Most central banks offer banks participating in large‐value real‐time gross settlement (RTGS) systems a free intraday overdraft facility to discourage banks from actively managing their daylight liquidity. In this paper, we ask whether this facility has kept the intraday interest rate at zero. Using a unique transaction‐level data set on collateralized interbank loans for 2006–12, we find that during periods of financial distress, rates for morning transactions are higher than those in the afternoon. Moreover, this intraday rate correlates with market liquidity, suggesting that rates contain a liquidity premium. This intraday pattern is reduced, but not eliminated by the Eurosystem's accommodative liquidity provision.