Méthode de provisionnement en assurance non-vie Solvency II & IFRS



Similar documents
International Financial Reporting for Insurers: IFRS and U.S. GAAP September 2009 Session 25: Solvency II vs. IFRS

Quantitative Impact Study 1 (QIS1) Summary Report for Belgium. 21 March 2006

SOLVENCY II HEALTH INSURANCE

Runoff of the Claims Reserving Uncertainty in Non-Life Insurance: A Case Study

Solvency Management in Life Insurance The company s perspective

CEIOPS-DOC-36/09. (former CP 42) October 2009

CEIOPS-DOC-47/09. (former CP 55) October 2009

Capital requirements for health insurance under Solvency II

Towards the strengthening and moderinsation of insurance and surety regulation

Embedded Value Report

One-year reserve risk including a tail factor : closed formula and bootstrap approaches

Solvency II for Beginners

Solvency II and catastrophe

AISAM-ACME study on non-life long tail liabilities

Solvency II Standard Formula and NAIC Risk-Based Capital (RBC)

Solvency II Standard Model for Health Insurance Business

Best Estimate of the Technical Provisions

An update on QIS5. Agenda 4/27/2010. Context, scope and timelines The draft Technical Specification Getting into gear Questions

SCOR inform - April Life (re)insurance under Solvency II

THE MULTI-YEAR NON-LIFE INSURANCE RISK

Preparing for ORSA - Some practical issues Speaker:

Tail-Dependence an Essential Factor for Correctly Measuring the Benefits of Diversification

CEIOPS-DOC-45/09. (former CP 53) October 2009

SOLVENCY II LIFE INSURANCE

Actuarial Risk Management

The Next Generation of the Minimum Capital Test - A Canadian Regulatory Capital Framework

Market Consistent Embedded Value Principles October CFO Forum

The Study of Chinese P&C Insurance Risk for the Purpose of. Solvency Capital Requirement

Market Value Margin: Practical calculations under the Solvency II Cost of Capital approach

Preparing for Solvency II Theoretical and Practical Issues in Building Internal Economic Capital Models Using Nested Stochastic Projections

Solvency II Introduction to Pillar 3. Friday 20 th May 2016

Market-Consistent Embedded Value (MCEV)

Treatment of technical provisions under Solvency II

How To Calculate Multi-Year Horizon Risk Capital For Non-Life Insurance Risk

ING Insurance Economic Capital Framework

CEIOPS-DOC-33/09. (former CP 39) October 2009

THE INSURANCE BUSINESS (SOLVENCY) RULES 2015

Solvency II Pillar III Quantitative Reporting Templates (QRTs) Sinead Clarke, Eoin King 11 th December 2012

SOLVENCY II HEALTH INSURANCE

Regulatory Updates MCT Guideline (Draft) and other regulatory reporting changes

BEL best estimate liability, deduced from the mean loss as a present value of mean loss,

EIOPACP 13/011. Guidelines on PreApplication of Internal Models

Society of Actuaries in Ireland

SOLVENCY II LIFE INSURANCE

CEIOPS Preparatory Field Study for Life Insurance Firms. Summary Report

Solvency II Technical Provisions under solvency II Detailed Guidance. March 2010

SA QIS3 Key changes and challenges The end is in sight

Central Bank of Ireland Guidelines on Preparing for Solvency II Pre-application for Internal Models

ERM from a Small Insurance Company Perspective

Insurance Groups under Solvency II

Modelling the Claims Development Result for Solvency Purposes

Implementation of Solvency II

Guidelines on the valuation of technical provisions

Actuary s Guide to Reporting on Insurers of Persons Policy Liabilities. Senior Direction, Supervision of Insurers and Control of Right to Practice

Solvency II Revealed. October 2011

Fourth study of the Solvency II standard approach

Regulations in General Insurance. Solvency II

CEIOPS-DOC-43/09. (former CP 50) October 2009

CEA Working Paper on the risk measures VaR and TailVaR

Solvency II Technical Provisions under solvency II Detailed Guidance. March 2011 update

Revised Annexes to the Technical Specifications for the Solvency II valuation and Solvency Capital Requirements calculations (Part I)

