June 6-7, 2005 CAS 2005 Seminar on Reinsurance 1 International Regulatory Changes Actuarial Applications By Eric Lecoeur, FIA SCOR, Group Chief Actuary

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 2 Disclaimer The following presentation focuses on international regulatory changes in progress in the framework of IFRS phase II and Solvency II. It reflects opinions and interpretations of available material at May Positions and interpretations on any issue raised may subsequently change, according to the publication of official directives concerning certain accounting standards. This presentation creates no contractual relationship with SCOR. The participant has to be aware that, in making this presentation available, SCOR is not providing professional advice and accepts no liability arising from reliance upon this presentation. Any decision by a participant in this session or other readers of this presentation to rely on the opinions expressed here shall be at the participant’s own risk.

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 3 Schedule Solvency I Müller Report in 1997 Solvency I project initiated Solvency I Completed (inforce by 2004) Directive of the European Parliament on reinsurance Proposal for the directive (21/04/2004) Proposal backed by the European Economic ans Social Committee Enforcement ? Solvency II Sharma Report (2001) : project initiated End of Phase I (design of the system) Exposure Draft finalised for Phase II : ? ICAS by FSA (UK) CP 190 (non life) + CP 195 (life)  Integrated Prudential Sourcebook FSA’s ICA review Exposure Draft for Phase I (31/07/03) IAS / IFRS Final Phase I Standards IFRS 4 (31/03/04) Phase I Balance Sheet (published at 31/12/05) Final Phase II standard : 2007, 2008 ? Phase II Financial Statements Published : 2009 ? …

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 4 Content IAS / IFRS – Their impact on liability assessment Solvency II – Their impact on liability assessment Conceivable actuarial approaches

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 5 IAS / IFRS Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 6 Phase I : IAS 39 / IFRS 4 IFRS 4 focuses on 3 points : Definition of an “insurance contract” Unbundling of deposit elements Separate embedded derivatives Enhanced disclosure sensitivity analyses risk management procedures Principle of “Fair Value” IAS 39 IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 7 Phase I : Accounting policies PROHIBITED Catastrophe and equalization provisions Offsetting reinsurance assets against insurance liabilities MANDATED Liability adequacy testing IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 8 Phase I : Accounting policies ALLOWED TO CONTINUE (but not implement) Undiscounted liability basis Deferred Acquisition Costs / Unearned Premium Reserve approach CAN BE IMPLEMENTED Use of market discount rates (if undiscounted liability is used) Use of shadow accounting (life insurance) IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 9 Phase II – Actuarial consequences on reserving 1/3 Catastrophe and equalization provisions are banned because they do not meet the criteria for liabilities Premiums and costs will no longer be smoothed over time (through deferred acquisition costs and unearned premium reserve) Liabilities measured at their “fair value”  Interpretation : discounted anticipated value, at the closing date, of future cash flows IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 10 Phase II – Actuarial consequences on reserving 2/3 Use of discounting : The discount rate is likely to be the return on a risk-free asset Still some discussions about whether the credit quality should impact the liability recorded Comments on the Credit Standing of the issuer: From a strictly theoretical point of view, the fair value of a liability should recognize that there is some possibility of default  reduction of the expected value of future cash flows and therefore the level of the liability Weaker insurers would reserve less than stronger players for the same liability … IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 11 Phase II – Actuarial consequences on reserving 3/3 A risk premium (Market Value Margin or MVM) must be taken into account because of the uncertainty of the liabilities Format of the Market Value Margin Adjusting the discount rate applied to expected cash flows … Incorporating a variability in loss reserve payment timing and then using a risk-free discount rate for the cash flows (it seems to have the preference of IASB) Comments on the Market Value Margin Making accounts more opaque (e.g. some capital may be hidden in the form of MVM) / An ability to be misused as a profit smoothing device Phase II is little developed. Some points are not yet solved, for instance the lack of diversification credit (the MVMs are likely to be additive between the pools or segments that they are calculated in) IAS / IFRS – Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 12 IFRS versus Solvency II Assets (market value) IFRS / Solvency II Liabilities (economic Value) Economic net assets Solvency II IAS Fair Value IFRS Phase II Market Value Margin Present Value of Future Cash flows 

