As mentioned in the chapter, it is often necessary to use stochastic modeling to price aGMDB feature. Assume you are pricing a variable annuity that has a GMDB feature that pays upon death the premium accumulated at 5% interest, if that amount is greater than the account value.

Given the mortality rates and investment performance assumptions in Table 13.13.1, calculate the cost of the GMDB design as a percentage of each scenario’s account value, assuming all deaths occur at the end of the year and discounting all present values at 5%.

Table 13.13.1 GMDB Scenarios t q Investment Performance Scenario

(a)

(b) (c)

1 0.005 3.0% 5.0% 3.0%

2 0.010 3.0 5.0 5.0 3 0.015 3.0 5.0 7.0

“ 0.020 3.0 5.0 3.0 2 0.025 3.0 5.0 —10.0