Use of Statistical Models on the Supervisory Process of ASSAL XVII Annual Meeting Liabilities, Technical Provisions, Sufficiency Analysis and Security Margins Use of Statistical Models on the Supervisory Process of Non-Life Claims Provisions Instituto de Seguros de Portugal 27/04/2006

ASSAL XVII Annual Meeting Agenda Non-Life Technical Provisions ISP Supervisory Process Ratio Analysis Statistical Approaches Examples Solvency II – expected future developments Best Estimate Risk Margin

ASSAL XVII Annual Meeting Non-Life Technical Provisions Claims Provisions Coverage of outstanding liabilities arising from past claims, reported and unreported, including claims management expenses Premium Provisions Coverage of liabilities arising from future claims, for policies in-force at the valuation date

ASSAL XVII Annual Meeting Non-Life Technical Provisions

ASSAL XVII Annual Meeting Non-Life Technical Provisions Ideally, technical provisions should correspond to the amount of discounted liabilities arising from insurance contracts However, value of liabilities is unknown today and it can only be estimated A single point estimate is not enough Increasingly, liabilities are estimated using assumptions of probability distributions for risk factors and stochastic properties Due to estimation uncertainty, security margins are needed to ensure that technical provisions are sufficient enough to ensure the run-off of liabilities or their transferability at a high confidence level

ASSAL XVII Annual Meeting ISP Supervisory Process ISP pays particular attention to the responsible actuary’s critical analysis of the technical provisions’ estimates Several ratios are computed and analysed ISP runs various statistical methods (deterministic and stochastic) to estimate the expected value and variability of non-life claims provisions A detailed technical and practical manual is available to ISP supervision staff as a guidance for the analysis of claims provisioning (off-site and on-site analysis)

ASSAL XVII Annual Meeting ISP Supervisory Process Ratio Analysis Ratios and indicators considered on ISP analysis of non-life claims provisions: Growth on Premiums Average Premium Loss Ratio Average Cost of New Claims Average Claims Provision Claims Frequency Development of Claims Payments “Speed” of Process closure Re-openings Claims Expenses Provisioning, including IBNR Readjustments Ratios are calculated individually and compared on a static and evolutionary perspective with peer group and market benchmarks 1- Growth on Premiums = Written Premiums (n) / Written Premiums (n-1) 2- Average Premium = Earned Premiums / Average nr. of insured cars Average nr. of insured cars = [ nr. of insured cars (n) + nr. of insured cars (n-1) ] / 2 3- Loss Ratio = Incurred Claims / Earned Premiums 4- Average Cost of New Claims = Incurred Claims (estimated on accident year) / Nr. Claims (incurred and reported at accident year) 5- Average Claims Provision = Claims Provision / Nr. of Claims outstanding 6- Claims Frequency = Nr. Claims incurred / Average nr. of insured cars 7- Development of Claims Payments = Paid amounts / Incurred Claims 8- “Speed” of Process closure = Nr. of claims incurred and closed at year / Nr. of claims incurred at year 9- Re-openings = Nr. of claims reopened at year / Nr. of claims closed at year 10- Claims Expenses = Claims Management Costs / Net Paid Amounts 11.1- Claims Provision / Earned Premiums 11.2- Claims Provision / Incurred Claims 11.3- Claims Provision / Paid Claims 11.4- Incurred Claims / Earned Premiums 12. Readjustments = Provision (n) + Paid Claims (n) – Provision (n-1)

ASSAL XVII Annual Meeting ISP Supervisory Process Statistical Approaches The statistical methods’ objective is to project the expected future claims experience, using assumptions based on past data analysis complemented with expert opinion The analysis should consist of: Analysis of results (particularly the estimation error), taking into account the theoretical assumptions underlying each model Analysis of relevant graphs and hypothesis tests to assess each models’ fitness

ASSAL XVII Annual Meeting ISP Supervisory Process Statistical Approaches Format of a Run-off triangle representing accident year x development year Run-off triangles may refer to: Number of claims Claims paid (common approach) Claims incurred, i.e. Claims paid + Claims provision Aim is to estimate the lower unknown triangle (shaded):

