Options based on LIBOR

Particularly for floating LIBOR, are they always settled next period?

When would you base the option payoff based on current LIBOR?

LIBOR is an interest rate . Interest is payable only upon maturity or when you reach the term . That applies to options too , where you your payoff is an interest rate. Its still an interest on a loan that is payable upon maturity , You may settle using a present value calculation which uses the rate and the future value to calculate the payoff today , but that is just a way to settle it. The terms of the loan would still say that the loan and and the interest are payable upon maturity or term