ORSA - The heart of Solvency II

LIFE INSURANCE CAPITAL FRAMEWORK STANDARD APPROACH

Consequences. Modelling. Starting Points. Timetable. Solvency II. Solvency I vs Solvency II. Solvency I

AXA s approach to Asset Liability Management. HELVEA Insurance Capital Adequacy and Solvency Day April 28th, 2005

CEIOPS-DOC-22/09. (former CP27) October CEIOPS e.v. Westhafenplatz Frankfurt Germany Tel

Solvency II Technical Provisions valuation as at 31st december submission template instructions

Asset Liability Management at Munich Reinsurance Company

Insights. Understanding market value margins in options prices. September Background

Solvency II New Framework for Risk Management Organisation. Dr. Maciej Sterzynski (Triglav Insurance, Ltd.) Matija Bitenc (Triglav Insurance, Ltd.

A Primer for Calculating the Swiss Solvency Test Cost of Capital for a Market Value Margin

CEIOPS-QIS5-06/10 6 September 2010

The standard formula requires further adjustments

Methodology. Discounting. MVM Methods

SOLVENCY II GENERAL INSURANCE

SWEDBANK FÖRSÄKRING AB European Embedded Value

Stochastic Analysis of Long-Term Multiple-Decrement Contracts

Insurance Accounting AUDIT COMMITTEE NEWS. Financial Reporting. Edition 43 / Q4 2013

Impacts of the Solvency II Standard Formula on health insurance business in Germany

Solvency II. Model validation guidance. April 2014

IASB Educational Session Non-Life Claims Liability

A reserve risk model for a non-life insurance company

Property Casualty Insurer Economic Capital using a VAR Model Thomas Conway and Mark McCluskey

Introduction. Coverage. Principle 1: Embedded Value (EV) is a measure of the consolidated value of shareholders interests in the covered business.

Actuarial Guidance Note 9: Best Estimate Assumptions

Guidance for the Development of a Models-Based Solvency Framework for Canadian Life Insurance Companies

Final Report. Public Consultation No. 14/036 on. Guidelines on application of outwards reinsurance. arrangements to the non-life

Solvency II. PwC. *connected thinking. Internal models requirements and an example

A New Chapter in Life Insurance Capital Requirements

CHALLENGES FOR BASEL II IMPLEMENTATION IN CHILE

Transcription:

Méthode de provisionnement en assurance non-vie Solvency II & IFRS A Revolution of the Insurance Business Model Journées d économétrie et d économie de l'assurance 22 octobre 2009 1 Yannick APPERT-RAULLIN Manager P&C Risk Modelling GRM AXA

Introduction 1 Solvency II project 2 CoC: Economic View of insurance Risks 3 QIS IV Standard model 4 Develop an internal model 5 Risks & opportunities 2 22/10/2009

3 22/10/2009 1 Solvency II project

Solvency II Moving to an Economic Framework Assets at market value (100) Surplus (10) SCR Solva II (20) Market value of liabilities (70) total capital 30 Financial market shock (-10) Adverse developments of claims (+10) (-10) Asset at Market value (90) Capital (10) Market value of liabilities (80) > SCR : level of capital such that assets are sufficient to absorb a 99,5% 1-year adverse scenario What does an Economic Framework mean? Asset/liability integrated view Diversification recognized Risk mitigation/risk transfer techniques recognized Convergence between regulatory treatment and company assessment 4 22/10/2009

Solvency II Through a Three Pillars Structure A three pillar approach as in Basle II Pillar I Quantitative capital requirements Technical reserves Capital Pillar II Prudential supervision Internal controls Risk management Capital add-on Pillar III Market discipline Financial statements Disclosures A two-tier approach : SCR (Solvency Capital Requirements), calculated with: Standard model (to be defined by CEIOPS / will be risk-based with factors applied on provisions or scenario-based with stress tests) Or Internal models (if validated by supervisors) MCR (Minimum Capital Requirements) Simple Absolute minimum 5 22/10/2009