ASSAL XVII Annual Meeting ISP Supervisory Process Statistical Approaches Deterministic methods Projection of past claims experience assuming fixed development factors Provides point estimates of the expected future claims amounts Various actuarial techniques are available Stochastic models Random nature of variables is considered Generally speaking, the future claims amounts are assumed to follow a specified probability distribution Allows for the measurement of the estimates variability, essential for the construction of confidence intervals for the estimates Various actuarial models are available

ASSAL XVII Annual Meeting Statistical Approaches Statistical Methods available at ISP ISP has in-house built programs that allow for the automatic testing of the following statistical methods: Some of the methods consider: Possibility for inflation correction Variant approaches based on different assumptions Advanced refinements to include reparameterization and expert opinion

ASSAL XVII Annual Meeting Statistical Approaches Example Results from running the programs for the previous run-off triangle:

ASSAL XVII Annual Meeting Statistical Approaches Example (cont.) Simulated empirical distribution of the total claims provision using Bootstrap ODP stochastic model:

ASSAL XVII Annual Meeting Statistical Approaches Example (cont.) Goodness-of-fit tests for the Analytic ODP stochastic model:

ASSAL XVII Annual Meeting Statistical Approaches Example (cont.)

ASSAL XVII Annual Meeting Solvency II – Expected Future Developments Harmonisation of technical provisions across the European Union: Rules for the valuation of the Best Estimate and Risk Margin Rules for inclusion of diversification benefits Reporting tools Supervisory techniques for sufficiency and adequacy assessment Main objective is to embed a risk management culture within the companies, across all functions

ASSAL XVII Annual Meeting Solvency II: Technical Provisions Can be decomposed on 2 components: Best Estimate Corresponds to the expected value of liabilities, i.e. the average of the corresponding probability distribution Risk or Security Margin An additional cushion that takes into account the volatility and uncertainty of liabilities Aimed at ensuring that provisions are enough to run-off or transfer liabilities with a high level of confidence Best Estimate Risk Margin

ASSAL XVII Annual Meeting Solvency II: Best Estimate Calculation per homogeneous risk group Based on realistic actuarial and economical assumptions, i.e. expected values of risk factors Should incorporate all the factors with impact on the amount, timing or probability of cash flows: Inflation Reinsurance Recoveries ... Should be based on more than past experience: expert opinion is crucial Allowance for future expected developments and trends Regular review of assumptions

ASSAL XVII Annual Meeting Solvency II: Risk Margin Main factors that can affect the volatility and uncertainty of the estimated liabilities: Statistically ‘normal’ market volatility Characteristics (riskiness) of the insurance portfolio held by the company, including concentration Quantity and quality of the data used for the estimation process Estimation model and parameter errors

ASSAL XVII Annual Meeting Solvency II: Risk Margin 2 main approaches are on discussion: Percentile approach Underlying philosophy is to ensure that provisions are enough to run-off the liabilities with an x% probability confidence level Risk margin corresponds to the difference between a specified x% quantile of the loss probability distribution and the best estimate Implicitly, Value-at-Risk is the risk measure used. Variant approaches can consider other risk measures, such as TailVaR.

ASSAL XVII Annual Meeting

ASSAL XVII Annual Meeting Motor – estimated BE+RM Claims Provision

ASSAL XVII Annual Meeting Motor – estimated BE+RM Premium Provision

ASSAL XVII Annual Meeting Solvency II: Risk Margin Cost-of-Capital Underlying philosophy is to ensure that liabilities can be transferred to a willing, rational, diversified counterparty in an arms’ length transaction under normal business conditions Risk margin corresponds to Market Value Margin, based on the cost of future regulatory capital required for on-going business MVM corresponds to the amount that a rational investor would demand in excess of the best estimate to take over the liabilities Technical provisions correspond to the fair value of liabilities, i.e. are, conceptually, fully market consistent

ASSAL XVII Annual Meeting Source: CRO Forum