Valuation models

Variable annuity guarantees

Monthly fund paths less fees, roll-ups and ratchets on the benefit base, Gompertz-Makeham mortality and lapses; the cost of a guaranteed minimum accumulation, death or withdrawal benefit against the rider fees, the fair rider fee, and delta and vega for hedging.

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Methodology

Conventions

  • Monthly lognormal fund paths less fund and rider fees.
  • GMAB pays the base less the account at term; GMDB the base less the account on death; GMWB the withdrawals once the account is empty.
  • Deaths from Gompertz-Makeham mortality, plus a constant lapse rate. The liability is the guarantee cost less the rider fees.

References

  • Bauer, Kling and Russ (2008)
  • Hardy (2003)

Formulas

Liability
E[Σ D_m ₘpₓ (benefit_m − f A_m Δt)]