Solvency II Strong Interactions with IFRS and EEV EEV Solvency II IFRS II Market Value Of Assets EEV NFR BEL Available Capital =? MVM =? BEL Sh. Equity Service Margin Risk margin BEL Strong rationale for convergence Synergies in producing the figures Streamline communications with markets/auditors/ supervisors Unify analysis framework however Different purposes Different timetables According to Milliman, - already 10 years of making an with at least 3 years to go until completion, the IASB insurance accounting project is a long haul by any measure - an agenda paper of the IASB («le CEIOPS des IFRS») outlines potential changes in priorities and identifies the insurance project as one that could be postponed 6 22/10/2009

Solvency II Overview of the Timetable and of the Processes 12/2005-2009 QIS (Quantitative Impact Studies) : assessment of technical reserves & capital? European Commission Drafting process 06/2004 02/2006 Technical works by CEIOPS 07/2007 Draft of directive Political Debate Implementation measures Begin. 2009 Final regulation 2012 Solvency II in force Participation to discussions within industry Network of correspondents within the Group Participation to QIS Technical works Political lobbying Final adaptation of data, IT models and internal models 7 22/10/2009

Solvency II The Main Players Comit é Europ é en des Assurances ( CEA) European industry position European Parliament Voting of the directive European Commission (Insurance Unit) Project management Drafting of the directive Committee of Ministries of Finance (EIOPC) / Council of ministers Validation of the main issues Voting of the framework directive Chief Financial Officers Forum (CFO Forum) Link with IFRS ph. 2 capital management issues Chief Risk Officers Group (CRO Group) Technical expertise in risk management from industry perspective + Analysts meetings, Articles, Committee of Insurance Supervisors (CEIOPS) Input on technical issues 8 22/10/2009

Solvency Définitions Solvency Margin (Regulatory framework): the required solvency margin is the regulatory capital that an insurance company must necessarily have in order to operate. Its role is to ensure business continuity in case of loss. The current calculation (Solvency I) based on a simple formula: Max (16% x Premium ; 23% x Losses). the available solvency margin corresponds to the elements of capital which can be used to fulfil the required solvency margin plus the unrealized capital gains. 9 22/10/2009

2 CoC : Economic view of Insurance risks 10 22/10/2009

Moving to an economic view General purposes (1/2) One principle : market consistent approach In order to be consistent with life value frameworks, Economic Value of P&C Insurance risks must be market consistent. However, assessing the market value of liabilities is particularly difficult for nonhedgeable risks where there is no observable market price. To overcome this difficulty, a cost of capital approach is proposed by CRO Forum for P&C risks and non-hedgeable risks : Mark-to-model approach with an explicit MVM. Market consistent to be in line with Solvency II and with life EEV 11 22/10/2009 AFR Tax cost of capital (Reserves = BEL +MVM) MVM (Market Value Margin) is the additional amount that an investor will require to take the BEL and the associated risk. To calculate MVM, we must assess the risk return expected by shareholder, to be applied to the SCR, the regulatory capital. For Life EEV, currently, non hedgeable risks are assessed through a tax cost of capital, and not through a full cost of capital. However, working groups of CFO Forum are currently developing a methodology to move to a full CoC, similar to the one we propose.

Moving to an economic view General purposes (2/2) Available Financial Resources AFR is calculated as the difference between market value of assets and BEL+MVM Best estimate liabilities (BEL) are estimated by discounting future expected cash flows at the risk-free rate. Only time value is considered : risk return is explicitly taken into account in the MVM. Market Value of Assets Run-off value AFR Tax cost of capital MVM Best Estimate Liability Market Value Margin (MVM), to measure the cost of risk. Two methods are possible in Solvency II, either through the observation of market price whenever possible (hedgeable risks) or through an explicit cost for the capital at stake to bear the risk. This Cost of Capital Approach (CoC) is calculated according to Solvency II approach. First, the capital hold year by year until complete run-off of the business (SCR). Note that only insurance risk capital is considered (asset risk excluded) : (Reserves = BEL +MVM) 1 2 3 4 Years We then apply the expected return by the financial market to bear P&C risk (see calculating risk cost of capital) 12 22/10/2009