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 13 Solvency II Their impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 14 Objectives of Solvency II Global solvency approach Protect policyholders Provide comparability, transparency and coherency Enhanced risk sensitiveness Reflect market developments (derivatives, ALM …) Encourage internal risk management SOLVENCY II – Its impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 15 Organisation of Solvency II Solvency II EC CEIOPS / EIOPC Actuaries  IAA  Groupe Consultatif Canadian project EU States’ project Basel II IAIS IASB US project Australian project APRACIAOSFI CAS SOANAIC « A global framework for insurer solvency assessment » (Jan. 2004) «Australian capital requirements for non-life insurers: Internal model Based Method» (2002) Switzerland Netherlands UK FSA

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 16 A « three pillars » approach Capital requirements Supervisory Review process Market transparency Disclosure Pillar IPillar IIPillar III SOLVENCY II SOLVENCY II – Its impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 17 SOLVENCY II – Its impact on liability assessment Final output

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 18 Spreads (Bonds) Market Risk Insurance Risk Credit Risk Operational Risk Share Price Interest Rates FX Volatility Liquidity Concentration Model Economic Factors Catastrophes New Business Old Business Concentration Model Loans / Debtors Reinsurers Model Concentration SOLVENCY II – Its impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 19 Spreads (Bonds) Market Risk Insurance Risk Credit Risk Operational Risk Economic Factors Catastrophes New Business Old Business Concentration Model Loans / Debtors Reinsurers Model Concentration Share Price Interest Rates FX Volatility Liquidity Concentration Model SOLVENCY II – Its impact on liability assessment Estimation of the reserving risk

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 20 Consequences on reserving Preservation of the equalization reserves (contrary to IFRS) Discount of the reserves with a risk-free rate corresponding to the average duration of the liabilities (coherent with IFRS approach) Necessary to replace deterministic approaches with stochastic one, in order to quantify the level of prudency. Different measures are proposed: the IFRS approach : best estimate + « market value margins » VaR / Tail-VaR Best-estimate loaded with a coefficient linked to the volatility of the LoB SOLVENCY II – Its impact on liability assessment

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 21 Consequences on reserving SOLVENCY II – Its impact on liability assessment VaR / Tail-VaR The Value at Risk (VaR) is the alpha-% quantile of the ultimate losses’ distribution. The Expected Shortfall (ES), or tail conditional expectation: expectation of the ultimate losses amount given that it exceeds the VaR. ES(alpha) = E[ X | X > VaR(alpha) ]

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 22 Conceivable actuarial approaches Review of regulations in Asia-Pacific

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 23 Conceivable actuarial approaches According to the Insurance Act (Chapter 142), the valuation of insurance policy liabilities of each line of business must comprise: Best estimate of the premiums liabilities Best estimate of the claims liabilities Provision for adverse deviation that relates to the inherent uncertainty in the best estimate value of both the premium and claims liabilities at a minimum 75% confidence level. The Singaporean point of view

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 24 Conceivable actuarial approaches Extract of the Australian Prudential Standard GPS 210 : “Insurance liabilities include both the insurer’s Outstanding Claims Liabilities, and its Premiums Liabilities.” “The Approved Actuary must provide advice on the valuation of insurance liabilities at a given level of sufficiency – that level is 75% (or, in some circumstances, the central estimate plus one half of the coefficient of variation).” “Insurance liabilities are to be valued on a discounted basis. The rate to be used in discounting is the risk-free rate; i.e. the gross redemption yield of a portfolio of sovereign risk securities with a similar expected payment profile to the insurance liabilities” The Australian point of view

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 25 Conceivable actuarial approaches Claims liability  “Stand alone” risk margins for the Net Outstanding Claims Liabilities for Primary Insurers  “Stand alone” risk margins for the Net Outstanding Claims Liabilities for Inwards Reinsurance: - For proportional inwards reinsurance : same coefficients - for non-proportional inwards reinsurance : coefficient to be applied to direct risk margin (about 2) The Australian point of view Coefficients for the risk margin computation from the report of Bateup&Reed

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 26 Conceivable actuarial approaches Premium liability  “Stand alone” risk margins for the Net Premium Liability : The recommended multiples of the net outstanding claims liability risk margin to be applied for determining premium liability risk margins, are as follows : for short tail lines of business for long tail lines of business The Australian point of view

