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 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.

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

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

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 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 factors so the value of the asset can be written as:

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

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

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

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

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Current EU position Used in this paper Life Total LVBGUKMTFRDEROPLES Nature of intervention Pure compensation to claimants XXxxXXXXX Continuation of contracts XX(1)XXX Eligible claimants Natural persons only XX Natural persons + SMEs xx Natural and legal persons except financial institutions X Natural and legal entity XXXXX Compensation limits and reductions Capping payouts XXXXn/a Capping payouts for non-compulsory insurance XX Level of coverage in percentage terms n/a Level of coverage in percentage terms (compulsory ins.) 100 Fixed deductible Other reduction in benefits XX Geographic scope An IGS in each MS with home state principle XXXXXXXX An IGS in each MS with host state principle XxXX Other X Types of policies covered Without exclusions XXXXXXX With exclusion XXX

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 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 15 All from CEA (the European insurance and reinsurance federation)

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Calibration of parameters: results for δ For LU, RO and HU the value is only based on the number of companies available as all other information is missing

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

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

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 EAD- home state principle, full coverage The results depends heavily the market covered, types of contracts covered and size of coverage Country EAD Total gross premiums written Country EAD Total gross premiums written (m€) Austria58,1887,141Latvia # 8353 Belgium168,16322,179Lithuania # Bulgaria # Luxembourg76,57110,093 Cyprus # 2,717358Malta # 1, Czech Republic6,5442,034Netherlands266,31726,437 Denmark118,09013,190Poland17,0596,743 Estonia # Portugal40,2979,205 Finland37,0992,784Romania # France1,189,627136,528Slovakia2, Germany765,18075,170Slovenia # 2, Greece # 7,6302,504Spain164,93823,455 Hungary5,2822,017Sweden191,51012,985 Ireland147,44437,563United Kingdom2,034,005305,184 Italy389,12661,438

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Results I: Share of portfolio lost Expected75.0%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%

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Results II: Losses as share of total premium Expected75%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%

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Position of an historical loss Insolvency of Mannheimer Lebenversicherung 2003, Germany amounted to €100m or 0.13% of the total premiums

6th Samos Conference in Actuarial Science and Finance, Samos, June 3-6 Comparison with existing funds Life LatviaMalta(#)FranceGermanyRomania 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% thenα =99.85%98.36%92.80%96.33%81.64%100.00% ρ=0.2, LGD=15%, PD=0.5% thenα =98.55%89.93%67.99%77.15%44.24%99.97% ρ=0.2, LGD=45%, PD= 0.1% thenα =99.15%94.62%81.38%63.32% 99.96% ρ=0.2, LGD=45%, PD= 0.5% thenα =94.49%77.39%45.94%53.99%24.00%98.96% ρ=0.2, α =90%, LGD=15% thenPD =2.35%0.50%0.14%0.05% 6.11% ρ=0.2, α =90%, LGD=45% thenPD =0.89%0.19%0.05%0.02% 1.91% ρ=0.2, α =90%, PD=0.1% thenLGD =662.41%95.84%20.97%7.52% % ρ=0.2, α =90%, PD=0.5% thenLGD =89.32%14.88%3.77%1.40% % 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

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