Moving to an economic view Calculate the MVM In order to determine it, a cost-of-capital methodology should be used. It bases the risk margin on the theoretical cost to third party to supply capital to the company in order to protect against risks to which it could be exposed. In other words, under a cost of capital approach, the market value margin is calculated as the present value of the cost of holding the solvency capital requirement for non-hedgeable risks during the whole run-off period of the in-force portoflio. Thus, one needs to estimate both the solvency capital requirement related to non-hedgeable risk and the annual cost of capital rate. The cost of capital in each year would be given by the product of the solvency capital requirement of each year and the underlying cost of capital rate. The market value margin is then obtained by discounting these amounts: The QIS 4 Technical Specifications stand that all participants should assume that this cost-ofcapital rate is 6% (above the relevant risk-free interest rate), following the figure of the Swiss Solvency Test. On the contrary the Chief Risk Officer Forum (2008) suggests that the cost-ofcapital rate should be in a range of 2.5%-4.5% per annum. 13 22/10/2009

Moving to an economic view Expected return (1/2): frictional costs approach The frictional capital costs represent the insurer s cost of taking insurance risk and capture the opportunity costs shareholders incur when investing capital via an insurance company rather than directly in the financial markets. CoC Rate = CoC DT + CoC FD The frictional costs are: The double taxation costs, The agency costs, The costs of regularity restrictions, The financial distress costs. CRO forum focuses only on double taxation costs and financial distress costs. 14 22/10/2009

Moving to an economic view Expected return (2/2): the full-information industry Beta The Capital Asset Pricing Model and the Fama-French two factors models provide with some estimators for the equity risk premium. The Fama-French two factors model has been developed in order to improve the explanation power of the CAPM by adding a second factor to the model. This factor is the ratio of the book value of equity to the market value of equity (BV/MV ratio). This ratio reflects the financial distress. In order to determine a pure cost of capital rate for life and nonlife insurance, and to take into account the fact that most of the companies participate in both industries, it is necessary to reflect the relative proportion of their entire portfolio of businesses. Accordingly Cummins and Phillips (2005) use the full- information industry beta which allows to decompose the individual company cost estimates into industry specific cost estimates. The underlying insight is that the observable beta for the overall firm is a weighted average of the unobservable betas of the underlying lines of business. 15 22/10/2009 Non Life Insurance 2003 2004 2005 2006 Market Systematic Risk Premium 3.1 3.2 3.8 5.6 BV-MV Risk Premium 0.4 0.4 0.5 0.8 Total Risk Premium 3.5 3.6 4.3 6.4

16 22/10/2009 3 QIS IV Standard model

Quantitative Impact Study Introduction The capital that will hold the companies will be dependent on the type of risk subscribed past as future (time horizon 1 year) and the asset structure. The QIS are studies conducted by regulators to quantify the impact of regulatory change on the balance sheet of the insurance companies. To make the results comparable, participants must calculate their SCR using standard parameters provided by CEIOPS. For some risk (underwriting risk, for example), the entities are partially allowed to use own specific data. Participants are also invited to present the results of their internal models. There was a study by year. The last (QIS 4) was completed in May 2008. QIS 5 is scheduled for July 2010. 17 22/10/2009

Quantitative Impact Study List of risks For non-life companies, the sources of risk identified are: Market risks by (equity, bonds..) Reserve risks Underwriting risks Catastrophe risks (natural events and man-made) Operational risks Counterparty default risks 18 22/10/2009

19 22/10/2009 Quantitative Impact Study (QIS 4) QIS 4: SCR & MCR definitions

20 22/10/2009 Quantitative Impact Study (QIS 4) Risk cartography and aggregation

Insurance risks LoB view QIS IV approach assume a fixed level of granularity: This may differ from the level of granularity at which companies have the habit of watching their business (income statement) and balance sheet (liabilities) or combine their products For each LoB, Premium & Reserve SCR are calculated with an «factor» approach LoB Number Lob Name 1 Motor, third party liability 2 Motor, other classes 3 Marine, Aviation, Transport (MAT) 4 Fire and Other Property Damage 5 Third party liability 6 Credit and surety ship 7 Legal Expenses 8 Assistance 9 Miscellaneous 10 Non-proportional Reinsurance property 11 Non-proportional Reinsurance casualty 12 Non-proportional Reinsurance - MAT 21 22/10/2009

