EU life insurance sector• Average fund size of respectively 0.50% and 1.52% of gross

premiums written would be sufficient to assure adequate coverage in 95% and 99% of all years

• Current IGS in place keep funds which are consistent with our results

6th samos conference in actuarial science and finance, samos, june 3-6 insurance guarantee schemes:...

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