D.1 Longevity Risk Case Study

Question 1

Longevity risk in SPIA

Answer 1

• factor based approach doesnt account for tail risk in SPIAs
• SPIA subject to two risks: Investment risk and Longevity risk
• RBC accounts for investment-related risks, but not longevity risks
• stochastic models with dynamic mortality assumptions show a much greater dispersion at later durations, reflecting tail risks

Question 2

Sources of Mortality Volatility

Answer 2

1. Mismatch between the population underlying the assumption
2. volatility in future mortality improvement
3. Extreme longevity events (such as medical breakthroughs)

Question 3

How EC can capture longevity risk in SPIA

Answer 3

Using the dynamic mortality analysis:

• Avg Economic Liab = average of all scenario results @ STAT reserve discount rate
• Longevity risk capital = Avg Economic Liab @ VaR 99.5 - Avg Economic Liab
• Asset Risk Capital = Economic Liab (4.75% disc) @ VaR 99.5 - Economic Liab (5.5% disc) @ VaR 99.5
• TAR is higher under EC than RBC - due to longevity risk captured in the EC model
• Dynamic longevity assumptions drives the longevity risks

Question 4

Cost of volatility

Answer 4

when modeling the EC for longevity risk:

• the dynamic longevity assumptions quantify the cost of volatility”
• measures the significant tail risk
• returns are asymmetric: there is limited upside when the annuitant dies early, but ‘unlimited’ downside if the annuitant lives for a long time
• this cannot be captured in a static assumption

Question 5

how insurers can manage longevity risk capital

Answer 5

• insurers who do not quantify the longevity volatility are vulnerable
• can diversify by issuing life insurance
• can be difficult to match risks
• Longevity bonds can reduce EC by transferring risk to investors