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 27 Conceivable actuarial approaches Diversification: “Rule of thumb”: Diversification discount = f (C, N, S) Where: C = coefficient of concentration = (Net insurance liability for largest LoB) / (Total net insurance liability) N = number of lines of business S = size of the insurer’s total insurance liabilities in $ million The Australian point of view

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 28 Conceivable actuarial approaches Risk Margin Estimation Risk margin estimation under some classical underlying distribution assumptions : Let X be the random variable “Ultimate Aggregate Loss” with average m (which is the best estimate) and standard deviation σ. What is the loading Lα to be applied to the best estimate to achieve a level of confidence of α percent? Notation: we will name AlphaEst the new estimate.

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 29 Conceivable actuarial approaches Risk Margin Estimation Assumption of log-normality : Let X follow a lognormal distribution with parameters μ and σ The random variable Y defined as ln X follows a N(M,S), with : Introducing the variation coefficient of X,, we have : which leads to the loading Note: under an assumption of normality, the loading is

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 30 Conceivable actuarial approaches Bootstrapping the Chain Ladder (simplified) Definitions Assume that the data consist of a triangle of incremental claims: The cumulative claims are defined by: and the loss development factors (LDF) of the chain-ladder technique are denoted by :

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 31 Conceivable actuarial approaches Bootstrapping the Chain Ladder (simplified) Obtain the standard chain-ladder development factors Obtain incremental fitted values by backwards recursion Calculate the unscaled Pearson residuals and the scale parameter Ф Resample with replacement the adjusted residuals Obtain pseudo data Use chain ladder and estimate future incremental payments

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 32 Conceivable actuarial approaches Bootstrapping the Chain Ladder (simplified) Simulate future payments from process distribution assuming the mean is the incremental value obtained Repeat many times, storing the reserve estimates, giving a predictive distribution Prediction error (variability in the data and variability due to the estimation) is then standard deviation of results Where SE bs (R i ) is the bootstrap standard error of the reserve estimate and p is the number of parameters estimated

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 33 Conceivable actuarial approaches Improving bootstrapping Variability often changes across in triangle. The idea is to divide the triangle into “zones” for simulation. Use of correlations between LoBs  use of rank correlations between the simulations of the triangles for each Line Of Business (see Kirschner, “Two approaches to calculating correlated reserve indications across multiple lines of business”) ZONE 1ZONE 2

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 34 Conceivable actuarial approaches Mack’s model The Mack’s model reproduces chain-ladder estimates. The model is distribution-free and only specifies the first two moments of the distribution. The hypothesis are similar to those of the Chain Ladder method, with in addition that the variance of D ij is equal to And consequently :

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 35 Conceivable actuarial approaches Mack’s model For 1 ≤ j ≤ n – 2 : The mean squared error of the estimated reserve R i can be estimated by : Under the assumption of independence between the accident years, the model provides estimators for λ j (Loss Development Factors of the chain ladder method) and

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 36 In this example, we use the same data as Verrall (1990, 1991) and Mack (1993) : Run-off triangle (accumulated figures) Conceivable actuarial approaches Example i

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 37 Bootstrapping the reserves allows to obtain the distribution (outputs from RESQ® of EMB) : Conceivable actuarial approaches Example Cumulative distributionDensity function

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 38 Conceivable actuarial approaches Example

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 39 Conceivable actuarial approaches Example Errors of estimates:

June 6-7, 2005 CAS 2005 Seminar on Reinsurance 40 Selected references England P.D., Verrall R.J. (1999) : « Analytic Bootstrap estimates of prediction error in claims reserving » Insurance : Math. And Econ. Vol. 25, Mack T. (1993) : « Distribution free calculation of the standard error of Chain Ladder reserve estimates » Astin Bull. Vol. 23, Prudential Standard GPS 210 : « Liability Valuation for General Insurers » FitchRatings (May 2004) : « Mind the GAAP: Fitch’s view on Insurance IFRS » Deloittewww.iasplus.com R. Bateup and I. Reed, (November 2001) : « Research and data analysis relevant to the development of standards and guidelines on Liability valuation for General Insurance »