Stochastic modeling of mortality and longevity

Stochastic modeling of mortality and longevity

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Speaker(s): Marc Slutzky (Milliman), Dan Theodore (Milliman), Stuart Silverman (Milliman)

Longevity risk can be described primarily as a "Tail Risk" for negative cash flows that occur years into the future after the original investment is exhausted. The setting of assumptions for future longevity requires a new approach that recognizes and quantifies the risk of results varying from the best estimate mortality and mortality improvement. Stochastic projections of future mortality rates help us to stratify and assign probabilities to the resulting scenarios.

We can use stochastic analysis to simulate these patterns to examine the financial impact of possible changes in future mortality rates. Instead of using deterministic margins, we can generate mortality rates using stochastic projections based on historical levels of mortality rate volatility and correlation in order to examine the potential change to future cash flows. The primary risks that we have modeled may be described as:

  1. Poisson risk (Random Dates of Death)
  2. Trend Risk (Volatility of Future Mortality Improvement)
  3. Basis Risk (the Degree to Which Assumed Mortality Not Consistent With Modeled Population)
  4. Extreme Long-Term Events Risk (Immediate Changes That Have Long-Term Effects Not Captured In Previous Risks)
  5. Long-Term Selection Risk (Uncertainty Regarding Rating Classifications, Wearing Off of Selection, and/or Level of Ultimate Mortality)
  6. Risk of Catastrophic Short-Term Events (Temporary Mortality Deviations Related to Specific Events)

We will address these various types of volatility risk associated with longevity and mortality, and describe a set of approaches that we have used in our modeling, with examples.

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