1. Risk-Based Capital Developments Glenn Meyers Insurance Services Office, Inc. CAS Spring Meeting May 19, 2003

2. Introduction A current initiative of the International Association of Insurance Supervisors (IAIS) is to develop a global framework for risk- based capital for insurers. Acting in support of the IAIS, the International Actuarial Association (IAA) has formed an Insurer Solvency Assessment Working Party (WP) to prepare a paper on the structure for a risk-based solvency assessment system for insurance.

3. Terms of Reference of the WP The WP should describe the principles and methods involved in the quantification of the total funds needed to provide a chosen level of confidence to policyholders and shareholders that the insurer’s policyholder obligations will be met.

4. Terms of Reference of the WP The paper should be specific and practical enough that its recommended principles and methods could be used as a foundation for a global risk-based solvency capital system for consideration by the IAIS.

5. Terms of Reference of the WP The paper should, starting from a coherent risk framework, identify risk measures that explicitly or implicitly can be used to measure the exposure to loss from risk and also any risk dependencies. The paper should also identify measures that are not effective in this regard.

6. Terms of Reference of the WP In balancing its focus between practical versus sophisticated methodologies, the working party will place greater weight on those methodologies with the greatest likelihood of practical implementation. However, since simple methodologies that can be applied to many insurers in a territory or across territories may prove insufficiently reliable or capital efficient, the working party should consider whether risk models developed internally by insurers can provide a useful and reliable approach.

7. Who is on the WP? Allan Brender (Canada) Peter Boller (Switzerland) Henk van Broekhoven (Netherlands) - Vice- Chairperson Tony Coleman (Australia) Jan Dhaene (Belgium) David Finnis (Australia) Marc Goovaerts (Belgium) Burt Jay (U.S.) R. Kannan (India) Toshihiro Kawano (Japan) Sylvain Merlus (France) Glenn Meyers (U.S.) Teus Mourik (Netherlands) Harry Panjer (Canada) Dave Sandberg (U.S.) Nylesh Shah (U.K.) Shaun Wang (U.S.) Stuart Wason (Canada) - Chairperson Hans Waszink (Netherlands) Bob Wolf (U.S.) Represented are several countries, life, health, P/C insurance company, consultants, regulators and academics.

8. Contents of Report Section 3 – The Purpose of Capital Section 4 – Supplements to Capital Section 5 – Working Party’s Approach Section 6 – Risks and Risk Measures Section 7 – Standardized Approaches Section 8 – Company Specific Approaches Section 9 – Reinsurance Section 10 – Total Company Requirement

9. Contents of Report Appendix A – Life Insurance Case Study Appendix B – Non-Life Insurance Case Study Appendix C – Health Insurance Case Study Appendix D – Market Risk Appendix E – Credit Risk Appendix F – Lessons from Insurer Failures Appendix G – Introduction to Insurance Risk Appendix H – Analytic Methods Appendix I – Copulas

10. Illustration – Non-Life Case Study Concentrates on insurance risk Includes a possible “standardized approach” and an “internal model.” Recall from the terms of reference –Need formula that can be implemented in practice –Consider whether internal models can provide a useful and reliable approach.

11. Requirements for Internal Models The insurer should have an independent internal risk management unit, responsible for the design and implementation of the risk-based capital model. The insurer’s Board and senior management should be actively involved in the risk control process, which should be demonstrated as a key aspect of business management.

12. Requirements for Internal Models The model should be closely integrated with the day-to-day management processes of the insurer. An independent review of the model should be carried out on a regular basis. (Amongst other considerations, it should be recognised that evolution of the modelling capabilities is to be encouraged) Operational risks should be fully considered

13. Desirable Properties of a Standard Formula Simplicity – The formula can be put on a spreadsheet. This may allow for some complexity in the formulas, as long as the objective of the formulas is clear. Input Availability – The inputs needed for the formula are either readily available, or can be reasonably estimated with the help of the appointed actuary. Conservative – When there is uncertainty in the values of the parameters, the parameters should be chosen to yield a conservative estimate of the required capital

14. A Proposal for a Standard Formula The formula is sensitive to: The volume of business in each line of business; The overall volatility of each line of insurance; The reinsurance provisions; and The correlation, or dependency structure, between each line of business.

15. Features of the Formula Input for insurance losses –Expected losses for current business –Loss Reserves (at expected values of payout) Parameters - Specified by regulator (??) –Claim severity distribution by line of business –Claim count distribution –Dependency model parameters (see next slide) Calculates first two moments of aggregate loss distribution. Using lognormal approximation: Capital = TVaR 99% – Expected Loss

16. Dependency Model Parameters Common shock model –Uncertainty in trend affects all lines simultaneously –Magnitude of shock varies by line of business Catastrophes treated separately Capital = TVaR 99% – Expected Loss + Cat PML Calculate Cat PML with a catastrophe model

17. Example on Spreadsheet Big Insurer – ABC Insurance Company Small Insurer – XYZ Insurance Company ABC Volume = 10 times XYZ Volume –Otherwise they are identical

18. ABC with no Reinsurance

19. ABC with Reinsurance

20. XYZ with no Reinsurance

21. XYZ with Reinsurance