Insurance risks Calibration of Non-Life SCR: Reserve risk (1/6) For each line of business the SCR is a function of standard deviations and volume measures of the premium risk and the reserve risk. The standard deviations for reserve risk and for premium risk in the main individual LOB are determined regardless of local specificity (country * company) : - Some countries like the UK for example may have higher volatility, the portfolios vary widely from year to year - The size of business lines (mutualization of diversifiable risk) Assuming a lognormal distribution of the underlying risk, the VaR 99.5% is roughly equal to 3 σ: 22 22/10/2009

Insurance risks Calibration of Non-Life SCR: Reserve risk (2/6) These coefficients have been calibrated not on Europe but on specific markets, often the most volatile (eg the UK). Thus, in most cases, the coefficients of QIS are conservative compared to internal models. Comparison for different entities "SCR Reserves" calculated by the approach QIS 4 and by internal models (by Thomas Mack) We note that the parameter used are often very distant from those estimated with traditional statistical models Although many methodologies exist to determine the historical volatility of reserves, the QIS does not yet recognize these results in standard formulas. 23 22/10/2009

Insurance risks Calibration of Non-Life SCR: MVM (3/6) In QIS, the MVM for reserves does not recognize the diversification Step 1: Calculation of "Run Off SCR", amount of capital required to cover the 99.5% risk of the annual Best Estimate diversion until extinction of the insurance obligations for each category (LoB) independently. Step 2: Calculating the Cost of Capital & discount at risk free rate (MVM by LoB) Step 3: Aggregation of MVM. 24 22/10/2009

Insurance risks Calibration of Non-Life SCR : LoBs aggregation (4/6) The overall SCR of the company is calculated like a LoB (σ tot *V tot ) with: V tot, the volume measures (premium and reserve risks) for the individual lines of business CorrLoB, the cells of the correlation matrix between LoB These techniques do not take into account what may happen "above" of the 1 in 200 year event. 25 22/10/2009

Insurance risks Calibration of Non-Life SCR : geographical diversification for groups(5/6) To take into account geographical diversification benefits the volume which applies volatility is weighted by a Herfindahl index: V lob = ( V (prem, lob) + V (res, lob) ) (0.75 + 0.25 DIV pr,lob ) Where: 26 22/10/2009

Insurance risks Calibration des SCR Non-Vie: risque Catastrophe (6/6) The CAT risk is calculated using the predefined scenario. Especially for France: Natural catastrophe scenario - Two windstorms (Lothar and Martin storms in 1999) resulting in a market loss of 14 bn - An earthquake on the south-east coast of France (could be regarded as a trans-national scenario) resulting in a market loss of 15 bn - A major flood in the Paris area from the Seine, resulting in an estimated insurance industry loss of 5bn; Man-made catastrophe scenario is a discretion of insurers: - Terrorist attack with aircraft (WTC Type), Motor Liability (Mont-Blanc type) But insurance companies can replace the scenarios from the software market (EQE, AIR, RMS) if they can justify it. To determine the SCR CAT, insurers are required to calculate the average quadratic scenarios previously defined. Aggregation with the SCR (Premiums & Reserves) is also quadratic mean 27 22/10/2009

Insurance risks Counterparty default risk Counterparty risk is estimated by applying to each reinsurer (i) a probability of default (PD) weighted by a factor of diversification with other reinsurers. SCR def (i) = Loss Given Default(i) Probability of Default(i) LGD(i) = 50% max (Best Estim. Recoverables + SCR gross SCRnet - deposit; 0) PD(i) = φ(public rating; correlation factor R) R = 0,5 + 0,5 Herfindahl Index The following table summarizes the amounts of SCR def according to different rating and correlations. there is a nonlinearity of the function for the high ratings, which in its present form, leads to a profit in low diversification. This formula will probably be amended to QIS 5. 28 22/10/2009

