An insurer is designing a 10-year single premium variable annuity policy with a guaranteed maturity benefit of 85% of the single premium.

(a) Calculate the value of the GMMB at the issue date for a single premium of $100.

(b) Calculate the value of the GMMB two years after issue, assuming that the policy is still in force, and that the underlying stock prices have decreased by 5% since inception. Basis and policy information:

Age at issue: 60

Front end expense loading: 2%

Annual management charge: 2% at each year end (including the first)

Survival model: Standard Ultimate Survival Model

Lapses: 5% at each year end except the final year

Risk-free rate: 4% per year, continuously compounded

Volatility: 20% per year