Theoretically, in pricing derivatives, most textbooks refer to the risk-free rate. What is obtainable in practice? The risk-free rate or the LIBOR rate?
Before 2007, LIBOR was commonly used for risk-free rate. It was a good proxy because it was quite close to the OIS rates. Since 2007, the LIBOR–OIS spread has spiked and became unstable. Therefore, LIBOR is no longer a good proxy for discounting. Nowadays, Banks usually use OIS for modelling.