Insurance risks Critics of the Non-Life community... towards QIS V The major criticism that comes from all insurers and reinsurers through the CRO Forum are the following: Too low recognition of specific data entity in the standard formulas. This should be improved in QIS 5. Volatility of reserves generally too high, especially in Motor Liability calibrated for the UK market. Too weak taken into account of the diversification effect: - Not taking into account the size of the portfolio - No diversification in the calculation of the MVM (MVM to each LoB are summed to calculate the MVM of the entity) - In counterparty risk (correlation minimum of 50% between counterparties, which promotes concentration to reinsurers rated) - between assets and liabilities (correlation fixed at 25%) - between subsidiaries of the same group (low weighting of the Herfindahl) Too little recognition of risk coverage (eg securitisation) 29 22/10/2009

4 Develop an internal model 30 22/10/2009

Develop an internal model LoB 1 1. Ultimate volatility vs. annual Accident Y1 Accident Y2 Correlations 2. Ultimate volatility : many models 3. Towards an annual volatility Accident Y1 Accident Y2 LoB 2 4. Annual volatility : QIS vs. Internal model 5. Triangles of the model chosen and calibrated 6. The 1 to 200 year event 7. Correlations 31 22/10/2009

Develop an internal model Ultimate volatility vs. annual volatility Until 2007, the models of risk of reserve in actuarial papers only treated the estimation of ultimate volatility For Run-Off, Solvency II implies the necessity to have a volatility split by year of deviation, ie. By P&L year. Mali at the balance for year N+1 Boni at the balance for year N+k+1 Ultimate deviation (mali) N N+1 N+2 N+3 N+4 N+5 N+k Cumulated Paid Reserves For Accident Years N and older N+k+1 Balance Year 32 22/10/2009

33 22/10/2009 Develop an internal model Ultimate volatility : many models The stochastic reserve models restricted to the question of possible deviation from the ultimate abound in the literature: «Distribution-Free Calculation of the Standard Error of Chain Ladder Reserve estimates», Mack 1993 (ASTIN Bulletin) : - Estimates the mean and MSEP reserves calculated by Chain-Ladder approach. The volatility includes estimation risk and process risk. Chain ladder bootstrap ( cf. «Stochastic Claims Reserving In General Insurance», England & Verrall 2002 ) : - Estimates distribution of the reserves : this approach calculates the upper triangle by chain ladder and by substraction with the triangle observed allow to estimate the Pearson residuals. Resampling the residuals (with replacement) gives M ( = 10 000 for example) new triangles. The chain-ladder model is applied to these bootstrap sample to obtain M sets of future cash-flows (estimation risk) which is added the process risk (intrinseq risk) and thus obtain M value of reserves. This approach works with paid or incurred trangles. GLMs ( cf. «Stochastic Claims Reserving In General Insurance», England & Verrall 2002 ) : - Gives the distribution of reserves by modelling the incremental payments by GLM (log-poisson model for example) with a row factor (accident year) and a column factor (development year). The modalities can sometimes be combined to increase the robustness of the model without damaging its predictivity The «Prediction Error of Bornhuetter/Ferguson», Mack 2008 (ASTIN Bulletin) : - It makes stochastic the BF model by modeling stochastically the CL pattern and the S / P. Etc. These models must be adapted to estimate the annual risk of diversion

Develop an internal model Towards an annual volatility (1/3) Take the example of the MSEP (mean square error of prediction) introduce by Mack 1993, relating to the risk of reserves to the past accident year "i" done at balance year "I" : Term related to the balance year «k» Intuitively, the risk of deviation from first year is estimated by keeping only the first term (k = I +1- i) the sum above But we will see that we must be wary of intuition 34 22/10/2009

Develop an internal model Towards an annual volatility (2/3) 1 1 J 1 1 J i i I Chain ladder projection I Chain ladder projection Is the average ultimate claims amount (for occurrence year i) estimated by Chain Ladder, at the balance year I is the average ultimate claims amount (for occurrence year i) estimated by Chain Ladder, at the balance year I+1 (projecting the triangle which integrates diagonal year I+1) The 1st year of deviation volatility of reserves is the same as that of [ - ] knowing D I I+1 35 22/10/2009

