Shall I use Libor rate, or not? Why shouldn't I use my cost of capital, especially if I do replication, and BS is derived using stock and bond...
No, it doesn't. The risk free rate is assumed to be constant in any theoretical model. The risk free rate effects the value of an option, but the market value of an option does not effect the risk free rate of interest. You can use LIBOR, but short term t-bills are probably better for options in the U.S. I've heard people use LIBOR, but your best bet is short term government securities. but the only time ho matters is if rates move a huge amount or with leaps where interest rates may change substantially over the life of the option