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PD-10 (P&C) IFRS: Solvency

PD-10 (P&C) IFRS: Solvency. Speaker: Christopher J. Townsend. Agenda. Highlights from PD-09 2007 AA Seminar Developments in last year Canadian P&C Response Future Plans. Highlights from 2007 Canadian Life Insurer Context. Basel II, Solvency II directly affects insurers’ competitors

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PD-10 (P&C) IFRS: Solvency

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  1. PD-10 (P&C) IFRS: Solvency Speaker: Christopher J. Townsend

  2. Agenda • Highlights from PD-09 2007 AA Seminar • Developments in last year • Canadian P&C Response • Future Plans PD-10 (P&C) IFRS:Solvency

  3. Highlights from 2007Canadian 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 PD-10 (P&C) IFRS:Solvency

  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 PD-10 (P&C) IFRS:Solvency

  5. 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 P&C Internal Economic Capital Survey PD-10 (P&C) IFRS:Solvency

  6. 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 Calibration Time horizon Probability Market values VAR or TVAR Aggregation – how to put the various risks together Diversification – within risks, and between risks Fungibility Two Companies then provided overviews of their models PD-10 (P&C) IFRS:Solvency

  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 - 208061e • IBC and OSFI exchanged formal letters • P&C MCT Advisory Committee formed • First meeting July 9, 2008 PD-10 (P&C) IFRS:Solvency

  8. P&C MCT Advisory Committee- OSFI Members PD-10 (P&C) IFRS:Solvency

  9. P&C MCT Advisory Committee- Industry Members PD-10 (P&C) IFRS:Solvency

  10. P&C MCT Advisory Committee- Other Members PD-10 (P&C) IFRS:Solvency

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

  12. 2nd P&C MCT Advisory Committee Meeting - Agenda • Minutes of last meeting • Presentation on techniques for calculation of insurance risk capital (Michel Dionne & Chris Townsend) • Revised mandate of P&C MCT Advisory Committee • Communication to the industry • Draft project plan • Key principles • Solvency framework • Other business • Next meetings PD-10 (P&C) IFRS:Solvency

  13. 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 2nd P&C MCT Advisory Committee Meeting - Content PD-10 (P&C) IFRS:Solvency

  14. Appendix 1Incurred log Method With apologies and thanks to Michel Dionne

  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 PD-10 (P&C) IFRS:Solvency

  16. Step 1: take a 10-by-10 triangle from past experience PD-10 (P&C) IFRS:Solvency

  17. Step 2: compute the LDF Sample Calculation: 1.4306 = 1,089,510/761,590 PD-10 (P&C) IFRS:Solvency

  18. Step 3: compute LN(LDF) Sample Calculation: 0.3581 = ln(1.4306) PD-10 (P&C) IFRS:Solvency

  19. Step 4: compute the means and variances for each development period (assume Normal distribution) and to ultimate Sample Calculation: 0.00415 = (0.0085 + 0.0003 + 0.0037)/3 0.00517 =  = (0.00102 + 0.00415) 0.00018 = Variance {0.0478, 0.0570, ..., 0.0403} 0.00037 = 2 = 0.00018 x ((nb + 1)/nb) + 0.00017, nb = 8 PD-10 (P&C) IFRS:Solvency

  20. Step 5: compute the distributional means and variances (assume Lognormal) Sample Calculation: 1.11694 = exp(0.11041 + 0.00037/2) i.e. Dist. Mean = 0.00046 = 1.11694^2 x (exp(0.00037)-1) i.e. Dist. Var. = PD-10 (P&C) IFRS:Solvency

  21. Step 6: project the ultimate incurred Sample Calculation: 1.0676 = exp(0.0654) 2,601,712 = 2,436,930 x 1.0676 164,782 = 2,601,712 – 2,436,930 PD-10 (P&C) IFRS:Solvency

  22. Step 7: Compute PfAD at various percentile using inverse std normal Sample Calculation: 70,541 = 1,992,460 x 1.645 x (0.00046)^0.5 i.e. 272,181 = sqrt{(250,665)^2 +…+ (3,215)^2} (assume independence in AY) Total reserve @ 95th = 1,729,887 = 1,457,706 + 272,181 PD-10 (P&C) IFRS:Solvency

  23. Step 8: Summarize the results • Outstanding Issues: • Accident Year Correlation • Correlation between multiple lines of business PD-10 (P&C) IFRS:Solvency

  24. Step 8: Summarize the results PD-10 (P&C) IFRS:Solvency

  25. References : Hertig, Joakim, Statistical Approach to IBNR- Reserves Marine Reinsurance; A (1985) • http://www.casact.org/library/astin/vol15no2/171.pdf PD-10 (P&C) IFRS:Solvency

  26. Appendix IIBOOTSTRAP PROCESS by Emily Huang for Chris Townsend August 28, 2008

  27. Table of Contents • 4x4 triangle example • Appendix 2.1: A 10-year example • Reference PD-10 (P&C) IFRS:Solvency

  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 PD-10 (P&C) IFRS:Solvency

  29. Step1: take a 4-by-4 triangle from past experience PD-10 (P&C) IFRS:Solvency

  30. Step 2:cumulative chain ladder method Sample Calculation: 1.0538 = (1,142,800+1,157,860)/(1,089,510+1,093,740) PD-10 (P&C) IFRS:Solvency

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

  32. Step 4: unscaled Pearson residuals Note: calculations are carried out on incremental values Sample Calculation: 47.57 = (1,077,950 – 1,029,684) /sqrt(1,029,684) i.e.: (Actual Payment – Fitted Payment)/sqrt (Fitted Payment) PD-10 (P&C) IFRS:Solvency

  33. Step 5: adjust for degrees of freedom Sample Calculation: 86.84 = 47.57*sqrt (n/(n-p)) n = number of data points p = number of parameters being estimated PD-10 (P&C) IFRS:Solvency

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

  35. Step 7: calculate a false history Sample Calculation: 991,091 = -38.03*sqrt(1,029,684) + 1,029,684 False History = Random Residual*sqrt(Fitted Payment) + Fitted Payment PD-10 (P&C) IFRS:Solvency

  36. Step 7A: cumulative false history Sample Calculation: 1,176,286 = 768,372 + 319,737 + 88,177 PD-10 (P&C) IFRS:Solvency

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

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

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

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

  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 PD-10 (P&C) IFRS:Solvency

  42. Step 13: final reserve estimate Final reserve estimate = sum of all entries under the dark line = 614,734 + 104,836 + 138,404 + 6,205 + 21,251 + 12,931 = 898,362 PD-10 (P&C) IFRS:Solvency

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

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

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

  46. Appendix 2.1: A 10-year example Data PD-10 (P&C) IFRS:Solvency

  47. Incremental triangle PD-10 (P&C) IFRS:Solvency

  48. Results PD-10 (P&C) IFRS:Solvency

  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): 32-38. PD-10 (P&C) IFRS:Solvency

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