Develop an internal model Towards an annual volatility (3/3) The article «Modelling the Claims Development Result For Solvency Purposes» (06/2008) by Merz & Wüthrich and presented to the ASTIN Colloquium in July 2008, gives a rogorous formula of the MSEP of 1st year of deviation linked to Chain-ladder method, and denoted «MSEP[ CDR i (I+1) / D I ]» where : «CDRi(I+1)» is the claims development result, ie the boni-mali term impacting the CR of year I+1 and coming from occurrence year i. «MSEP[. / D I ]» is the MSEP conditional to the information of the triangle known up to balance year I This MSEP is equal to : A A correspond to the first term in the sum of Mack 93 formula, which was rather intuitive B is positive and implies a 1st year of deviation volatility which is larger than the one obtained with the previous intuitive formula. This term comes form the fact that one computes the risk of re-evaluation of the ultimate amount between balance years I and I+1 (concerning occurrence year i), the estimation of the ultimate amount for the balance year I+1 being done using a triangle which integrates the diagonal of year I+1 which was unknown at balance year I. Note that actually the MSEP computed with the intuitive formula (only term «A») is often not very different from that computed with the rigorous formula (term «A»+term «B»). B 36 22/10/2009

Develop an internal model Annual Volatility: the MVM requires volatility for all years of developement «R(N,k)» is the amount of reserves at the balance year «N+k» for the occurrence year «N» and before According QIS, the CoV (coefficient of variation) of "R (N, k)" related to the risk of first year of deviation, depends only on the LoB QIS (motor liability, etc..) Using an internal model to estimate the CoV of the «R(N,k)», we find that the CoV depends mainly on the horizon "k" CV N N+1 N+2 N+3 N+4 N+5 N+k QIS Internal model : different configurations N+k+1 Balance year 37 22/10/2009

Develop an internal model Triangles of the model chosen and calibrated «There is no ONE mean (resp. volatility, distribution) of the reserves but the mean (resp. volatility, distribution) linked to a model» Triangles of Paid vs. Incurred : Models based on the one or other one. Which one? Paid or incurred? Models estimating two jointly approach Models based on assumptions of type "link ratio": Assumptions are : (H1) independance between accident year, (H2) independance between subsequent development factors, (H3) same average development for each accident year - These assumptions are they checked on the triangle? Row effect (size of the accident year), column effect (loss development) but no diagonal effect (calendar year) - Note : daigonal effects (inflation, over-inflation, change in legal practice, Introduction of a new claims handling system) : they can be taken into account by a GLM model Risk Model: a model still based on assumptions that must be validated. In addition we seek to model the future not the past, such attention to inflation... For a given model : process risk vs. parameter risk Parameters yes but not too much attention to over-parameterization Calibration: should we exclude or retain the "outliers"? A simple exclusion of outliers leads to underestimate volatility 38 22/10/2009

Develop an internal model The 1 to 200 year event The models mentioned above are calibrated in 10 years, 20 years, more often 30 years of history... On this basis, we can pretend to estimate a quantile at 75 % or possibly 90 % but certainly not 99, 5% Distribution We can model the risk of reserves by splitting it into 2 parts: «Moderate» risks : - Can be assess with triangle and an adapted model (see actuarial litterature) «Extreme» risks : - modelled by "stresses" scenarios characterized by: - Identified «risk drivers» - Severity and return period - Examples : - Over-inflation - Change in legal practice - Emerging risk : a new «asbestos»? 0 Q-50% Q-90% Q-99,5% Quantile Trangle + Model Stress scenarios (risk drivers) 39 22/10/2009

Develop an internal model Correlations (1/3) The correlations are significant and multiple sources and natures. For example: Correlation between accident year : - reserves estimated by Chain Ladder : we project the triangle with the same coefficient of development applied to all accident years - Inflation - ( ) Correlation between LoB : - Inflation - Cat nat related the lob Motor, Household, - Damage mixed motor claims : joint managment of liability and damage - ( ) 40 22/10/2009

