2008 Seminar for the Appointed Actuary Colloque pour l’actuaire désigné Seminar for the Appointed Actuary Colloque pour l’actuaire désigné 2008 Speaker: Christopher J. Townsend PD-10 (P&C) IFRS: Solvency

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 2 Agenda Highlights from PD AA Seminar Developments in last year Canadian P&C Response Future Plans Highlights from PD AA Seminar Developments in last year Canadian P&C Response Future Plans

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 3 Highlights from 2007 Canadian Life Insurer Context Basel II, Solvency II directly affects insurers’ competitors MCCSR Advisory Committee (MAC) – formed in 2006 OSFI, IGIF, CLHIA, CIA, individual companies CIA Solvency Framework Sub-Committee – of Risk Management and Capital Requirements Key Documents on OSFI and IGIF websites – Draft technical papers on CIA website

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 4 Initial CIA P&C Preparation Formed P&C Subcommittee of Risk Management and Capital Requirements Committee Mandate - To further the development of actuarial techniques in the area of risk management for property and casualty insurance and to provide guidance and standards to the actuarial profession with respect to work in this area. To develop appropriate measurement bases for risk and capital, and work with regulators and other stakeholders in the development of capital requirements. The sub-committee will liaise with the P&C Financial Reporting Committee to ensure alignment of philosophy and approach. –Current Members - Grant Kelly(IBC), Eric Keen, Michel Dionne (chair), Nathalie Ouellet, Linda Goss, Bernard Dupont, Sylvain St. Georges, Ron Miller, Pierre Laurin, Ernest Segal

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 5 P&C Internal Economic Capital Survey Only six respondents have an approach in place Eight of remaining 32 are using stochastic modeling Five of the six existing models use an approach developed by parent/affiliate Stochastic Modeling is used for: Pricing/ratemaking, including large accounts Reinsurance and catastrophe modelling Economic capital is used for the above plus: Capital Management Investment Strategy/Market Risk Management

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 6 Two Companies then provided overviews of their models Type of Risks 1) Credit risk 2) Market risk 3) Business risk 4) Operational risk 5) Life risk (Non-applicable to P&C) 6) P&C risk 7) Morbidity risk (Non- applicable to P&C) Key Issues 1)Calibration 1)Time horizon 2)Probability 3)Market values 4)VAR or TVAR 2)Aggregation – how to put the various risks together 3)Diversification – within risks, and between risks 4)Fungibility

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 7 Progress since September 2007 IAIS papers, including “Guidance … on use of internal models for risk and capital …” Life MAC has made progress on –Interest rate risk –Report – Risk Assessment Models e IBC and OSFI exchanged formal letters P&C MCT Advisory Committee formed –First meeting July 9, 2008

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 8 P&C MCT Advisory Committee - OSFI Members MichaelBeanDirector, Capital Division AllanBrenderSenior Director, Capital Division BernardDupontDirector, Capital Division (co-chair) DavidOakdenManaging Director, Actuarial Division JudithRobergeSenior Analyst, Capital Division MarkWhite Senior Director, Capital, Accounting and Research Division

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 9 P&C MCT Advisory Committee - Industry Members ClaudeBoivinFinance InvestmentsAxa Canada MichelDionneVP and actuary, corporateING Canada Inc. JamesHarvey Vice President, CFO & Corporate Secretary Allstate Insurance Companies of Canada DougHogan Senior Vice President and CFO Dominion of Canada General Insurance Company SharonLudlowSenior VP & CFO Swiss Reinsurance Company Canada SteveMcManusVice President, FinanceLombard Canada Ltd. AndyTaylorDirector of Finance Gore Mutual Insurance Company ChrisTownsend VP & Corporate Actuary (co-chair) Aviva Canada Inc. ChrisWalton Assistant Vice President (co-chair) General Reinsurance Corporation

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 10 P&C MCT Advisory Committee - Other Members GrantKelly Director, Policy Development and Senior Economist Insurance Bureau of Canada DarrellLeadbetterManager (Research)PACICC DouglasMcLean Director, Provincial Operations Financial Institutions Commission Sylvain St- Georges Analyste en normalisation actuarielle des institutions financières Autorité des marchés financiers

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 11 Diagram of the Participants Decision Makers OSFI AMF CCIR P&C Industry Input IBC Finance Committee Other companies Existing Internal models PACCIC Advisors CIA RMCR SFSC (life) Others P&C SC P&C MAC

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 12 2nd P&C MCT Advisory Committee Meeting - Agenda I.Minutes of last meeting II.Presentation on techniques for calculation of insurance risk capital (Michel Dionne & Chris Townsend) III.Revised mandate of P&C MCT Advisory Committee IV.Communication to the industry V.Draft project plan VI.Key principles VII.Solvency framework VIII.Other business IX.Next meetings

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 13 2nd P&C MCT Advisory Committee Meeting - Content Handouts at Session If agreed by P&C MAC –Mandate –Project Plan –Key Principles –Solvency framework Presentation on Techniques (extracts) Appendix –Incurred Log Michel Dionne –Bootstrap Chris Townsend

2008 Seminar for the Appointed Actuary Colloque pour l’actuaire désigné Seminar for the Appointed Actuary Colloque pour l’actuaire désigné 2008 Appendix 1 Incurred log Method With apologies and thanks to Michel Dionne

