The question was: Do immediate annuities offer inflation protection features, and if so, how do these features work?
The answer is: Most immediate annuities are fixed in amount. Although a few contracts offer the option of either a fixed amount or an annuity increasing as a set percentage each year (usually no more than 3% – 5%), most do not.
For those that do, the amount of the first year's annuity payment will be less than that of contracts without this option. The greater the guaranteed annual increase, the lower the initial payment for any amount invested.
The authors are not aware of any contract providing that annuity payments will vary directly with the unknown future fluctuations in the rate of inflation (as measured by an index such as the Consumer Price Index).
Why such a contract has not yet been introduced is a puzzlement.