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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
Centre Unit for Econometrics and Applied
Statistics The views expressed in this paper are
those of the authors and should not be attributed
to the European Commission or Member States.
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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

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

• 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

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The model

• IGS protect policyholders/claimants from credit
  risk of insurers
• Employ 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 factorsso the value of the asset
  can be written as

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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, ?.

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Extension of the model

• Model assumption is infinite and homogeneous
  market
• BUT
• only a finite number of exposures
• not all insurance companies are equally large

• Inclusion of additional correction term
  granularity factor d
• 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

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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 a
• 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 a

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Application
IGS for the Life insurance sector in each EU
member states

• 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

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Current EU position
  Used in this paper Life   Life   Life   Life   Life   Life   Life   Life   Total
  Used in this paper LV BG UK MT FR DE RO PL ES
Nature of intervention
Pure compensation to claimants X X x x X X X X X
Continuation of contracts X X(1) X X X
Eligible claimants
Natural persons only X X
Natural persons SMEs x x
Natural and legal persons except financial institutions X
Natural and legal entity X X X X X
Compensation limits and reductions
Capping payouts X X X X n/a
Capping payouts for non-compulsory insurance X X
Level of coverage in percentage terms 100 100 70 90 75 100 100 50 n/a
Level of coverage in percentage terms (compulsory ins.) 100 100
Fixed deductible
Other reduction in benefits X X
Geographic scope
An IGS in each MS with home state principle X X X X X X X X
An IGS in each MS with host state principle X x X X
Other X
Types of policies covered
Without exclusions X X X X X X X
With exclusion X X X
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Calibration of parameters

• Calibration of the VaR parameters
• For the probability of default PD 0.1
• Standard and Poors 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 ? 20
• In line with Basel II IRB risk model
  recommendations
• For the granularity adjustment d 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 15
• All from CEA (the European insurance and
  reinsurance federation)

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Calibration of parameters results for d
For LU, RO and HU the value is only based on the
number of companies available as all other
information is missing
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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 a 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 beneficiaries
• This 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

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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 CEA
• Note adjusted TP refers to correction from
  Solvency I to Solvency II

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EAD- home state principle, full coverage
 Country EAD Total gross premiums written  Country EAD Total gross premiums written
 Country (m) (m)  Country (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      
The results depends heavily the market covered,
types of contracts covered and size of coverage
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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
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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
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Position of an historical loss
Insolvency of Mannheimer Lebenversicherung 2003,
Germany amounted to 100m or 0.13 of the total
premiums
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Comparison with existing funds
Life Life Life Life Life Life
    Latvia Malta() France Germany Germany Romania
Actual fund size (OXERA, latest available figures) (in m) 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 The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters The model used in this study would produce results identical to the actual fund size with the following parameters
?0.2, LGD15, PD 0.1 then a 99.85 98.36 92.80 96.33 81.64 100.00
?0.2, LGD15, PD0.5 then a 98.55 89.93 67.99 77.15 44.24 99.97
?0.2, LGD45, PD 0.1 then a 99.15 94.62 81.38 63.32 63.32 99.96
?0.2, LGD45, PD 0.5 then a 94.49 77.39 45.94 53.99 24.00 98.96
?0.2, a 90, LGD15 then PD 2.35 0.50 0.14 0.05 0.05 6.11
?0.2, a 90, LGD45 then PD 0.89 0.19 0.05 0.02 0.02 1.91
?0.2, a 90, PD0.1 then LGD 662.41 95.84 20.97 7.52 7.52 922.67
?0.2, a 90, PD0.5 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 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 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 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 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 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 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 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
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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