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 15 Overview of Hertig Method Method do not use simulation –Easily & rapidly implemented –Not computer intensive We obtain a distribution of results rather than a point (mean) estimate We still need to make assumptions on: – LOB correlation when aggregating reserves –Accident Year Correlation

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 16 Step 1: take a 10-by-10 triangle from past experience

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 17 Step 2: compute the LDF Sample Calculation: = 1,089,510/761,590

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 18 Step 3: compute LN(LDF) Sample Calculation: = ln(1.4306)

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 19 Step 4: compute the means and variances for each development period (assume Normal distribution) and to ultimate Sample Calculation: = ( )/ =  = ( ) = Variance {0.0478, ,..., } =  2 = x ((nb + 1)/nb) , nb = 8

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 20 Step 5: compute the distributional means and variances (assume Lognormal) Sample Calculation: = exp( /2) i.e. Dist. Mean = = ^2 x (exp( )-1) i.e. Dist. Var. =

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 21 Step 6: project the ultimate incurred Sample Calculation: = exp(0.0654) 2,601,712 = 2,436,930 x ,782 = 2,601,712 – 2,436,930

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 22 Step 7: Compute PfAD at various percentile using inverse std normal Sample Calculation: 70,541 = 1,992,460 x x ( )^0.5 i.e. 272,181 = sqrt{ (250,665)^2 +…+ (3,215)^2}  (assume independence in AY) Total 95 th = 1,729,887 = 1,457, ,181

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 23 Step 8: Summarize the results Outstanding Issues: Accident Year Correlation Correlation between multiple lines of business

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 24 Step 8: Summarize the results

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 25 References : Hertig, Joakim, Statistical Approach to IBNR-Reserves Marine Reinsurance; A (1985)

2008 Seminar for the Appointed Actuary Colloque pour l’actuaire désigné Seminar for the Appointed Actuary Colloque pour l’actuaire désigné 2008 Appendix II BOOTSTRAP PROCESS by Emily Huang for Chris Townsend August 28, 2008

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 27 Table of Contents 4x4 triangle example Appendix 2.1: A 10-year example Reference

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 28 Overview of Bootstrap Process A stochastic resampling process Structured, mathematically rigorous Less judgment used Generates a range of data, more informative A consistent and repeatable process Computer-intensive

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 29 Step1: take a 4-by-4 triangle from past experience

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 30 Step 2:cumulative chain ladder method Sample Calculation: = (1,142,800+1,157,860)/(1,089,510+1,093,740)

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 31 Step 3: fitted triangle with development factors Sample Calculation: 802,442 = 1,157,860/ (1.3693*1.0538)

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 32 Step 4: unscaled Pearson residuals Note: calculations are carried out on incremental values Sample Calculation: = (1,077,950 – 1,029,684) /sqrt(1,029,684) i.e.: (Actual Payment – Fitted Payment)/sqrt (Fitted Payment)

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 33 Step 5: adjust for degrees of freedom Sample Calculation: = 47.57*sqrt (n/(n-p)) n = number of data points p = number of parameters being estimated

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 34 Step 6: randomly select adjusted Pearson residuals Note: We are excluding the top right and bottom left cells, as they are always zero.

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 35 Step 7: calculate a false history Sample Calculation: 991,091 = *sqrt(1,029,684) + 1,029,684 False History = Random Residual*sqrt(Fitted Payment) + Fitted Payment

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 36 Step 7A: cumulative false history Sample Calculation: 1,176,286 = 768, , ,177

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 37 Step 8:recalculate development factors Note: Calculated by the cumulative chain ladder method.

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 38 Step 9: square the triangle Sample Calculation: 1,458,258 = 1,348,901*1.081

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 39 Step 10:calculate incremental payments Sample Calculation: 468,751 = 1,657,567 – 1,188,817

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 40 Step 11: calculate the scale parameter Scale parameter = Pearson chi-squared statistic Number of degrees of freedom = 15,667/ (10 – 7) = 5,222

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 41 Step 12: random draw from a gamma distribution Note: mean = absolute value of the incremental payment from step 10 Variance = mean * scale parameter from step 11

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 42 Step 13: final reserve estimate Final reserve estimate = sum of all entries under the dark line = 614, , , , , ,931 = 898,362

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 43 N% tail variance = variance of the largest K*(100-N)% data points Possible estimates of capital required at 95 th percentile –95 th percentile = 814,190 – 620,424 = 193,766 –90 th tail variance = average(largest 0.1K data points) – 620,424 = 240,667 –Normal Approximation = 1.96*107,969 = 211,619 Step 14: Repeat step 6 to 13 K times

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 44 Note: Gamma column shows the 100-time simulated results from Step 12; w/o Gamma is from Step 10.

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 45 Summary Gamma distribution provides a wider reserve range A consistent and repeatable process 100+ simulations, computer-intensive

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 46 Appendix 2.1: A 10-year example Data

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 47 Incremental triangle

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 48 Results

2008/09/26 PD-10 (P&C) IFRS:Solvency Page 49 Reference Kirschner, Gerald S., Colin Kerley, and Belinda Isaacs. "Two Approaches to Calculating Correlated Reserve Indications Across Multiple Lines of Business." Variance 02 (2008):