Develop an internal model Correlations (2/3) «Numerical» approach : Calibration on the observed (triangles ) «linear correlation» (correlation matrix) : - The example of QIS Many actuarial papers showing correlations with non-linear phenomenon of tail dependence «non-linear» correlation (copula) : - Choice of copula and parameter estimation are difficult and not robust - It is more a tool of "stress test": - «If you want change your economic capital, change the copula» «Scenarios» approach with «Risk Drivers» : Those scenarios irradiate the whole reserves, generating correlations not only between accident years, but also between lines of business They also model tail dependencies and have an impact on the tails of distributions : extreme scenarios. 41 22/10/2009

Develop an internal model Correlations (3/3) Wherever we know a causal dependence we model it explicitly: E.g. : inflation Systematically usage of non-symmetric copulas to take into account unknown /un-explained / un-modelled dependences How to calibrate copulas? - Wherever there is enough data, we calibrate statistically the parameters - In absence of data, we use stress scenarios to estimate conditional probabilities Need of credibility with Standard Model Correlation How to ensure technical feasibility? Wherever it is possible to simulate copulas into internal tools, we run simulations framework to derive the entire distribution of risks In absence of technical feasibility, we use a two step process: - First step: to compute marginal distribution - Second step: to aggregate marginal risk according to correlation matrix 42 22/10/2009

5 Risks and opportunities 43 22/10/2009

44 22/10/2009 Risks and Opportunities a. Main objective : Regulatory Benefits from Efficient Risk Management Solvency II should aim at full recognition of diversification at every levels Diversification should be recognized between lines of business, between insurance and market risk, between life and non-life entities, and between countries Current solvency II model : standard diversification for the first three levels, but very insufficient at geographical level - Only P&C technical risk gets geographical diversification - Non-European countries are excluded from diversification Need to better recognize geographical diversification : a key advantage for Insurance Groups The goal is not to have less capital but to improve the identification and assessing of own risks to manage them. Recognition of risk transfer and mitigation techniques Securitization, reinsurance pooling Hedging programs Use of internal model for solvency assessment An advantage for sophisticated, international and dynamic risk management

45 22/10/2009 Risks and Opportunities b. Adapt the Economic Approach to Insurance Business Multiyear management is at the core of the insurance business Provider of long term protections - Pension products - Long-tail professional liability protections - High renewal of P&C contracts in some countries... Matched with a long term view on investment - Equity shares - Private equity These areas present large opportunities for the insurance sector Challenge for the regulation : Provide the adequate level of safety while not standardize investment strategies of the insurers Necessity to strike the right balance between a one year safety level and a proper recognition of long term nature of insurance assets (Equity, property) and liabilities (long-term or high renewal business)

Risks and Opportunities c. For a truly Harmonized European Market A simple standard model, with limited options and right calibration Credibility rather than conservatism is key for a level playing field A clear standard for technical provisions: Market consistent value with market value margins for insurance and operational risks, based on a cost of capital approach. Limit the possibility for local supervisor to gold plate the European system through No supplementary asset rules at local level No discretionary capital add-on based on qualitative assessment An opportunity to streamline the management of a pan- European Activity 46 22/10/2009

Risks and Opportunities d. Streamlining of Group Supervision A key role for the lead supervisor Focus group supervision on group SCR - Include geographic diversification - Controlled by the lead supervisor, building on expertise of local supervisors Local MCR as an absolute minimum Foster cooperation and convergence of practices inside Europe Group supervisory colleges should promote cooperation and exchange of information for supervisors of a group Need for a European supervisory team to validate internal model of groups. From national separated views and responsibilities on groups Redundancies different rules and implementation to European a common view on groups shared in group supervisory college a unique point of contact for groups convergence of rules and implementation 47 22/10/2009

Risks and Opportunities e. A Competitive Advantage for the European industry Economic framework rather than arbitrary rules: Foster market innovation (securitization, innovative forms of capital, ) Allow to develop sophisticated insurance products Incentive to elaborate risk management techniques Solvency II is on the front of international developments Will set a standard for further international convergence Streamlining of supervision and harmonization of rules will shape a single European insurance market A key issue for an European insurance group competing at the international level 48 22/10/2009