(a) Until the first payment on account of the retirement allowance becomes normally due, any beneficiary may elect, by filing written application with the board, to convert the retirement allowance otherwise payable on his account after retirement into a retirement allowance of equivalent actuarial value under one of the optional forms named below:

(1) Option One shall consist of a reduced retirement allowance payable during the beneficiary's life, with the provision that the reduced allowance shall continue after his death to and for the life of the contingent beneficiary designated by him in such application, if such contingent beneficiary survives him; and

(2) Option Two shall consist of a reduced retirement allowance payable during the beneficiary's life, with the provision that one-half of the reduced allowance shall continue after his death to and for the life of the contingent beneficiary designated by him in such application, if such contingent beneficiary survives him.

(b) Any other provisions of this Code section or of this chapter to the contrary notwithstanding, the board of trustees may, by rule or regulation, require that when a member or a retired member dies and the beneficiary is a person other than the surviving spouse of the member, the benefits payable to the beneficiary shall be paid to the beneficiary within a definite time period immediately following the death of the member or retired member.