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CS-12 IAA Progress on RBC Life Case Study Les Rehbeli

July 29, 2003. CS-12 IAA Progress on RBC Life Case Study Les Rehbeli. Contents. 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance. Introduction. Purpose of case study

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CS-12 IAA Progress on RBC Life Case Study Les Rehbeli

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  1. July 29, 2003 CS-12 IAA Progress on RBCLife Case StudyLes Rehbeli

  2. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  3. Introduction • Purpose of case study • To demonstrate approaches to determine solvency provisions for various risks • To illustrate concepts for advanced internal modeling • To highlight issues a factor-based approach must address

  4. Internal Modeling • Develop models to quantify various risks being considered • Analyze each risk separately • Generate scenarios in which liabilities vary only on the risk being measured • Aggregate into total company solvency requirement • Focus on total solvency provisions • Sum of reserves and capital

  5. Internal Modeling • Model cash flows over time horizon appropriate to risk being modeled • Systematic (non-diversifiable) risks over entire term of liability • Non-systematic (diversifiable) risks over shorter horizon • Liabilities defined as present value of future liability cash flows discounted at risk-free rate • Solvency provision defined as difference between average liabilities of worst 1% of scenarios and best estimate liabilities • CTE(99) minus CTE(0) • approximately equivalent to 99.5th percentile

  6. Risks Analyzed in the Case Study • Mortality (systematic risks) • Mortality level risk • Mortality trend risk • Lapse (systematic risks) • Lapse level risk • Non-systematic insurance risks • Mortality volatility risk • Mortality catastrophe risk • Lapse volatility risk • Market risks • Credit risk • Mismatch risk

  7. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  8. The Insurance Company • Medium-sized insurance company • term, whole life and immediate annuity non-participating products • Assets managed at the segment level • segments for insurance products, annuity products and surplus • liabilities supported by high grade fixed income securities • surplus also invested in stocks • Various reinsurance arrangements in place

  9. The Insurance Company Company Segmentation

  10. Total Solvency Provisions ($ millions)

  11. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  12. Mortality Risks • Level risk • misestimation of the mean • Trend risk • deterioration of the mean • Volatility risk • statistical fluctuations • Catastrophe risk • spike in mortality experience

  13. Mortality Level Risk • Misestimation of the mean • Mortality assumptions based on mortality studies and industry data • but mortality studies are based on observations that are volatile • In a mortality study, we may presume that historical observations represent the best estimate level of mortality • but it is possible that the observations are in the tail of the true mortality distribution

  14. Mortality Level Risk Setting of Best Estimate Mortality Assumption % of Industry Table

  15. Mortality Level Risk • The smaller the portfolio, the larger the range of possible outcomes for future mortality • might also partially rely on industry data • To evaluate mortality level risk, assume that observations were actually at, say, 99th percentile of the true distribution • by using inverse Normal Power approximation • or by simulating claims experience and using 99th percentile • For case study, revalue liabilities with mortality assumption distribution to calculate CTE(99) • or simply revalue liabilities at 99.5th percentile of assumptions

  16. Mortality Level Risk Liabilities ($ millions)

  17. Mortality Trend Risk • Deterioration of the mean • misestimation of the trend • We can estimate a “best estimate trend” based on past observations and expert opinions • uncertain due to volatility in past observations • also due to systematic changes in the trend • Quantify trend uncertainty by revaluing liabilities under other trend assumptions

  18. Mortality Trend Risk • For case study, assume annual rate of mortality improvement is normally distributed • mean and standard deviation of 0.50% improvement per year • limit improvement to 40 years • limit range to -3.0% and 3.0% • Apply to all products simultaneously • determine which direction will increase liabilities on a company basis • consider reinsurance

  19. Mortality Trend Risk Liabilities ($ millions)

  20. Mortality Volatility Risk • Statistical fluctuations around the expected assumptions • assume that the best estimate assumption is correct • Time horizon • level and trend risks were measured over the entire term of the liability • volatility risk can be diversified by management action • project out for a two year time horizon • Simulation approach taken for case study • analytic methods are also feasible to quantify volatility risk

  21. Mortality Volatility Risk Claims over two year horizon ($ millions)

  22. Mortality Volatility Risk ($ millions)

  23. Mortality Catastrophe Risk • One-time spike in mortality experience • for example, Spanish Flu • Highly subjective • Deterministic approach taken for case study • doubling of mortality for one year • Interaction between catastrophe risk and volatility risk • capital for catastrophe risk is difference between CTE(99) at higher mortality and CTE(99) at normal mortality

  24. Mortality Catastrophe Risk Claims over two year horizon ($ millions)

  25. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  26. Lapse Risks • Can be analyzed in similar fashion to mortality risks • But several other factors to consider: • lapse rates may be correlated with economic assumptions for some portfolios • very difficult to model • lapse assumption highly dependent on product and how it is sold • impact to company can vary for different policy durations and products • Case study analyzes inaccuracies due to statistical error

  27. Lapse Risks • Level risk • Misestimation of the best estimate • Volatility risk • Statistical fluctuations

  28. Lapse Level Risk • Misestimation of the best estimate • From lapse studies, we can determine best estimate lapse rates and their standard deviations • we can assume a distribution for the lapse rates and solve for lapse rates at alternate percentiles • e.g. assume lapses are normally distributed and grade from 10% to 1% over 12 years • 90th percentile lapse assumption may be 12.4% grading to 1.2% • 10th percentile lapse assumption may be 8.7% grading to 0.8% • Need to account for policyholder behavior / economic environment • Statistical error may not always be one-sided

  29. Lapse Level Risk Liabilities ($ millions)

  30. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  31. Market Risks • Mismatch risk • ALM risk • Asset default risk • credit risk

  32. Mismatch Risk • ALM risk • the risk that best estimate asset cash flows do not match best estimate liability cash flows • reinvestment and disinvestment risk • the risk that the market price of assets changes unfavorably at a time when those assets need to be liquidated • Case study projects best estimate asset and liability liabilities under many future reinvestment rate scenarios

  33. Mismatch Risk Assets Required to Back Liabilities ($ millions)

  34. Asset Default Risk • Credit risk • Case study uses factors derived from existing regulatory regime • Since other provisions for risk use the risk-free discount rate, the provision for credit risk on assets backing liabilities is not necessary • included all assets in case study for demonstration purposes

  35. Asset Default Risk Capital Requirements ($ millions)

  36. Contents 1. Introduction 2. The Insurance Company 3. Mortality Risk 4. Lapse Risk 5. Market Risk 6. Effects of Reinsurance

  37. Effects of Reinsurance • Factor-based systems cannot fully capture the characteristics of the risks a company faces • especially when reinsurance is used • Case study analyzes six reinsurance arrangements: • YRT 45% coinsurance at neutral reinsurance rates • YRT excess reinsurance at neutral insurance rates • YRT 90% coinsurance at neutral reinsurance rates • YRT 45% coinsurance at low reinsurance rates • YRT excess reinsurance at low insurance rates • Quota share

  38. Effects of Reinsurance Capital for Mortality Risks ($ millions)

  39. Conclusions • Advanced models can be developed to better understand the net risks faced by an insurance company • These models can be used to develop a standardized approach for risks that are well understood and for which there is ample historical data • difficult to accurately capture the impact of reinsurance • Must exercise care for risks not modeled in the case study: • impact of policyholder behavior • complex options in policies • complex interactions between risks

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